Research Article An Evaluation of the Use of Simulated ...downloads.hindawi.com/journals/ijfr/2015/173042.pdf · log 10 = 5.529749 1.780184 log 10, ( ) 1 = + , Ry =, ( ) where is

Research ArticleAn Evaluation of the Use of Simulated Annealing toOptimize Thinning Rates for Single Even-Aged Stands

Kai Moriguchi Tatsuhito Ueki and Masashi Saito

Interdisciplinary Graduate School of Science and Technology Shinshu University 8304 MinamiminowaKami-ina-gun Nagano 399-4511 Japan

Correspondence should be addressed to Kai Moriguchi 14st403fshinshu-uacjp

Received 18 June 2015 Revised 27 October 2015 Accepted 10 November 2015

Academic Editor Ignacio Garcıa-Gonzalez

Copyright copy 2015 Kai Moriguchi et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We evaluated the potential of simulated annealing as a reliable method for optimizing thinning rates for single even-aged standsFour types of yield models were used as benchmark models to examine the algorithmrsquos versatility Thinning rate which wasconstrained to 0ndash50 every 5 years at stand ages of 10ndash45 years was optimized to maximize the net present value for one fixedrotation term (50 years) The best parameters for the simulated annealing were chosen from 113 patterns using the mean of the netpresent value from 39 runs to ensure the best performance We compared the solutions with those from coarse full enumeration toevaluate the methodrsquos reliability and with 39 runs of random search to evaluate its efficiency In contrast to random search the bestrun of simulated annealing for each of the four yield models resulted in a better solution than coarse full enumeration Howevervariations in the objective function for two yield models obtained with simulated annealing were significantly larger than those ofrandom search In conclusion simulated annealing with optimized parameters is more efficient for optimizing thinning rates thanrandom search However it is necessary to execute multiple runs to obtain reliable solutions

1 Introduction

Optimizing the thinning rate for single stands is a fundamen-tal problem in improving the economy of forestmanagementIn Japan the proportion of small-scale forest holders islarge For example 654 of private forest owners in NaganoPrefecture own areas lt 1 ha in extent and 906 own areassmaller than 5 ha [1] They therefore have little leeway inperforming spatial optimization and it is important to opti-mize the thinning rates applied to single stands to improveprofitability Fortunately recent developments in computingenable rapid quantitative optimization with no experimentalknowledge

The problem may be optimized in a straightforwardmanner using full enumeration (FE) that is enumeratingand examining all patterns Because calculation cost increasesexponentially with the number of control variables (referredto as ldquothe curse of dimensionalityrdquo) this however tends to beimpractical Approaches that reduce the computing costs aretherefore required Many algorithms for solving this problemhave been proposed and can be grouped as follows dynamic

programming (DP) [2ndash6] nonlinear programming (NP) [78] and heuristic methods such as random search (RS) [9]tabu search or greedy algorithms [10] Of these DP and NPhave beenwidely used andhave been further developed basedon comparison with each other

Roise [7] reported that two NP approaches the meth-ods of Hooke and Jeeves [8] and Powell [11] were moreefficient than the discrete DP algorithm which served asa baseline comparison On the other hand Paredes et al[4] proposed a new DP algorithm named PATH (projectionalternative technique) that wasmore efficient than traditionalDP algorithms Yoshimoto et al [3] developed an extendedPATH algorithm namedMSPATH (multistage PATH) whichcan reflect long-term effects such as an increase in logprice with diameter and showed that it could provide bettersolutions than PATH [6 12] Yoshimoto et al [6] developedan improved PATH algorithm named RLS-PATH (region-limiting strategies PATH) to deal with yieldmodels includingmany variables and reported that in many cases it providedbetter solutions than Hooke and Jeevesrsquo method Each ofthese methods has been used to optimize thinning rates for

Hindawi Publishing CorporationInternational Journal of Forestry ResearchVolume 2015 Article ID 173042 15 pageshttpdxdoiorg1011552015173042

2 International Journal of Forestry Research

single stands (eg NP [13ndash21] DP [22ndash32]) In particularthe MSPATH algorithm is more appropriate than PATHwhen long-term effects caused by competition-density effectsor fluctuations of log price with diameter are taken intoaccount [12] Yoshimoto [12] developed a way to apply it toyield models based on stand density management diagram(SDMD) [33] a type of forest growth model incorporatingcompetition-density effects that is commonly used in Japanwhich has been applied in several studies [27ndash32] Howeverit is necessary to consider carefully whether such optimizedresults represent a ldquobetter choicerdquo or ldquothe best choicerdquo

With respect to the spatial planning of forests it hasbeen argued that it is important to validate optimizationalgorithms [34]This also applies to algorithms for optimizingthinning rates for single stands but existing algorithms haveas yet only been compared with each other not against exactoptimal solutions as provided by FE Producing a solutionthat is validated as close to the optimal solution is potentiallynot always essential if the user is only using the optimizationalgorithm as a way to improve the current situation inother words for them ldquooptimizedrdquo means ldquobetter choicerdquoHowever in some cases a solution close to the optimum isneeded For example it is difficult to manage forests withoutsubsidy in Japan In this case the result of a stand-leveloptimization analysis can determine whether a stand canbe managed successfully under optimized conditions andwhether it is worth subsidizing Such an analysis can provideimportant information for regional zoning and in this case ahigh degree of reliability that is confidence that the methodprovides solutions close to ldquothe best choicerdquo is necessary tosatisfy accountability requirements especially towards forestowners who have applied for rezoning andwhose forest is notsubsidized The same considerations may apply to countriesor regions in situations similar to Japan that is little leewayin performing spatial optimization and a limited supply offunding

In a previous study [35] RS with 106 iterations andMSPATH were compared with coarse FE (CFE) by splittingvariables into a lattice comparing them using two simpleSDMD-base small-scale yield models (differing only in theirprice functions) as benchmark and setting net present value(NPV) for 50 years as the objective function The NPV ofthe nonmonotonic pricing yieldmodel provided byMSPATHwas 60419 yenha less than that derived using CFE and themonotonic pricing yield model provided by MSPATH was30920 yenha less In contrast those provided by RS were3755 yenha and 5487 yenha less respectively than thatderived using CFE On the other hand MSPATH reducedthe calculation cost by 10minus52sim10minus51 times relative to CFE and10minus26sim10minus25 times relative to RS MSPATH therefore confersa great advantage in terms of calculation cost but it isnot possible to rely on it providing ldquothe best choicerdquo Thuswe need to establish a more reliable method of optimizingthinning rates for single stands

There are diverse thinning rate models for single standsas a result of differences in the complexity of the models (egwhether they consider variation in trees [26 27] or in loggingand lumbering [31]) in the objective function used (eg NPV

[10 12 29 32] or in soil expectation value (SEV) [14 36]) or inother criteria [26 27] It is difficult to deal with the necessarycomplexity using NP algorithms since the various trade-offrelationships for example between yield volume at thinningand that at final cutting may require multimodality of yieldmodels and the incorporation of logging processes makesthem discontinuous On the other hand theoretical proofsare required to ensure the reliability of the DP algorithmhowever it may be difficult to obtain sufficient proof tosupport complex yield models We therefore suggest thatsimulated annealing (SA) [37 38] a stochastic algorithminspired by the annealing process of metals may satisfythe requirements It is worth noting that SA has beentheoretically proven to provide the global optimum for awide variety of problems [38] such as the traveling salesmanproblem [37 38] and the knapsack problem [39] as long asthe ldquotemperaturerdquo parameter is decreased gradually enough

In the field of forestry SA has usually been used for forestplanning under spatial constraints [40ndash42] or with a specialobjective function such as that defined based on ldquoforest spatialvaluerdquo [43 44] Lately the performance of SA itself has beenanalyzed for example its sensitivity to the parameters used[45] and its application in neighborhoodmethods [46]ThusSA is commonly used in the field and its performance isevaluated However this approach has never been used tooptimize thinning rates for single stands and its performancein this area has not been evaluated It is therefore necessaryfirst to evaluate whether SA can be used reliably to optimizethinning rates for single stands

In this study we evaluate the potential performance ofSA in optimizing thinning rates for single even-aged standsusing plural yield models based on SDMD We set thethinning interval in eachmodel at five years and the objectivefunction as the NPV before planting for one rotation termThe age of the rotation is one of the most important variablesfor improving the financial viability of stand-level forestmanagement However we fixed this variable in our modelbecause a change in rotation age leads to a change inthe number of dimensions of the model (the number ofvariables in this case the number of thinning ages) Tooptimize both rotation age and thinning rates it would thusbe necessary to define several models with different rotationages optimize them and then choose the best one Thesearching performance of the model with a fixed rotation agetherefore determines performance in optimizing amodel thattreats rotation age as a variable

