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Metaheuristic Algorithms:A Critical Analysis
Xin-She YangMiddlesex University London
ICHSA 2017
Xin-She Yang Nature-Inspired Computation ICHSA2017 1 / 54
The Essence of an Algorithm The Essence of an Algorithm
The Essence of an Algorithm
Essence of an Optimization Algorithm
To move to a new, better point x(t+1) from an existing location x
(t).
x1
x2
x(t)
x(t+1)
?
Population-based algorithms use multiple, interacting paths.
Different algorithms
Different strategies/approaches in generating these moves!
Xin-She Yang Nature-Inspired Computation ICHSA2017 2 / 54
The Essence of an Algorithm The Essence of an Algorithm
The Essence of an Algorithm
In essence, an algorithm can be written (mathematically) as
xt+1 = A(x t , α),
For any given xt , the algorithm will generate a new solution x
t+1.
Functional or a Dynamical System?
We can view the above equation as
an iterative functional (with fixed points),
or a dynamical system (with attractors),
or a self-organization system (with organized structures),
or a Markov chain (e.g., Markov chain Monte Carlo).
The behavoir of the system (algorithm) can be controlled by A and α.
For details, please refer to: Xin-She Yang et al., Swarm Intelligence and
Bio-Inspired Computation: Theory and Applications, Elsevier, (2013).Xin-She Yang Nature-Inspired Computation ICHSA2017 3 / 54
The Essence of an Algorithm What’s Wrong with Traditional Algorithms?
What’s Wrong with Traditional Algorithms?
Some issues with traditional optimization algorithms such as theNewton-Raphson Method, pattern search, quadratic programming, etc.
Traditional algorithms are mostly local search, thus cannot guaranteeglobal optimality (except for linear programming and convexoptimization).
Results often depend on the initial starting points (except linear andconvex problems).
Methods tend to be problem-specific (e.g., k-opt, branch and bound).
Cannot deal with highly nonlinear optimization problems efficiently.
Struggle to cope problems with discontinuity.
Xin-She Yang Nature-Inspired Computation ICHSA2017 4 / 54
The Essence of an Algorithm Nature-Inspired Optimization Algorithms
Nature-Inspired Optimization Algorithms
Almost all nature-inspired metaheuristic optimization algorithms (heuristicor metaheuristic algorithms, as a global optimizer) strive to
Increase the probability of finding the global optimality (as a globalsearch tool);
Solve a wider class of problems (treating them as a black-box);
Try to deal with highly nonlinear problems, problems withdiscontinuity, and even NP-hard combinatorial problems;
Draw design inspiration from Nature.
Xin-She Yang Nature-Inspired Computation ICHSA2017 5 / 54
Nature-Inspired Algorithms Nature-Inspired Optimization Algorithms
Nature-Inspired Optimization Algorithms
Genetic algorithms (1960s/1970s), evolutionary strategy (Rechenberg& Swefel 1960s), evolutionary programming (Fogel et al. 1960s).
Simulated annealing (Kirkpatrick et al. 1983), Tabu search (Glover1980s), ant colony optimization (Dorigo 1992), genetic programming(Koza 1992), particle swarm optimization (Kennedy & Eberhart1995), differential evolution (Storn & Price 1996/1997)
harmony search (Geem et al. 2001), , artificial bee colony(Karaboga, 2005).
Firefly algorithm (Yang 2008), cuckoo search (Yang & Deb 2009), batalgorithm (Yang, 2010), flower pollination algorithm (2012), ...
For details, please refer to:Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 6 / 54
Nature-Inspired Algorithms Three different ways of thinking ...
Three different ways of thinking ...
Particle swarm optimization: swarm intelligence
Harmony search: music-inspired
Cuckoo search: swarm intelligence and also scale-free search
Xin-She Yang Nature-Inspired Computation ICHSA2017 7 / 54
Swarm Intelligence Seeking Inspiration in Nature: Swarm Intelligence
Seeking Inspiration in Nature: Swarm Intelligence
Swarm Intelligence
Ants, bees, birds, fish ...Simple rules lead to complex behaviour.