Whereas the ldquoperformancerdquo of an optimization methodincludes both reliability and efficiency we must first improveits reliability and only then enhance its efficiency whilemaintaining reliabilityThe emphasis is therefore on securingreliable optimawith proven orthodox SAmethods Howeverthe combination of parameters used has strong effects onthe performance of SA approaches [45] In addition SA isa stochastic algorithm and as a result the solution obtainedfrom each searching process varies We therefore search forldquothe bestrdquo combination of SA parameters using CFE toensure the best possible performance using the mean NPVfrom 39 runs of the SA as the objective function We alsocompare the 39 NPVs from the solutions obtained using

International Journal of Forestry Research 3

optimized SA parameters with those obtained using CFE toevaluate whether SA can provide solutions close to the globaloptimum Finally we statistically compared these values withthose obtained using RS with five times iterations to evaluatethe comparative merit of SA

2 Materials and Methods

21 Benchmark Model A hypothetical even-aged stand ofJapanese larch (Larix kaempferi) in Nagano Prefecture withmedium site quality and a density of 2500 planted treeshawas used as a benchmark stand Minimum thinning age wasfixed in 10 years and the thinning interval in five years Therotation age was fixed in 50 years since this value would stillallow application of CFE

211 Objective Function We defined the objective functionas NPV before planting for one rotation term

NPV =

119899

sum

119894=1

119868119894(1 + 001119903)

minus119905119894minus 119862119903 (1)

where 119868119894is the income from the 119894th cutting (yenha) 119903 is the

annual interest () 119905119894is the stand age at the 119894th cut (year)

and 119862119903is the cost of regeneration (yenha) Annual interest

was set at 09 [47] As mentioned above 119905119894values were fixed

to increments of five years over a range of 10ndash50 years

212 Growth Model We used SDMD to define the growthmodel The formulae for larch in Nagano Prefecture are asfollows [48]

1

119881

= 119860 +

119861

119873

(2)

119867119865 = 0578096 + 0460651119867 +

004259119867

100

radic119873 (3)

119866 =

119881

119867119865

(4)

119889119892 = 200radic119866

120587119873

(5)

119889 = minus0155598 + 0982606119889119892 (6)

log10119873119877119891= 5529749 minus 1780184 log

10119867 (7)

1

119881119877119891

= 119860 +

119861

119873119877119891

(8)

Ry = 119881

119881119877119891

(9)

where 119881 is the stand stem volume per area (m3ha)119867 is themean height of dominant trees (m)119873 is the present numberof trees per area (treesha)119867119865 is the stand form height (m)119866 is the basal area (m2ha) 119889119892 is the diameter at breast height(DBH) of the mean basal area (cm) 119889 is the mean DBH (cm)119873119877119891

is the number of trees per area on the full-density curve

(treesha)119881119877119891

is the stand volume per area on the full densitycurve (m3ha) and Ry is the relative yield index (the standarddensity index for the SDMD) 119860 and 119861 are parameters thatchange with the mean height of the dominant trees and aredefined as follows

119860 = 0095669119867minus1274434

119861 = 88334119867minus3054618

(10)

Note that these formulae are common to the aforemen-tioned previous study [35] but the aspects of the modeldescribed in the rest of this section and in the next onehave been modified The present model is more appropriatebecause it simulates self-thinning after the first thinning

We modeled self-thinning using Tadakirsquos model [49]calculated as follows [50]

119873 = minus

119904

2

+radic1199042

4

+

119873119904119861

119860

if 0417216119873119904lt minus

119904

2

+radic1199042

4

+

119873119904119861

119860

(11)

119873 = 101198881111986711988812 if minus 119904

2

+radic1199042

4

+

119873119904119861

119860

le 0417216119873119904

(12)

where 119873119904is ldquoinitial number of trees per areardquo (treesha) a

parameter of the self-thinning curve 119904 is given as follows

119904 =

119861

119860

+

11987317159002

119904

2396313119860

minus 119873119904 (13)

Equation (11) is the self-thinning curve before the standreaches the full-density condition After that self-thinningproceeds according to (12) the full-density curve which takesthemean height of the dominant trees as a variable119873

119904is what

the number of trees per area at age 0 would be if the standhad only been subject to self-thinning but not to additionalthinning by humans 119873

119904is therefore only ever equal to the

planted number of trees per area if the forest is never thinnedWe call this parameter 119873

119904to avoid confusion with planted

number of trees per area and initial values of optimizationSDMD is a function of the mean height of the dominant

trees and the number of trees per area It hypothesizes thatonly the number of trees per area not the mean height ofthe dominant trees is affected by thinning In other wordsSDMD simulates thinning by translating the self-thinningcurve under a specific mean height of dominant trees Thevalue of119873

119904corresponds to the self-thinning curve in (11) As

the relationship between the number of trees per area under aspecific mean height of dominant trees and119873

119904is monotonic

we can simulate thinning by decreasing119873119904

It is easy to calculate the number of trees per area basedon 119873119904under an arbitrary mean height of dominant trees

using (11) and (12) However if number of trees per area atan arbitrary mean height of dominant trees is given we firstneed to identify 119873

119904with a numerical approximation with

(11) to simulate self-thinning after that age Moreover after


the stand has reached full-density condition we cannotcompute 119873

119904using (12) and given the number of trees per

area because the full-density curve as (12) is independent of119873119904 To address these problems we define thinning rate as the

ratio of the difference between 119873119904before and after thinning

as follows

119877 = 100

119873119904all minus 119873119904main119873119904all

(14)

where 119877 is the thinning rate () 119873119904all is 119873119904 before the

thinning and119873119904main is119873119904 after the thinning

To simulate the growth of the standwith age using SDMDthe mean height growth curve of the dominant trees isrequired The growth curve of Japanese larch at an averagesite inNaganoPrefecture can be predicted using the followingformula [51]

119867 = 2581 1 minus 1182 exp (minus005119905) (15)

where 119905 is the stand age (years) Since SDMD assumes lowerthinning the mean height of the dominant trees will not beaffected by thinning

213 Volume and Diameter of Yield Trees The total stemvolume of cut trees per area is calculated as follows

119881cut (119873cut 119905) = 119881 (119873all 119905) minus 119881 (119873main 119905) (16)

where 119881cut(119873cut 119905) is the cut stem volume per area when119873cut trees per area are cut at time 119905 119881(119873 119905) is the standingtree volume per area calculated using (2) and (15) where thenumber of trees per area is119873 at time 119905119873cut is the number ofcut trees per area 119873main is the number of standing trees perarea and 119873all is the total number of standing and cut treesper area This equation can be applied to both thinning andfinal cutting Mean stem volume per tree can be calculated bydividing the left side of (16) by119873cutThemeanDBH of the cuttrees was calculated using the formula

119889cut =119889all119873all minus 119889main119873main

119873cut (17)

where the subscripts of 119889 are the same as those of 119873 in (16)SDMD does not describe variation in stem volume so weassumed a constant size for all cut trees for a given stand age

214 Constraints of Thinning Rates and the Number of Treesper Area Because the parameters of SDMD were estimatedusing data from real forests subjected to standard silviculturalprocesses unusual conditions such as extremely small num-ber of trees per area should be avoidedwhen using thismodelAccordingly the lower bound of 119873

119904was set to 200 treesha

In addition it is recommended that a high thinning ratebe avoided when using SDMD however intensive thinningis often performed to reduce thinning costs For this studywe placed emphasis on actual practice and restricted thethinning rates to the range 0ndash50

Table 1 Relationship between end diameter and log price

End diameter (cm) Log price (yenm3)0ndash5 06ndash11 1050012ndash14 700016ndash18 1100020ndash22 1230024+ 12500Source Hokushin log market [53]

215 Stem Profile We used a stem profile curve to calculatethe small end diameter of the logs in a complex yield model(defined in Section 218(2))The Behre equation given belowis a widely used relative stem profile curve

119889

11988909

=

2119909

119886 + 119887119909

(18)

where 119909 is the height for which stemwidth is being calculatedrelative to total tree height (scaled from 0 to 1) 119889 is thediameter at relative height 119909 and 119889

09is the diameter at

relative height 09 Parameters 119886 and 119887 are calculated asfollows [52]

119886 = 09 (2 minus 119887)

119887 =

180120593 minus 126120575

20120593 minus 63120575 + 70120575120593

120575 = 119889bhradic

7

10

1205871198671015840

4V1015840

(19)

where V1015840 is stem volume 1198671015840 is the total height of the tree 120593is the relative height at breast height and 119889bh is the DBH

Equation (18) can be transformed as follows to providethe relationship between the diameter at any height and theDBH

119889 = 119889bh119909

120593

(

119886 + 119887120593

119886 + 119887119909

) (20)

216 Log Price The relationship between the end diameterof 4m long Japanese larch logs and the value in a real marketin Nagano Prefecture [53] is shown in Table 1 Although thereis a briskmarket for 6ndash11 cm logs for log piles the value of 12ndash14 cm logs is lower as there is less demand for this size Thisprice model adds multimodality to the NPV

217 Cost of Regeneration and Yield The thinning cost wasset to 4588 yenm3 based on the mean total cost of loggingand transportation of Japanese larch [54] assuming a 50subsidy is provided and the cost of final cutting was setto 5987 yenm3 assuming no subsidies Usually no subsidyfor final cutting is provided however for the purpose ofexamining a range of patterns we also tested the modelon a scenario in which the final cost was similarly reducedto 2994 yenm3 Hereafter we refer to the two scenarios as


F (full) and H (half) respectively The difference betweenscenarios affects the flatness of the NPV The present costsfor regeneration are calculated as 1078590 yenha accordingto standard government sources [55] which includes groundclearance of a typicalmeadow at the beginning of the plantingyear planting 2500 treesha prevention of mammal damageby spreadingZiram solution in three years bush cutting everyyear from one to five years tree trimming and crosscutting in10 and 15 years 8 consumption tax 09 annual interestand 50 subsidy This total was applied to 119862

119903in (1)

218 Yield Model We defined two types of yield models thatdiffer in the degree of difficulty involved in optimizing them

(1) Simple YieldModelThismodel calculates the yield volumeby simply multiplying the yield rate by the stem volume ofthe harvested trees We calculated income based on the pricein Table 1 corresponding to the DBH of the harvested treesThe thinning and final cutting yield rates were set to 58 and65 respectively Gaps in the classes in Table 1 were linearlyinterpolatedThe income from a cut was calculated as follows

119868 =

119910

100

119881cut (119875cut minus 119862cut) (21)

where 119868 is the income from a cutting per area (yenha) 119910is the yield rate () 119881cut is the total volume of cut treesper area (m3ha) 119875cut is the price of a cut tree per volume(yenm3) and 119862cut is the cutting cost per volume (yenm3)Hereafter we refer to this model as S and in combinationwith the half and full scenarios described in Section 217 S-H and S-F model are defined The models are identical tothe nonmonotonic pricing yield models used in a previousstudy [35] except for the self-thinning model and volumecalculation used

(2) Logging YieldModelThis model takes the logging processinto consideration As many 4m logs (with 01m margin) aspossible were bucked from stump height (05m) to the top ofthe harvested tree Diameters were calculated at every heightfrom 46m to the top of the tree in 41m increments usingthe stemprofile curve andwere assumed to be end diametersThe Japanese Agricultural Standard for logs [56] was appliedto the calculations of diameter and volumeThe thinning andfinal cutting yield rates were set to 80 and 90 respectivelyIncome from a cut was calculated as follows

119868 =

119910

100

119873cut

119896

sum

119895=1

V119895(119875119895minus 119862cut) (22)

where 119895 is the index number of a log from its stump 119875119895is the

price of the 119895th log (yenm3) V119895is the volume of the 119895th log

(m3) calculated as

V119895= 4(

119889119895

100

)

2

(23)

where 119889119895is the end diameter of the 119895th log (cm) (omitted for

multiples of two for diametersgt 14 cmand omitted for natural

numbers otherwise) and 119896 is the number of bucked logs froma harvested tree calculated as follows

119896 = floor(119867 minus 05

41

) (24)

where ldquofloorrdquo rounds down to the next lower integerBecause the number of bucked logs from a tree and the

end diameters were restricted to integers the NPV was adiscontinuous multimodal function Hereafter we refer tothis model as L and in combination with the half and fullscenarios described in Section 217 L-H and L-F model aredefined

22 Optimization Method This section details the imple-mentation of SA its application to the thinning rate opti-mization problem and the method we used to evaluate itsperformance

221 Simulated Annealing SA was developed based onthe metal annealing process which finds the global mini-mum ldquoenergyrdquo required by gradually decreasing a parameternamed ldquotemperaturerdquo At the beginning the temperatureis high so frequent transitions occur for both low-energyand high-energy states This makes it possible to find theglobal optimum by searching a wide solution space As thetemperature cools the frequency of transitions to a higher-energy state decreases and the system tends to transitionto a lower-energy state more frequently Using these fea-tures approximate global minima can be found heuristicallyThe flowchart is shown in Figure 1 The procedure can bedescribed as a Metropolis algorithm [57] with changes intemperature SA is an adaptable method that requires thefollowing four components (1) a cooling function whichcontrols the rate of decrease in temperature (2) a proposaldensity function which is a probability distribution function(PDF) that generates candidate variables that is thinningrates (3) an energy function which is the metaobjectivefunction to be minimized and (4) an acceptance probabilitya temperature-dependent PDF that decides whether or notthe proposed state is accepted

The cooling function is defined as an exponential decayfunction that is a decreasing rate determined by the initialand final temperatures is multiplied with temperature at time119905 to obtain temperature at time 119905 + 1 The proposal density isdefined by a normal distribution with a mean of the presentvalue of the target variable and a standard deviation that isoptimized as described later The energy function is definedas follows

119864 =

NPVmax1015840 minusNPVNPVmax1015840 minusNPVmin1015840

(25)

where 119864 is the energy function NPVmin1015840 is the tentativeminimumNPV andNPVmax1015840 is the tentativemaximumNPVSince our aim was to maximize the NPV the problem wasto minimize the negative NPV This definition limits thedifferential of the energy function to the range 0-1 We set


Start

Set new temperature

End

YesNo

Calculate energy value and acceptance probability

YesNo

Accept candidate state variables and energy value

Save the energy value and statevariables as tentative optimal solution

Is the solution feasible and is the energy value the lowest so far obtained

Yes

Yes

No

No

Discard candidate statevariables and energy value

Output optimal solution and the value of objective function

Set initial temperature final temperature (or rate of cooling)

and number of iterations per temperature

Initialize state variables and temperature

Generate candidate state variables

Set i = i + 1

Set i = 0

Is the number of iterations per temperature lt i

Is the present temperature lt final temperature

Random (0 1) lt acceptance probability

Figure 1 Flowchart of SA procedure

the acceptance probability as the Boltzmann distribution asfollows

119901119886= exp(

119864119888minus 119864119901

119879

) (26)

where 119901119886is the acceptance probability 119864

119888is the energy of the

candidate state and 119864119901is the energy of the present state It

is difficult to set appropriate temperature bounds to control

the acceptance probability since this depends on the unitsof the objective function when it is set directly as the energyfunction The limits inherent in (25) facilitate control of theacceptance probability

The following SA parameters are required (1) numberof iterations per temperature (2) number of total iterations(3) initial temperature (4) final temperature (5) standarddeviation of the proposal density Because of the practical


constraints of computing costs we fixed parameters 1 and2 to 5 times 103 and 2 times 105 respectively We then obtainedthe best combinations of parameters 3ndash5 using CFE Takinginto consideration that log-transformed parameters are moresuited for optimization and that final temperature must belower than initial temperature we chose the best combina-tions from 113 (1331) patterns as shown below using the meanNPV of 39 runs with random initial thinning as the objectivefunction to ensure average performance

119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)

where 119879119904is initial temperature 119879

119891is final temperature Sd

119905is

the standard deviation of the proposal density (cut rate )and 119903119904 119903119891 and 119903sd are the variables to be selected

222 Control of Variables The variables to be optimizedare 119873

119904for each thinning age Each of these is restricted

to be lower than or equal to that at the previous thinningage Controlling them directly requires changing the boundsaccording to the value of 119873

119904at the previous and next

ages However this restriction can always be satisfied byconstraining the thinning rate at each age to the range 0ndash50 No thinning is simulated by setting the thinning rateto 0 We implemented this method because it simplifiescontrolling119873