Swarming Starlings (YouTube Video)
Xin-She Yang Nature-Inspired Computation ICHSA2017 8 / 54
Swarm Intelligence PSO
PSO
Particle Swarm Optimization (Kennedy and Eberhart, 1995)
x i
g∗
x j
vt+1i = v
ti + αǫ1(g
∗ − xti ) + βǫ2(x
∗
i − xti ),
xt+1i = x
ti + v
t+1i .
α, β = learning parameters, ǫ1, ǫ2=random numbers.
Xin-She Yang Nature-Inspired Computation ICHSA2017 9 / 54
Swarm Intelligence PSO Demo and Disadvantages
PSO Demo and Disadvantages
The updating equations in PSO form a linear system:
x i
v i
t+1
=
1 1
−(αǫ1 + βǫ2) 1
x i
v i
t
+
0
αǫ1g∗ + βǫ2x
∗
i
.
PSO Demo Premature convergence
Xin-She Yang Nature-Inspired Computation ICHSA2017 10 / 54
Swarm Intelligence Firefly Algorithm
Firefly Algorithm
Firefly Video (YouTube)
Firefly Behaviour and Idealization (Yang, 2008)
Fireflies are unisex and brightness varies with distance.
Less bright ones will be attracted to bright ones.
If no brighter firefly can be seen, a firefly will move randomly.
xt+1i = x
ti + β0e
−γr2ij (x j − x i ) + α ǫti .
⋄ The objective landscape maps to a light-based landscape, and firefliesswarm into the brightest points/regions.
⋄ There is no g∗, therefore, there is no leader. Also, a highly nonlineariterative system, so subdivision into multiswarms is possible.
Xin-She Yang Nature-Inspired Computation ICHSA2017 11 / 54
Swarm Intelligence FA Demo and Advantages
FA Demo and Advantages
Paths of fireflies for 3D Rosenbrock function (Husselmann, 2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 12 / 54
Swarm Intelligence Why is FA so efficient?
Why is FA so efficient?
FA Demo Multimodal optimality
Advantages of Firefly Algorithm over PSO
Automatically subdivide the whole population into subgroups, andeach subgroup swarms around a local mode/optimum.
Control modes/ranges by varying γ.
Control randomization by tuning parameters such as α.
Suitable for multimodal, nonlinear, global optimization problems.
Xin-She Yang Nature-Inspired Computation ICHSA2017 13 / 54
Swarm Intelligence Firefly algorithm is Not PSO
Firefly algorithm is Not PSO
Though both algorithms (in fact, almost all algorithms) use a populationand some update equations, FA is not PSO (not even similar to PSO).
Main differences
FA uses a nonlinear attraction mechanism (inverse-quare law plusexponential decay). PSO mechanism is simply linear (x ti − g∗).
The population in the FA can subdivide into subgroups and thus canform multi-swarm automatically (PSO cannot).
The standard FA does not use g∗ (though PSO uses g∗).xt+1i = x
ti + β0e
−γr2ij (x j − x i) + α ǫti .
FA can find multiple optimal solutions simultaneously (PSO cannot).
FA has a fractal-like search structure (PSO cannot).
Xin-She Yang Nature-Inspired Computation ICHSA2017 14 / 54
Swarm Intelligence Harmony Search
Harmony Search
Zong Woo Geem et al. (2001). Music-inspired metaheuristic.Now almost 14,000 papers [Google scholar] with diverse applications:
Variants for specific applications:
Continuous optimization ...
Discrete variants for scheduling, travelling-salesman problem,combinatorial optimization ...
Water distribution, network optimization ...
Clustering, classifications and feature selection ...
Multiobjective harmony search ...
Hybridization with other algorithms.
A diverse range of applications, for example, see ICHSA2017.
Xin-She Yang Nature-Inspired Computation ICHSA2017 15 / 54
Swarm Intelligence Cuckoo Breeding Behaviour
Cuckoo Breeding Behaviour
Cuckoo Behavior (YouTube Video)
Evolutionary Advantages
Parallism: Dumps eggs in the nests of (multiple) host birds and letthese host birds raise their chicks, so minimum efforts and maximumsuccess.