119904

223 Controlling for Infeasible Solutions If high thinningrates are used at multiple cutting ages119873

119904at the final cutting

may be lt200 treesha Penalty functions are often definedfor infeasible solutions but may be difficult to define appro-priately [42 46] The quality of definition has a significantinfluence on performance Because we placed emphasis onthe potential performance of SA and on fair comparisonwith RS (by random sampling only see next section) thegeneration of infeasible solutions was not prevented rathercandidate variables from the proposal density were sampledrepeatedly until the generated solution was feasible Thisdiffers from defining the energy function as infinity forinfeasible solutions in that the lattermethod does not increaseiterations if generated solutions were infeasible

23 Evaluation We derived feasible approximate globaloptima using CFE (Figure 2) The ldquocombinatorial staterdquo inthis case is all patterns of repeated permutations of candidatethinning rates ranging from 0 to 50 in 5 increments Sincethis solution was just an approximation based on a coarsethinning rate it is possible to obtain better solutions (or atleast solutions sufficiently close to the optimum) using otheralgorithms given satisfactory performance

We also applied RS to the same yield models for thepurposes of assessing the effectiveness of SA (Figure 3)Independent combinations of thinning rates with a uniformdistribution over the range 0ndash50 were generated at eachcutting age Since this method was implemented as random

Start

Generate the pool of all lattice points

Calculate the value of objective function

Is the value the best so far obtainedand is the solution feasible

Save the value and state variables as tentative optimal solution

No

Yes

Is the pool emptyNo

End

YesOutput optimal solution and the

value of objective function

Extract one element of the pool without restoration

Splitting continuous variables as lattice

Figure 2 Flowchart of CFE procedure

sampling rather than a random walk all solutions for eachsample were independent of each other A total of 106 feasiblesolutions were simulated We ran each model 39 times andthe optimal NPVs were sampled for comparison with thosegenerated by SA

Because the thinning rates are initiated randomly at thebeginning of each SA process the results can be testedstatistically [44 58 59] We tested our results to confirmindependence between the initial and optimal solutionsdifferences between solutions generated by SA and RS anddifferences between yield models

3 Results

31 Examination of the Basis of Data Thebest values of 119903119904 119903119891

and 119903sd were 12 60 and 19 respectively for the S-H model08 15 and 16 for L-H 00 55 and 10 for S-F and 00 20and 10 for L-F There was no significant correlation betweenthe initial and the optimal NPV for any model (Spearmanrsquoscorrelation test S-H 119901 = 083 L-H 119901 = 069 S-F 119901 = 086L-F 119901 = 028) This indicates that the optimal solutionsprovided by SA can be regarded as independent of their initialsolutions

32 Comparing SA with CFE and RS TheNPV derived usingCFE was 674765 yenha for the S-H model 769711 yenhafor L-H 177065 yenha for S-F and 185302 yenha for L-F119873119904at final cutting was 2000 819 205 and 819 treesha for S-

H L-H S-F and L-F respectively The numerical differences


Table 2 Differences between optimal NPVs produced by SA and RS and that derived using CFE

Model S LFinal cutting cost H F H FAlgorithm SA RS SA RS SA RS SA RSMinimum (yenha) 374 minus225876 minus86140 minus199149 minus180759 minus248514 minus266834 minus254235Median (yenha) 380 minus151184 19090 minus147528 minus14202 minus194280 minus75545 minus174728Maximum (yenha) 382 minus78036 22971 minus72519 89264 minus8189 54035 minus21492Mean (yenha) 379 minus147293 10081 minus145693 minus21736 minus183475 minus95576 minus170854Standard deviation (yenha) 018 349704 274748 316354 569451 476674 817371 480485

Start

Generate all state variables randomly


Is the value the best so far obtained and is the solution feasible


No

Yes

No

End

Yes

Output optimal solution and thevalue of objective function

Set i = 0

Is the number of total iterations lt i

Set i = i + 1

Figure 3 Flowchart of RS procedure

between the optimal NPVs produced by SA and RS and thosederived using CFE are presented in Table 2 The median andmean optimal NPVs provided by SA were better than thoseproduced by the RS In addition some of the SA runs for eachmodel provided better solutions than the CFE Comparisonof eachmodelrsquosNPVsprovided by SAwith those byRS revealsdistinct differences in the level of variability (Figure 4)

With respect to S-H the standard deviation of the optimalNPVs was less than 1 yenha much smaller than that for theothermodels (Table 2) SA also provided some low-variabilityoutcomes for the S-F model (Figure 4) however some of theruns might have converged to local optima (Figure 4) thatcaused the relatively large standard deviation for this model(Table 2) SA provided better solutions than RS for the L-H and L-F models particularly with respect to the median

maximum and mean optimal NPVs although the standarddeviationswere larger (Table 2) Each of these values followedthe Gumbel distribution (Kolmogorov-Smirnov test L-Husing SA 119901 = 050 and using RS 119901 = 017 L-F using SA119901 = 058 and using RS 119901 = 020) A Gumbel distribution isdefined by two parameters location (equal to the mode) andscaleThere are four possible SARS parameter combinationsto describe the density of the data common scale andlocation independent scale and location common scale andindependent location and independent scale and commonlocation A likelihood ratio test (using the 1205942 test) betweenall patterns for each model revealed significant differences(119901 lt 005) between SA and RS for both the scale andlocation parameters Using maximum likelihood estimationthe estimated L-H location parameters were minus5128 for SA andminus20390 for RS For the L-F model they were minus13663 for SAand minus19216 for RS The estimated L-H scale parameters were6362 for SA and 3352 for RS and for the L-F model they were8013 for SA and 3796 for RS

33 Number of Updates In a comparison of the models theorder of performance of the models in terms of the medianor mean number of updates (Table 3) is the same as theorder of performance in terms of the standard deviation ofoptimal NPVs (Table 2) The same pattern was apparent forthe number of iterations at last update however the order ofperformance is reversed with respect to the medians of theL-H and L-F model results (Table 3) There were significantcorrelations between the optimal NPVs and the number ofiterations at last update or the number of updates for eachmodel except S-H (Spearmanrsquos test iterations at last updateS-H119901 = 058 S-F119901 lt 0001 L-H119901 lt 0001 L-F119901 lt 0001number of updates S-H 119901 = 079 S-F 119901 lt 0001 L-H119901 lt 001 L-F 119901 lt 001)

Fluctuations in NPVs of the worst best andmedian runsof SA for each model are shown in Figure 5 Those of the S-H model included many updates and the trajectories weresmoothThis indicates that for thismodel SA achieved its aimat each stage that is rough global sampling at the beginningand local optimization at the end However the updates ofthe S-F model were concentrated in the final stages The L-Fmodel runs contained the fewest updates over all stages

34 119873119904Trajectory Thinning rates at each age provided by the

best median and worst runs of SA for each model are shownin Table 4There were some differences between the thinning


SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15

Difference in NPV from CFE (103 yenha)

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS

Figure 4 The difference between the optimal NPVs produced by SA (black bars) or RS (gray bars) and that derived using CFE (upper Slower L left H right F)

rates reached for each age by CFE and the best SA runs sincethe thinning rates of CFE were split into 5 increments TheNPV of the best runs was higher than that of CFE so thesolutions produced by the best runs are closer to the global

optima However there was some variation between the SAruns of each model except S-H Even if the thinning rate isconstant the numbers of cut trees differ if numbers of treesper area are different Figure 6 presents the 119873

119904trajectories


Table 3 Summary of the updating processes of SA

Attribute Number of iterations at last update Number of updatesModel S L S LFinal cutting cost H F H F H F H FMinimum 177060 48003 2249 426 370 25 29 11Median 197820 151933 118836 128301 506 98 66 21Maximum 199987 199518 199967 194512 633 162 105 40Mean 195634 148959 114566 123378 503 103 70 23Standard deviation 56598 410607 541786 476517 701 295 184 74CV () 289 2757 4729 3862 139 286 263 328CV coefficient of variation

Table 4 Optimized thinning rates () provided by CFE and SA

Age S-H S-F L-H L-FCFE Best Median Worst CFE Best Median Worst CFE Best Median Worst CFE Best Median Worst

10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13

for each model which indicate the changes in the numberof trees per area as the stand ages Those of the worst bestand median S-H model runs were very similar (Figure 6)reflecting almost identical thinning rates (Table 4)The othermodels showed some discrepancy between the trajectoriesproduced by theworst runs and those produced byCFEor thebest runs With respect to the S-F model119873

119904trajectory of the

worst runs differed from the others in 35 years but convergedagain in 40 years (Figure 6) In contrast all 119873

119904trajectories

of the L-H model differed at almost every age 119873119904trajectory

of the worst runs for the L-F model varied greatly from theothers and that of median also differed from those of the bestand CFE at most ages However the trajectory of the best runfor each model matched that of the CFE closely

4 Discussion

There were no significant correlations between the NPVscalculated with the initial solution and that calculated withthe optimized solution for any of the models This indicatesthat an SA process using optimized parameters could providesolutions regardless of the initial solutions

The best runs for all models provided better solutionsthan the respective CFE whereas the RS never provided suchsolutions The 119873

119904trajectory of the best runs of each yield

model was almost identical to that of the respective CFEThese results suggest that SA can provide an approximateglobal optimum for similar yield models to those used in thisstudy if the parameters are optimized and the best solutionis chosen from multiple runs The S-H and S-F models are

identical to the nonmonotonic pricing yield models used ina previous study [35] (see Introduction) except for the self-thinning model and volume calculation used Our resultstherefore suggest that SA may be a better algorithm thanMSPATH for optimizing thinning rates for single even-agedstands for the purposes of obtaining reliable solutions

Compared with RS SA provided highly reliable solutionsfor the S-H model as indicated by the negligible differencebetween the minimum andmaximumNPVs provided by theSA runs (lt1 yenha) With respect to the S-F model a fewof SA runs may have converged on local optima althougheven those NPVs were higher than most of those producedby the RS runs In contrast the scale and location parametersof the Gumbel distribution of NPVs produced by SA for theL-H and L-Fmodels were both significantly larger than thoseproduced by the RS The difference in location parametersmeans that NPVs produced by SA runs were higher overallthan those produced by RS However the scale parameterdetermines the variance of the Gumbel distribution so thisindicates that the variation in NPVs produced by SA waslarger than those produced by RS

The only difference between the H and F model defini-tions was the final cutting cost but this resulted in substantialdifferences in the variance of the optimal NPVs and theamounts of variation in the119873

119904trajectories It is possible that

the high degree of sensitivity of the yield model caused largechanges in the form of the objective function In fact in theS-Fmodel optimal119873

119904at final cutting was 205 treesha based

on CFE which is close to the lower bound of 119873119904values

whereas in the S-Hmodel it was 2000 treeshaThis difference


0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst

100 100001Number of iterations




Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50

Figure 5 Updating processes of NPV of SA (upper S lower L left H right F)

indicates that the change in final cutting cost resulted in largechanges in the optimal solutionThis suggests that the degreeof variation in NPVs provided by SA was strongly influencedby the yield model

Bettinger et al [60] examined the performance of eightoptimizing algorithms for spatial forest planning using threebenchmark models They showed that SA the parameters ofwhich were decided based on ldquoseveral trialsrdquo could provide

values close to the global optima or assumed ldquobestrdquo values fortwo of themodelswith a high probability but not for the othermodel or the other algorithms Our study shows that this is acommon problem for the optimization of thinning rates forsingle stands hence the variation in the solutions provided bySA depends on the model In cases where the performanceof SA is influenced by the parameters [45] this can bereduced by optimizing the parameters of SA themselves as in


20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

Figure 6 Trajectories of119873119904produced by SA and CFE (upper S lower L left H right F)

the present study However our results suggest that this prob-lem cannot be solved entirely by optimizing the parameters

Considering these results we suggest that using SA asdemonstrated here has the potential to achieve the approx-imate global optima for thinning rates for single standsif the controlling parameters are optimized However itis necessary to execute multiple runs and choose the bestsolutions from among them

Despite the above the reliability of SA is weakened bythe large variation between the L-H and L-F models and it isimportant to decrease this variation The results of updatingprocesses (in Section 33) indicate that few updates of L-Hand L-F are the main cause of the large variation Whereasthe controlling parameters have been optimized there is littleroom to improve them and a simple increase in the numberof iterations leads to increased computing time Therefore

other approaches may be advisable In this study we usedorthodox SA because it is widely used However differentapproaches to SA implementation may be more efficient forexample fast annealing [61] or adaptive annealing [62] orother types of SA such as the great deluge algorithm [63] usedby Bettinger et al [60] At the same time Borges et al [46]showed that improving the neighborhood search methodcan enhance the performance of SA for spatial planningAttempting to decrease the variation in optimal NPVs of SAand enhancing its reliability using all of these methods maybe worthwhile

5 Conclusion

With the aim of establishing a reliable method for optimizingthinning rates for single even-aged stands we evaluated


the performance of SA by comparing it with RS and CFEusing optimized parameters and four benchmark models Acomparison of 39 runs of the SA (2 times 105 iterations of feasiblesolutions) and RS (106 iterations) indicated that SA generallyprovided better solutions than RS Further the best SA run ofeach model provided better solutions than CFE did for thatmodelTherefore if the controlling parameters for the SA areoptimized as in this study the best ofmultiple runs has a highprobability of approximating the global optimum Becausestand-level thinning optimization methods have rarely beencompared with exact solutions such as those provided byCFE their reliability has not previously been tested Atpresent SA is the only method validated to provide solutionssuperior to those provided by CFE for the same problem

However the variance of the NPVs provided by SAdiffered noticeably between yield models for the S-H modelthe standard deviation of the optimal NPVs was lt1 yenhabut for the L-H and L-F models it was substantially largerthan that provided by RSThe dependence of the variance onthe yield model decreases the reliability of SA and makes itnecessary to select the best from among multiple runs Toincrease the reliability of the SA method the variation ofoptimal solutions within and between yield models shouldtherefore be decreased

Conflict of Interests

The authors declared that there is no conflict of interests

Acknowledgment

This work was supported by JSPS (Japan Society for thePromotion of Science) KAKENHI Grant no 15J04607

References

[1] Nagano Prefectural Government Present Conditions of Forestin Nagano Prefecture at Fiscal 2014 2014 (Japanese) httpwwwprefnaganolgjprinseisangyoringyotoukeiminyurinh26html

[2] T Arimizu ldquoRegulation of the cut by dynamic programmingrdquoJournal of the Operations Research Society of Japan vol 1 no 4pp 175ndash182 1958

[3] A Yoshimoto V G L Paredes and J D Brodie ldquoEfficientoptimization of an individual tree growth model In the 1988symposium on systems analysis in forest resourcesrdquo GeneralTechnical Report RM vol 161 pp 154ndash162 1988

[4] V Paredes L Gonzalo and J D Brodie ldquoEfficient specificationand solution of the even-aged rotation and thinning problemrdquoForest Science vol 33 no 1 pp 14ndash29 1987

[5] R G Haight J D Brodie and W G Dahms ldquoA dynamicprogramming algorithm for optimization of lodgepole pinemanagementrdquo Forest Science vol 31 no 2 pp 321ndash330 1985

[6] A Yoshimoto R G Haight and J D Brodie ldquoA comparison ofthe pattern search algorithm and themodified PATH algorithmfor optimizing an individual tree modelrdquo Forest Science vol 36no 2 pp 394ndash412 1990

[7] J P Roise ldquoA nonlinear programming approach to standoptimizationrdquo Forest Science vol 32 no 3 pp 735ndash748 1986

[8] R Hooke andT A Jeeves ldquolsquoDirect searchrsquo solution of numericaland statistical problemsrdquo Journal of the ACM vol 8 no 2 pp212ndash229 1961

[9] S H Bullard H D Sherali and W D Klemperer ldquoEstimatingoptimal thinning and rotation for mixed-species timber standsusing a random search algorithmrdquo Forest Science vol 31 no 2pp 303ndash315 1985

[10] PWikstrom andLO Eriksson ldquoSolving the standmanagementproblemunder biodiversity-related considerationsrdquo Forest Ecol-ogy and Management vol 126 no 3 pp 361ndash376 2000

[11] M J D Powell ldquoAn efficient method for finding the minimumof a function of several variables without calculating deriva-tivesrdquoThe Computer Journal vol 7 no 2 pp 155ndash162 1964

[12] A Yoshimoto ldquoA dynamic programmingmodel for forest standmanagement using MSPATH algorithmrdquo Proceedings of theInstitute of StatisticalMathematics vol 51 no 1 pp 73ndash94 2003

[13] D M Adams and A R Ek ldquoOptimizing the management ofuneven-aged forest standsrdquoCanadian Journal of Forest Researchvol 4 no 3 pp 274ndash287 1974