Timing: Cuckoo’s eggs hatch slightly earlier.
Fitness: Similarity of eggs in terms of texture, colour, etc.
Xin-She Yang Nature-Inspired Computation ICHSA2017 16 / 54
Swarm Intelligence Cuckoo Search (Yang and Deb, 2009)
Cuckoo Search (Yang and Deb, 2009)
Cuckoo Behaviour and IdealizationEach cuckoo lays one egg (solution) at a time, and dumps its egg in arandomly chosen nest.
The best nests with high-quality eggs (solutions) will carry out to thenext generation.
The egg laid by a cuckoo can be discovered by the host bird with aprobability pa and a nest will then be built.
Xin-She Yang Nature-Inspired Computation ICHSA2017 17 / 54
Swarm Intelligence Cuckoo Search
Cuckoo Search
Local random walk:
xt+1i = x
ti + s ⊗ H(pa − ǫ)⊗ (x t
j − xtk).
[x i , x j , xk are 3 different solutions, H(u) is a Heaviside function, ǫ is arandom number drawn from a uniform distribution, and s is the step size.
Global random walk via Levy flights:
xt+1i = x
ti + αL(s, λ), L(s, λ) =
λΓ(λ) sin(πλ/2)
π
1
s1+λ, (s ≫ s0).
Generation of new moves by Levy flights, random walk and elitism.
Xin-She Yang Nature-Inspired Computation ICHSA2017 18 / 54
Swarm Intelligence
The normal distribution
p(x ;µ, σ2) =1
σ√2π
exp[−(x − µ)2
2σ2], −∞ < x <∞.
Isotropic Random Walks
SN =
N∑
i=1
Xi = X1 + ...+ XN = SN−1 + XN ,
s
Xin-She Yang Nature-Inspired Computation ICHSA2017 19 / 54
Swarm Intelligence Levy Distribution and Levy Flights
Levy Distribution and Levy Flights
L(s) =1
π
∫
∞
0cos(τs)e−α τγdτ, (0 < γ ≤ 2),
=
√
γ
2πexp
[
−γ
2(s − µ)
] 1
(s − µ)3/2, 0 < µ < s <∞ (for steps µ > 0).
s
Self-similar, multi-scale, global random walks.Xin-She Yang Nature-Inspired Computation ICHSA2017 20 / 54
Swarm Intelligence Bat Algorithm (Yang, 2010)
Bat Algorithm (Yang, 2010)
BBC Video
Microbats use echolocation for hunting
Ultrasonic short pulses as loud as 110dB with a short period of 5 to20 ms. Frequencies of 25 kHz to 100 kHz.
Speed up pulse-emission rate and increase loudness when homing at aprey.
Xin-She Yang Nature-Inspired Computation ICHSA2017 21 / 54
Swarm Intelligence Bat Algorithm
Bat Algorithm
Acoustics of bat echolocation
λ =v
f∼ 2 mm to 14 mm.
Rules used in the bat algorithm:
fi = fmin + (fmax − fmin)β, β ∈ [0, 1],
vt+1i = v ti + (x t
i − x∗)fi , xt+1i = x
ti + v
ti .
Variations of Loudness and Pulse Rate
At+1i ← αAt
i , α ∈ (0, 1], r t+1i = r0i [1− exp(−γt)].
Xin-She Yang Nature-Inspired Computation ICHSA2017 22 / 54
Swarm Intelligence Other Algorithms
Other Algorithms
Genetic algorithms
Differential evolution
Artificial immune system
Flower pollination algorithm
Memetic algorithm
...
Reviews
Yang, X. S., Nature-Inspired Optimization Algorithms, Elsevier,(2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 23 / 54
Applications Applications
Applications
Design optimization: structural engineering, product design ...
Scheduling, routing and planning: discrete, combinatorial problems ...
Image processing and data Mining: image segmentation, featureselection ...
Applications in almost all areas (e.g., finance, economics, engineering,industry, ...)