[14] J R Gonzalez-Olabarria M Palahı T Pukkala and A Tra-sobares ldquoOptimising the management of Pinus nigra Arnstands under endogenous risk of fire in Cataloniardquo InvestigacionAgraria Sistemas y Recursos Forestales vol 17 no 1 pp 10ndash172008

[15] J H Gove and M J Ducey ldquoOptimal uneven-aged stockingguides an application to spruce-fir stands in New EnglandrdquoForestry vol 87 no 1 pp 61ndash70 2014

[16] J H Gove and S E Fairweather ldquoOptimizing the managementof uneven-aged forest stands a stochastic approachrdquo ForestScience vol 38 no 3 pp 623ndash640 1992

[17] T Marutani ldquoThe effect of site quality on economically optimalstand managementrdquo Journal of Forest Economics vol 16 no 1pp 35ndash46 2010

[18] J Miina ldquoOptimizing thinning and rotation in a stand of Pinussylvestris on a drained peatland siterdquo Scandinavian Journal ofForest Research vol 11 no 1ndash4 pp 182ndash192 1996

[19] M Palahı andT Pukkala ldquoOptimising themanagement of Scotspine (Pinus sylvestris L) stands in Spain based on individual-tree modelsrdquo Annals of Forest Science vol 60 no 2 pp 105ndash1142003

[20] T Pukkala J Miina M Kurttila and T Kolstrom ldquoA spatialyieldmodel for optimizing the thinning regime of mixed standsof Pinus sylvestris and Picea abiesrdquo Scandinavian Journal ofForest Research vol 13 no 1ndash4 pp 31ndash42 1998

[21] O Tahvonen T Pukkala O Laiho E Lahde and S NiinimakildquoOptimal management of uneven-aged Norway spruce standsrdquoForest Ecology and Management vol 260 no 1 pp 106ndash1152010

[22] G J Arthaud and W D Klemperer ldquoOptimizing high andlow thinnings in loblolly pine with dynamic programmingrdquoCanadian Journal of Forest Research vol 18 no 9 pp 1118ndash11221988

[23] D H Graetz J Sessions and S L Garman ldquoUsing stand-level optimization to reduce crown fire hazardrdquo Landscape andUrban Planning vol 80 no 3 pp 312ndash319 2007

[24] T Heikkinen ldquoOn optimal forest management a dynamic pro-gramming approachrdquo International Journal of Society SystemsScience vol 3 no 3 pp 217ndash235 2011

[25] A Manabe ldquoStudies on the optimal thinning schedule forTodomatsu (Abies sachalinensis) plantationsrdquo Bulletin of Forestyand Forest Products Research Institute vol 328 pp 43ndash106 1984


[26] P Bettinger D Graetz and J Sessions ldquoA density-dependentstand-level optimization approach for deriving managementprescriptions for interior northwest (USA) landscapesrdquo ForestEcology and Management vol 217 no 2-3 pp 171ndash186 2005

[27] N A Ribeiro P Surovy and A Yoshimoto ldquoOptimal regen-eration regime under continuous crown cover requirements incork oak woodlandsrdquo FORMATH vol 11 pp 83ndash102 2012

[28] K Nakama T Ota N Mizoue and S Yoshida ldquoEffects ofrecovering logging residues on strategy and benefits of foreststandmanagementrdquo Journal of the Japanese Forestry Society vol93 no 5 pp 226ndash234 2011

[29] T Ota S Takahira K Nakama S Yoshida and N MizoueldquoEffectiveness of low-density planting in terms of planting costreduction and felling income reductionrdquo Journal of the JapaneseForestry Society vol 95 no 2 pp 126ndash133 2013

[30] S Takahira T Murakami N Mizoue S Yoshida and HKaga ldquoEvaluation of yield regulation with mathematical prog-rammingmdashcomparison with the management by Kyushu Elec-tric Power Co Incrdquo Kyushu Journal of Forest Research vol 59pp 154ndash157 2006

[31] S Takahira T Murakami N Mizoue S Yoshida and H KagaldquoOptimization of harvest scheduling to produce wood-basedmaterials with dynamic programming a case study in the forestof Kyushu Electric Power Co Incrdquo FORMATH vol 6 pp 57ndash752007

[32] A Yoshimoto andRMarusak ldquoEvaluation of carbon sequestra-tion and thinning regimes within the optimization frameworkfor forest stand managementrdquo European Journal of ForestResearch vol 126 no 2 pp 315ndash329 2007

[33] T Ando ldquoEcological studies on the stand density controlin even-aged pure standrdquo Bulletin of the Forestry and ForestProducts Research Institute vol 210 pp 1ndash153 1968

[34] P Bettinger J Sessions and K Boston ldquoA review of thestatus and use of validation procedures for heuristics used inforest planningrdquo Mathematical and Computational Forestry ampNatural-Resource Sciences vol 1 no 1 pp 26ndash37 2009

[35] K Moriguchi ldquoComparison of solutions of three operationsresearch methods for forest stand managementrdquo Journal of theJapanese Forest Society vol 95 no 4 pp 199ndash205 2013

[36] J R Gonzalez T Pukkala and M Palahı ldquoOptimising themanagement of Pinus sylvestris L stand under risk of fire inCatalonia (north-east of Spain)rdquo Annals of Forest Science vol62 no 6 pp 493ndash501 2005

[37] V Cerny ldquoThermodynamical approach to the traveling sales-man problem an efficient simulation algorithmrdquo Journal ofOptimization Theory and Applications vol 45 no 1 pp 41ndash511985

[38] S Kirkpatrick C D Gelatt Jr and M P Vecchi ldquoOptimizationby simulated annealingrdquo Science vol 220 no 4598 pp 671ndash6801983

[39] A Drexl ldquoA simulated annealing approach to the multicon-straint zero-one knapsack problemrdquo Computing Archives forScientific Computing vol 40 no 1 pp 1ndash8 1988

[40] K Ohman and L O Eriksson ldquoAllowing for spatial consid-eration in long-term forest planning by linking linear prog-ramming with simulated annealingrdquo Forest Ecology and Man-agement vol 161 no 1ndash3 pp 221ndash230 2002

[41] K Ohman and L O Eriksson ldquoThe core area concept in form-ing contiguous areas for long-term forest planningrdquo CanadianJournal of Forest Research vol 28 no 7 pp 1032ndash1039 1998

[42] C Lockwood and T Moore ldquoHarvest scheduling with spatialconstraints a simulated annealing approachrdquo Canadian Journalof Forest Research vol 23 no 3 pp 468ndash678 1993

[43] C BoWang and K V Gadow ldquoTimber harvest planning withspatial objectives using the method of simulated annealingrdquoForstwissenschaftliches Centralblatt vereinigt mit Tharandterforstliches Jahrbuch vol 121 no 1 pp 25ndash34 2002

[44] L Dong P Bettinger Z Liu and H Qin ldquoSpatial forest harvestscheduling for areas involving carbon and timber managementgoalsrdquo Forests vol 6 no 4 pp 1362ndash1379 2015

[45] B M Strimbu and M Paun ldquoSensitivity of forest plan value toparameters of simulated annealingrdquo Canadian Journal of ForestResearch vol 43 no 1 pp 28ndash38 2013

[46] P Borges T Eid and E Bergseng ldquoApplying simulated anneal-ing using different methods for the neighborhood search inforest planning problemsrdquo European Journal of OperationalResearch vol 233 no 3 pp 700ndash710 2014

[47] Japan Finance Corporation The Interest Catalogue for Agri-culture Forestry and Fisheries at 18062014 Japan FinanceCorporation 2014 (Japanese)

[48] Japan Forestry Agency Stand Density Management DiagramJapan Forest Technology Association 1981 (Japanese)

[49] Y Tadaki ldquoThe pre-estimating of stem yield based on thecompetition-density effectrdquo Bulletin of the Forestry and ForestProducts Research Institute vol 154 pp 1ndash19 1963

[50] Y Ejiri ldquoDecisions on optimal thinning by a recurring decision-making model (I) a maximization of total gains of stemvolumerdquo Journal of the Japanese Forestry Society vol 72 no 4pp 304ndash315 1990

[51] Forestry Division of Nagano Prefectural Government Guidefor Long Rotation Forest Management of Private Japanese LarchStand in Nagano Prefecture Forestry Division of Nagano Pre-fectural Government 1991 (Japanese)

[52] A Inoue and Y Kurokawa ldquoA new method for estimatingrelative stem profile equations application to system yieldtablesrdquo Journal of the Japanese Forestry Society vol 83 no 1 pp1ndash4 2001

[53] Hokushin LogMarketThe Log Prices at the 932ndMarket 2012(Japanese)

[54] Policy Planning Division of Japan Forestry Agency Report ofCost for Log Production at Fiscal the 2011 Policy PlanningDivision of Japan Forestry Agency 2013 (Japanese)

[55] Nagano Prefectural Government ldquoStandard unit cost table forlsquoShinshu no mori zukurirsquordquo service at fiscal 2014 (for project atfiscal 2013) (Japanese)

[56] Forestry and Fisheries Ministry of Agriculture Japanese Agri-cultural Standard for Log Forestry and Fisheries Ministry ofAgriculture 2007 (Japanese)

[57] N Metropolis A W Rosenbluth M N Rosenbluth A HTeller and E Teller ldquoEquation of state calculations by fastcomputing machinesrdquo The Journal of Chemical Physics vol 21no 6 pp 1087ndash1092 1953

[58] P Bettinger J Sessions and K N Johnson ldquoEnsuring thecompatibility of aquatic habitat and commodity productiongoals in eastern Oregon with a tabu search procedurerdquo ForestScience vol 44 no 1 pp 96ndash112 1998

[59] B L Golden and F B Alt ldquoInterval estimation of a globaloptimum for large combinatorial problemsrdquo Naval ResearchLogistics Quarterly vol 26 no 1 pp 69ndash77 1979


[60] P Bettinger D Graetz K Boston J Sessions and W ChungldquoEight heuristic planning techniques applied to three increas-ingly difficult wildlife planning problemsrdquo Silva Fennica vol 36no 2 pp 561ndash584 2002

[61] H Szu and R Hartley ldquoFast simulated annealingrdquo PhysicsLetters A vol 122 no 3-4 pp 157ndash162 1987

[62] L Ingber ldquoVery fast simulated re-annealingrdquoMathematical andComputer Modelling vol 12 no 8 pp 967ndash973 1989

[63] G Dueck ldquoNew optimization heuristics the great delugealgorithm and the record-to-record travelrdquo Journal of Compu-tational Physics vol 104 no 1 pp 86ndash92 1993

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Applied ampEnvironmentalSoil Science

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Atmospheric SciencesInternational Journal of



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Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

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Geological ResearchJournal of

EarthquakesJournal of


BiodiversityInternational Journal of


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OceanographyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


ClimatologyJournal of


single stands (eg NP [13ndash21] DP [22ndash32]) In particularthe MSPATH algorithm is more appropriate than PATHwhen long-term effects caused by competition-density effectsor fluctuations of log price with diameter are taken intoaccount [12] Yoshimoto [12] developed a way to apply it toyield models based on stand density management diagram(SDMD) [33] a type of forest growth model incorporatingcompetition-density effects that is commonly used in Japanwhich has been applied in several studies [27ndash32] Howeverit is necessary to consider carefully whether such optimizedresults represent a ldquobetter choicerdquo or ldquothe best choicerdquo

With respect to the spatial planning of forests it hasbeen argued that it is important to validate optimizationalgorithms [34]This also applies to algorithms for optimizingthinning rates for single stands but existing algorithms haveas yet only been compared with each other not against exactoptimal solutions as provided by FE Producing a solutionthat is validated as close to the optimal solution is potentiallynot always essential if the user is only using the optimizationalgorithm as a way to improve the current situation inother words for them ldquooptimizedrdquo means ldquobetter choicerdquoHowever in some cases a solution close to the optimum isneeded For example it is difficult to manage forests withoutsubsidy in Japan In this case the result of a stand-leveloptimization analysis can determine whether a stand canbe managed successfully under optimized conditions andwhether it is worth subsidizing Such an analysis can provideimportant information for regional zoning and in this case ahigh degree of reliability that is confidence that the methodprovides solutions close to ldquothe best choicerdquo is necessary tosatisfy accountability requirements especially towards forestowners who have applied for rezoning andwhose forest is notsubsidized The same considerations may apply to countriesor regions in situations similar to Japan that is little leewayin performing spatial optimization and a limited supply offunding

In a previous study [35] RS with 106 iterations andMSPATH were compared with coarse FE (CFE) by splittingvariables into a lattice comparing them using two simpleSDMD-base small-scale yield models (differing only in theirprice functions) as benchmark and setting net present value(NPV) for 50 years as the objective function The NPV ofthe nonmonotonic pricing yieldmodel provided byMSPATHwas 60419 yenha less than that derived using CFE and themonotonic pricing yield model provided by MSPATH was30920 yenha less In contrast those provided by RS were3755 yenha and 5487 yenha less respectively than thatderived using CFE On the other hand MSPATH reducedthe calculation cost by 10minus52sim10minus51 times relative to CFE and10minus26sim10minus25 times relative to RS MSPATH therefore confersa great advantage in terms of calculation cost but it isnot possible to rely on it providing ldquothe best choicerdquo Thuswe need to establish a more reliable method of optimizingthinning rates for single stands

There are diverse thinning rate models for single standsas a result of differences in the complexity of the models (egwhether they consider variation in trees [26 27] or in loggingand lumbering [31]) in the objective function used (eg NPV

[10 12 29 32] or in soil expectation value (SEV) [14 36]) or inother criteria [26 27] It is difficult to deal with the necessarycomplexity using NP algorithms since the various trade-offrelationships for example between yield volume at thinningand that at final cutting may require multimodality of yieldmodels and the incorporation of logging processes makesthem discontinuous On the other hand theoretical proofsare required to ensure the reliability of the DP algorithmhowever it may be difficult to obtain sufficient proof tosupport complex yield models We therefore suggest thatsimulated annealing (SA) [37 38] a stochastic algorithminspired by the annealing process of metals may satisfythe requirements It is worth noting that SA has beentheoretically proven to provide the global optimum for awide variety of problems [38] such as the traveling salesmanproblem [37 38] and the knapsack problem [39] as long asthe ldquotemperaturerdquo parameter is decreased gradually enough

In the field of forestry SA has usually been used for forestplanning under spatial constraints [40ndash42] or with a specialobjective function such as that defined based on ldquoforest spatialvaluerdquo [43 44] Lately the performance of SA itself has beenanalyzed for example its sensitivity to the parameters used[45] and its application in neighborhoodmethods [46]ThusSA is commonly used in the field and its performance isevaluated However this approach has never been used tooptimize thinning rates for single stands and its performancein this area has not been evaluated It is therefore necessaryfirst to evaluate whether SA can be used reliably to optimizethinning rates for single stands

In this study we evaluate the potential performance ofSA in optimizing thinning rates for single even-aged standsusing plural yield models based on SDMD We set thethinning interval in eachmodel at five years and the objectivefunction as the NPV before planting for one rotation termThe age of the rotation is one of the most important variablesfor improving the financial viability of stand-level forestmanagement However we fixed this variable in our modelbecause a change in rotation age leads to a change inthe number of dimensions of the model (the number ofvariables in this case the number of thinning ages) Tooptimize both rotation age and thinning rates it would thusbe necessary to define several models with different rotationages optimize them and then choose the best one Thesearching performance of the model with a fixed rotation agetherefore determines performance in optimizing amodel thattreats rotation age as a variable

Whereas the ldquoperformancerdquo of an optimization methodincludes both reliability and efficiency we must first improveits reliability and only then enhance its efficiency whilemaintaining reliabilityThe emphasis is therefore on securingreliable optimawith proven orthodox SAmethods Howeverthe combination of parameters used has strong effects onthe performance of SA approaches [45] In addition SA isa stochastic algorithm and as a result the solution obtainedfrom each searching process varies We therefore search forldquothe bestrdquo combination of SA parameters using CFE toensure the best possible performance using the mean NPVfrom 39 runs of the SA as the objective function We alsocompare the 39 NPVs from the solutions obtained using






NPV =

119899

sum

119894=1

119868119894(1 + 001119903)

minus119905119894minus 119862119903 (1)







1

119881

= 119860 +

119861

119873

(2)

119867119865 = 0578096 + 0460651119867 +

004259119867

100

radic119873 (3)

119866 =

119881

119867119865

(4)

119889119892 = 200radic119866

120587119873

(5)

119889 = minus0155598 + 0982606119889119892 (6)

log10119873119877119891= 5529749 minus 1780184 log

10119867 (7)

1

119881119877119891

= 119860 +

119861

119873119877119891

(8)

Ry = 119881

119881119877119891

(9)