10 Examples in Science and Engineering
Xin-She Yang Nature-Inspired Computation ICHSA2017 24 / 54
Applications Pressure Vessel Design Optimization (Example 1)
Pressure Vessel Design Optimization (Example 1)
r
d1
r
L d2
Xin-She Yang Nature-Inspired Computation ICHSA2017 25 / 54
Applications Pressure Vessel Design
Pressure Vessel Design
This is a well-known test problem for optimization (e.g., see Cagnina et al.
2008) and it can be written as
minimize f (x) = 0.6224d1rL+ 1.7781d2r2 + 3.1661d2
1L+ 19.84d21 r ,
subject to
g1(x) = −d1 + 0.0193r ≤ 0g2(x) = −d2 + 0.00954r ≤ 0g3(x) = −πr2L− 4π
3 r3 + 1296000 ≤ 0g4(x) = L− 240 ≤ 0.
The simple bounds are
0.0625 ≤ d1, d2 ≤ 99× 0.0625, 10.0 ≤ r , L ≤ 200.0.
The best solution (Yang, 2010; Gandomi and Yang, 2011)
f∗ = 6059.714, x∗ = (0.8125, 0.4375, 42.0984, 176.6366).
Now we have a set of analytical solutions (Yang et al., 2013).Xin-She Yang Nature-Inspired Computation ICHSA2017 26 / 54
Applications Speed Reducer/Gear Box Design (Example 2)
Speed Reducer/Gear Box Design (Example 2)
Mixed-Integer Programming:
Continuous variables and integers.
Xin-She Yang Nature-Inspired Computation ICHSA2017 27 / 54
Applications
f (x1, x2, x3, x4, x5, x6, x7) = 0.7854x1x22 (3.3333x
23 + 14.9334x3 − 43.0934)
−1.508x1(x26 + x27 ) + 7.4777(x36 + x37 ) + 0.7854(x4x26 + x5x
27 ),
subject to
g1 =27
x1x22 x3− 1 ≤ 0, g2 =
397.5x1x
22 x
23− 1 ≤ 0,
g3 =1.93x34x2x3d
41− 1 ≤ 0, g4 =
1.93x35x2x3d
42− 1 ≤ 0,
g5 =1
110x36
√
(745x4hx3
)2 + 16.9 × 106 − 1 ≤ 0,
g6 =1
85x37
√
(745x5hx3
)2 + 157.5 × 106 − 1 ≤ 0,
g7 =x2x340 − 1 ≤ 0, g8 =
5x2x1− 1 ≤ 0,
g9 =x1
12x2− 1 ≤ 0, g10 = 1.5x6+1.9
x4− 1 ≤ 0,
g11 = 1.1x7+1.9x5
− 1 ≤ 0.
Simple bounds are 2.6 ≤ x1 ≤ 3.6, 0.7 ≤ h ≤ 0.8, 17 ≤ x3 ≤ 28,7.3 ≤ x4 ≤ 8.3, 7.8 ≤ x5 ≤ 8.3, 2.9 ≤ x6 ≤ 3.9, and 5.0 ≤ x7 ≤ 5.5. zmust be integers.
Xin-She Yang Nature-Inspired Computation ICHSA2017 28 / 54
Applications Dome Design (Example 3)
Dome Design (Example 3)
120-bar dome: Divided into 7 groups, 120 design elements, about 200 constraints
(Gandomi and Yang 2011; Yang et al. 2012).
Xin-She Yang Nature-Inspired Computation ICHSA2017 29 / 54
Applications Tower Design (Example 4)
Tower Design (Example 4)
26-storey tower: 942 design elements, 244 nodal links, 59 groups/types, > 4000
nonlinear constraints (Yang et al. 2011; Gandomi & Yang 2012).
Xin-She Yang Nature-Inspired Computation ICHSA2017 30 / 54
Applications Car Door Design (Example 5)
Car Door Design (Example 5)
Design better, safer and energy-efficient cars
Minimize weight, low crash deflection (< 32 mm), lower impact force (< 4kN), .... Even a side barrier has 11 design variables!
Xin-She Yang Nature-Inspired Computation ICHSA2017 31 / 54
Applications Scheduling(Example 6)
Scheduling(Example 6)
MK Marichelvam, T Prabaharan, XS Yang, Improved cuckoo search algorithm for hybrid flow
shop scheduling problems to minimize makespan, Applied Soft Computing, vol. 19, no. 1,pp.
93-101 (2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 32 / 54
Applications Soft Testing and Path Generation
Soft Testing and Path Generation
Srivastava, Mallikarjun, Yang (2013). Optimal test sequence generationusing firefly algorithm, Swarm and Evolutionary Computation, 8(2013)44-53.
Xin-She Yang Nature-Inspired Computation ICHSA2017 33 / 54
Applications Travel Salesman Problem (Example 7)
Travel Salesman Problem (Example 7)
Xin-She Yang Nature-Inspired Computation ICHSA2017 34 / 54
Applications Cuckoo Search for TSP
Cuckoo Search for TSP
Aziz Ouaarab, Belad Ahiod, Xin-She Yang, Discrete cuckoo search algorithm for the travelling
salesman problem, Neural Computing and Applications, (2013).
http://link.springer.com/article/10.1007/s00521-013-1402-2.
Xin-She Yang Nature-Inspired Computation ICHSA2017 35 / 54
Applications Data Mining: Feature Selection (Example 8)
Data Mining: Feature Selection (Example 8)
Bat algorithm and cuckoo search are very competitive (Papa et al, 2013; 2014).
Also effective at dimension reduction (in terms of number of key features).
Dataset # samples #features #classes
Diabetes 768 8 2
DNA 2000 180 3
Mushrooms 8124 112 2
OPF BA CS FA ICS PSO0
10
20
30
40
50
60
70
80
Accura
cy [%
]
61 61 5961 61 6160 61 61 62 6263 62 62 62 61
Mushrooms
BaselineBinarySigmoidHyperbolic Tangent
Xin-She Yang Nature-Inspired Computation ICHSA2017 36 / 54
Applications Image Processing (Example 9)
Image Processing (Example 9)
Satellite images and flooding estimates (Senthilnath & Yang, 2014)
Xin-She Yang Nature-Inspired Computation ICHSA2017 37 / 54
Applications Satellite images
Satellite images
Three methods are compared, and FA obtained the best results.
Algorithms Optimal Worst Mean
GA 0.8044 0.7528 0.7824
PSO 0.8057 0.8009 0.8051
FA 0.8126 0.8019 0.8076
Also, Senthilnath et al. compared 14 different algorithms for classifications,and they found that the firefly algorithm seems to be most efficientamong 14 different classification methods.
Xin-She Yang Nature-Inspired Computation ICHSA2017 38 / 54
Applications Classifications and Clustering (Example 10)
Classifications and Clustering (Example 10)
K-means clustering with nature-inspired algorithms can produce far betterresults than K-means methods (Fong, Deb, Yang, Zhang, 2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 39 / 54
Applications Theoretical Analysis
Theoretical Analysis
Though it still lacks a solid mathematical framework, theoretical studiesstart to emerge:
Dynamic system theory
Bayesian statistics
Intermit search theory
Markov chain Monte Carlo
Self-organization theory
Convergence analysis
Exploration and exploitation
Xin-She Yang Nature-Inspired Computation ICHSA2017 40 / 54
Applications Self-Organization
Self-Organization
Self-organizing systems are everywhere,physical, chemical, biological, social, artificial ...
Xin-She Yang Nature-Inspired Computation ICHSA2017 41 / 54
Applications Similarities Between Self-Organization and Optimization
Similarities Between Self-Organization and Optimization
Self-organization:
High degrees of freedom, a sufficient number of states.
Noise, perturbation =⇒ diversity.
Selection mechanism =⇒ structure.
Far-from-equilibrium and large perturbation =⇒ potentially faster tore-organize.
Optimization Algorithms:
A sufficient larger population.
Randomization, stochastic components, exploration=⇒ to escape local optima.