(treesha)119881119877119891


119860 = 0095669119867minus1274434

119861 = 88334119867minus3054618

(10)



119873 = minus

119904

2

+radic1199042

4

+

119873119904119861

119860

if 0417216119873119904lt minus

119904

2

+radic1199042

4

+

119873119904119861

119860

(11)

119873 = 101198881111986711988812 if minus 119904

2

+radic1199042

4

+

119873119904119861

119860

le 0417216119873119904

(12)



119904 =

119861

119860

+

11987317159002

119904

2396313119860

minus 119873119904 (13)


119904is what









119904is monotonic











as follows

119877 = 100


(14)




119867 = 2581 1 minus 1182 exp (minus005119905) (15)






119873cut (17)








119889

11988909

=

2119909

119886 + 119887119909

(18)




119886 = 09 (2 minus 119887)

119887 =

180120593 minus 126120575

20120593 minus 63120575 + 70120575120593

120575 = 119889bhradic

7

10

1205871198671015840

4V1015840

(19)



119889 = 119889bh119909

120593

(

119886 + 119887120593

119886 + 119887119909

) (20)





119903in (1)



119868 =

119910

100

119881cut (119875cut minus 119862cut) (21)



119868 =

119910

100

119873cut

119896

sum

119895=1

V119895(119875119895minus 119862cut) (22)



(m3) calculated as

V119895= 4(

119889119895

100

)

2

(23)




119896 = floor(119867 minus 05

41

) (24)






119864 =


(25)



Start

Set new temperature

End

YesNo


YesNo




Yes

Yes

No

No







Set i = i + 1

Set i = 0






119901119886= exp(

119864119888minus 119864119901

119879

) (26)









119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics



















NPV =

119899

sum

119894=1

119868119894(1 + 001119903)

minus119905119894minus 119862119903 (1)







1

119881

= 119860 +

119861

119873

(2)

119867119865 = 0578096 + 0460651119867 +

004259119867

100

radic119873 (3)

119866 =

119881

119867119865

(4)

119889119892 = 200radic119866

120587119873

(5)

119889 = minus0155598 + 0982606119889119892 (6)

log10119873119877119891= 5529749 minus 1780184 log

10119867 (7)

1

119881119877119891

= 119860 +

119861

119873119877119891

(8)

Ry = 119881

119881119877119891

(9)



(treesha)119881119877119891


119860 = 0095669119867minus1274434

119861 = 88334119867minus3054618

(10)



119873 = minus

119904

2

+radic1199042

4

+

119873119904119861

119860

if 0417216119873119904lt minus

119904

2

+radic1199042

4

+

119873119904119861

119860

(11)

119873 = 101198881111986711988812 if minus 119904

2

+radic1199042

4

+

119873119904119861

119860

le 0417216119873119904

(12)



119904 =

119861

119860

+

11987317159002

119904

2396313119860

minus 119873119904 (13)


119904is what









119904is monotonic











as follows

119877 = 100


(14)




119867 = 2581 1 minus 1182 exp (minus005119905) (15)






119873cut (17)








119889

11988909

=

2119909

119886 + 119887119909

(18)




119886 = 09 (2 minus 119887)

119887 =

180120593 minus 126120575

20120593 minus 63120575 + 70120575120593

120575 = 119889bhradic

7

10

1205871198671015840

4V1015840

(19)



119889 = 119889bh119909

120593

(

119886 + 119887120593

119886 + 119887119909

) (20)





119903in (1)



119868 =

119910

100

119881cut (119875cut minus 119862cut) (21)



119868 =

119910

100

119873cut

119896

sum

119895=1

V119895(119875119895minus 119862cut) (22)



(m3) calculated as

V119895= 4(

119889119895

100

)

2

(23)




119896 = floor(119867 minus 05

41

) (24)






119864 =


(25)



Start

Set new temperature

End

YesNo


YesNo




Yes

Yes

No

No







Set i = i + 1

Set i = 0






119901119886= exp(

119864119888minus 119864119901

119879

) (26)









119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics



















as follows

119877 = 100


(14)




119867 = 2581 1 minus 1182 exp (minus005119905) (15)






119873cut (17)








119889

11988909

=

2119909

119886 + 119887119909

(18)




119886 = 09 (2 minus 119887)

119887 =

180120593 minus 126120575

20120593 minus 63120575 + 70120575120593

120575 = 119889bhradic

7

10

1205871198671015840

4V1015840

(19)



119889 = 119889bh119909

120593

(

119886 + 119887120593

119886 + 119887119909

) (20)





119903in (1)



119868 =

119910

100

119881cut (119875cut minus 119862cut) (21)



119868 =

119910

100

119873cut

119896

sum

119895=1

V119895(119875119895minus 119862cut) (22)



(m3) calculated as

V119895= 4(

119889119895

100

)

2

(23)




119896 = floor(119867 minus 05

41

) (24)






119864 =


(25)



Start

Set new temperature

End

YesNo


YesNo




Yes

Yes

No

No







Set i = i + 1

Set i = 0






119901119886= exp(

119864119888minus 119864119901

119879

) (26)









119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics
















119903in (1)



119868 =

119910

100

119881cut (119875cut minus 119862cut) (21)



119868 =

119910

100

119873cut

119896

sum

119895=1

V119895(119875119895minus 119862cut) (22)



(m3) calculated as

V119895= 4(

119889119895

100

)

2

(23)




119896 = floor(119867 minus 05

41

) (24)






119864 =


(25)



Start

Set new temperature

End

YesNo


YesNo




Yes

Yes

No

No







Set i = i + 1

Set i = 0






119901119886= exp(

119864119888minus 119864119901

119879

) (26)









119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics















Start

Set new temperature

End

YesNo


YesNo




Yes

Yes

No

No







Set i = i + 1

Set i = 0






119901119886= exp(

119864119888minus 119864119901

119879

) (26)









119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics
















119879119904= 10minus119903119904 119903119904= 00 04 40

119879119891= 10minus(119903119904minus119903119891)

119903119891= 10 15 60

Sd119905= 50 times 10

minus119903sd 119903sd = 10 13 40

(27)



119905is







119904






Start





No

Yes

Is the pool emptyNo

End








3 Results








Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics

















Start





No

Yes

No

End

Yes


Set i = 0


Set i = i + 1










SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics















SARS

SARS

0

10

20

30

40N

umbe

r of p

roce

sses

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0

10

20

30

40

Num

ber o

f pro

cess

es

0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash1

0

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


0ndash5

10

ndash

ndashminus30

5ndash10

minus5

ndash0

minus10

ndashminus5

minus25

ndashminus20

minus15

ndashminus10

minus30

ndashminus25

minus20

ndashminus15


SARS

SARS




119904trajectories






10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics



















10 00 00 00 00 00 01 01 07 00 13 24 20 00 07 23 5915 00 00 00 00 150 213 204 208 300 268 194 217 300 268 196 1220 200 185 185 185 500 500 497 500 00 17 46 63 00 40 46 3025 00 00 00 00 00 00 00 00 200 257 191 11 200 223 154 2530 00 00 00 00 00 00 00 495 100 14 77 388 100 62 89 16035 00 00 00 00 500 408 433 00 350 367 295 164 350 353 231 21540 00 00 00 00 300 394 363 194 00 02 30 15 00 00 29 43345 00 00 00 00 450 434 448 500 00 01 14 81 00 03 26 13




119904trajectories



4 Discussion














0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics















0

BestMedianWorst

BestMedianWorst

BestMedianWorst

BestMedianWorst





Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

Diff

eren

ce in

NPV

from

CFE

(103

yen

ha)

minus150

minus100

minus50

0

50

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

minus500

minus450

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

50

minus250

minus200

minus150

minus100

minus50

0

50






20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics















20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

20 30 40 5010Age (year)

Ns

(tree

sha

)N

s(tr

ees

ha)

Ns

(tree

sha

)N

s(tr

ees

ha)

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst

CFEBest

MedianWorst






5 Conclusion







Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics



















Acknowledgment


References






































































Journal of












Volume 2014

Advances in









Geophysics


























































Journal of












Volume 2014

Advances in









Geophysics























Journal of












Volume 2014

Advances in









Geophysics


















Journal of












Volume 2014

Advances in









Geophysics














Documents

Research Article An Evaluation of the Use of Simulated ...downloads.hindawi.com/journals/ijfr/2015/173042.pdf · log 10 = 5.529749 1.780184 log 10, ( ) 1 = + , Ry =, ( ) where is