Selection and exploitation =⇒ convergence & optimal solutions.
High-degrees of randomization=⇒ more likely to reach global optimality (but may be slow).
Xin-She Yang Nature-Inspired Computation ICHSA2017 42 / 54
Applications But there are significant differences!
But there are significant differences!
Self-Organization:
Avenues to self-organization may be unclear.
Time may not be important.
Optimization (especially metaheuristics):
How to make an algorithm converge is very important.
Speed of convergence is crucial(to reach truly global optimality with the minimum computingefforts).However, we lack good theories to understand either self-organizationor metaheuristic optimization.
Xin-She Yang Nature-Inspired Computation ICHSA2017 43 / 54
Applications Multi-Agent System (Swarm Intelligence?)
Multi-Agent System (Swarm Intelligence?)
For a multi-agent system or a swarm, an algorithm can be considered as aset of interacting Markov chain or a complex dynamical system
x1
x2...xn
t+1
= A[x1, ..., xn; ǫ1, ..., ǫm; p1(t), ..., pk (t)]
x1
x2...
xn
t
.
A population of solutions xt+1i (i = 1, ..., n) are generated from x
ti ,
controlled by k parameters and m random numbers.
In principle, the behaviour of an algorithm is controlled by the eigenvaluesof A, but in practice, it is almost impossible to figure out the eigenvalues(apart from very simple/rare cases).
Xin-She Yang Nature-Inspired Computation ICHSA2017 44 / 54
Exploration & Exploitation Key Components in All Metaheuristics
Key Components in All Metaheuristics
So many algorithms – what are the common characteristics?
What are the key components?
How to use and balance different components?
What controls the overall behaviour of an algorithm?
Xin-She Yang Nature-Inspired Computation ICHSA2017 45 / 54
Exploration & Exploitation Exploration and Exploitation
Exploration and Exploitation
Characteristics of Metaheuristics
Exploration and Exploitation, or Diversification and Intensification.
Exploitation/Intensification
Intensive local search, exploiting local information.E.g., hill-climbing.
Exploration/Diversification
Exploratory global search, using randomization/stochastic components.E.g., hill-climbing with random restart.
Xin-She Yang Nature-Inspired Computation ICHSA2017 46 / 54
Exploration & Exploitation Summary
Summary
Exploitation
Exploration
uniformsearch
steepestdescent
Tabu Nelder-Mead
CS
PSO/FAEP/ESSA Ant/Bee
Genetic algorithms
Newton-Raphson
Best?
Free lunch?
Xin-She Yang Nature-Inspired Computation ICHSA2017 47 / 54
The Future – Some Open Problems (Swarm Intelligence) The Future – Some Open Problems (Swarm Intelligence)
The Future – Some Open Problems (Swarm Intelligence)
Origin of Swarm Intelligence: What are the main mechanisms toproduce collective intelligence from seemingly simple local rules?Any theory for the rise of swarm intelligence?
Mathematical Analysis: A unified mathematical framework (e.g.,Markov chain theory, dynamical systems) is needed.
Comparison: What are the best/fair performance measures?
Parameter tuning: How to tune the algorithm-dependentparameters so that an algorithm can achieve the best performance?Is there a general framework for this?
Scalability: Can the algorithms that work for small-scale problems bedirectly applied to large-scale/high-dimensional problems (ford > 1000) ?
Intelligence: Smart algorithms may be a buzz word, but can trulyintelligent algorithms be developed?
Xin-She Yang Nature-Inspired Computation ICHSA2017 48 / 54
The Future – Some Open Problems (Swarm Intelligence) Intelligent Algorithms?
Intelligent Algorithms?
Xin-She Yang Nature-Inspired Computation ICHSA2017 49 / 54
The Future – Some Open Problems (Swarm Intelligence) Books on Nature-Inspired Algorithms
Books on Nature-Inspired Algorithms
Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014).
Xin-She Yang, Cuckoo Search and Firefly Algorithm, Springer, (2014).
Xin-She Yang Nature-Inspired Computation ICHSA2017 50 / 54
The Future – Some Open Problems (Swarm Intelligence) Thank you :) Any questions?
Thank you :) Any questions?
Xin-She Yang et al., Swarm Intelligence and Bio-Inspired Computation:Theory and Applications, Elsevier, (2013).
Xin-She Yang, Artificial Intelligence, Evolutionary Computing andMetaheuristics, (2013).
Xin-She Yang Nature-Inspired Computation ICHSA2017 51 / 54
The Future – Some Open Problems (Swarm Intelligence) References
References
Xin-She Yang, Nature-Inspire Optimization Algorithm, Elsevier, (2014).
Xin-She Yang, Gebrail Bekdas, Sinan Melih Nigdeli, Metaheuristics and Optimization in
Civil Engineering, Springer, (2016).
Xin-She Yang and Suash Deb, Multiobjective cuckoo search for design optimization,Computers & Operations Research, 40(6), 1616–1624 (2013).
X. S. Yang and S. Deb, Cuckoo search: recent advances and applications, NeuralComputing and Applications, vol. 24, no. 1, pp. 169-174 (2014).
X. S. Yang and X. S. He, Bat algorithm: literature review and applications, Int. J.Bio-Inspired Computation, vol. 5, no. 3, pp. 141-149 (2013).
A. H. Gandomi, S. Talatahari and X. S. Yang, S. Deb, Design optimization of trussstructures using cuckoo search algorithm, Structural Design of Tall and Special Buildings,vol. 22, no. 17, pp. 1330-1340 (2013).
A. H. Gandomi and X. S. Yang, Chaotic bat algorithm, Journal of Computational Science,vol. 5, no. 2, pp. 224-232 (2014).
P. R. Srivastava, A. Varshney, P. Nama, X. S. Yang, Software test effort estimation: amodel based on cuckoo search, Int. J. Bio-Inspired Computation, vol. 4, no. 5, pp.278-285 (2012).
Xin-She Yang Nature-Inspired Computation ICHSA2017 52 / 54
The Future – Some Open Problems (Swarm Intelligence)
X. S. Yang, M. Karamanoglu, X.S. He, Flower pollination algorithm: A novel approach formultiobjective optimization, Engineering Optimization, Vol. 46, No. 9, 1222-1237 (2014).
M. K. Marchelvam, T. Prabaharan, X. S. Yang, A discrete firefly algorithm for multi-objectivehybrid flowshop scheduling problems, IEEE Trans. Evolutionary Computation, vol. 18, no. 2,pp. 301-205 (2014).
P. R. Srivastava, B. Millikarjun, X. S. Yang, Optimal test sequence generation using fireflyalgorithm, Swarm and Evolutionary Computation, vol. 8, no. 1, pp. 44-53 (2013).
D. Rodrigues, L. A. M. Pereira, R. Y. M. Nakamura, K. A. P. Costa, X. S. Yang, A. N. Souza,J. P. Papa, A wrapper approach for feature selection and Optimum-Path Forest based on BatAlgorithm, Expert Systems with Applications, vol. 41, no. 5, pp. 2250-2258 (2014).
X. S. Yang, M. Karamanoglu, X. S. He, Multi-objective flower algorithm for optimization,Procedia Computer Science, Vol. 18, pp. 861-868 (2013).
X. S. Yang and J. P. Papa, Bio-inspired Computation and Applications in Image Processing,Elsevier (2016).
J. Senthilnath, S. Kulkarni, J. A. Benediktsson, X. S. Yang, A novel approach for multispectralsatellite image classification based on the bat algorithm, IEEE Geoscience and Remote Sensing
Letters, Vol. 13, No. 4, 599-603 (2016).
A. Chakri, R. Khelif, M. Benouaret, X. S. Yang, New directional bat algorithm for continuousoptimization problems, Expert Systems with Applications, Vol. 69, 159-175 (2017).
Xin-She Yang Nature-Inspired Computation ICHSA2017 53 / 54
Thank you :) Any generic tool for optimization?
Any generic tool for optimization?
Xin-She Yang Nature-Inspired Computation ICHSA2017 54 / 54