Vip Planopt Manual

VIP-PLANOPT 2006 Users Manual

Engineering Optimization Software vvv Feb 2006

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VIP-PLANOPT 2006

USERS MANUAL

vvv Engineering Optimization Software

1386 Pritchett Industrial Drive, Austell, GA 30168, USA E-mail: [email protected]



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CONTENTS COPYRIGHT.............................................................................................................................................................................5

DISCLAIMER ...........................................................................................................................................................................6

INTRODUCTION.....................................................................................................................................................................7

MOTIVATION................................................................................................................................................................7FILLING THE GAP.........................................................................................................................................................7UNMATCHED FUNCTIONALITY ................................................................................................................................8OPTIMIZATION ALGORITHM ....................................................................................................................................8

TERMINOLOGY................................................................................................................................................................... 10

MODULE ......................................................................................................................................................................10MODULE ASPECT RATIO .........................................................................................................................................11MODULE AREA ..........................................................................................................................................................11MODULE TYPE...........................................................................................................................................................11HARD (RIGID) MODULE ............................................................................................................................................11SOFT (FLEXIBLE) MODULE......................................................................................................................................11MODULE POSITION....................................................................................................................................................11MODULE PLACEMENT ..............................................................................................................................................12ANCHORED MODULE ................................................................................................................................................12FORBIDDEN AREA MODULE (FAM).......................................................................................................................12MODULE ORIENTATION...........................................................................................................................................12MODULE PADDING ....................................................................................................................................................12PICK-UP & DROP-OFF POINTS..................................................................................................................................13BOUNDARY SHAPE ....................................................................................................................................................13ENCLOSURE .................................................................................................................................................................14FLOW MATRIX ...........................................................................................................................................................14UNIT COST MATRIX..................................................................................................................................................15COST MATRIX ............................................................................................................................................................15

DISTANCE NORMS............................................................................................................................................................. 16

RECTILINEAR NORM .................................................................................................................................................16EUCLIDEAN NORM .....................................................................................................................................................16SQUARED EUCLIDEAN NORM ..................................................................................................................................16

COST FUNCTIONS.............................................................................................................................................................. 17

COST FUNCTION F1 ...................................................................................................................................................17COST FUNCTION F2 ....................................................................................................................................................17COST FUNCTION F3 ....................................................................................................................................................18COST FUNCTION F4 ....................................................................................................................................................18

PRIMARY INPUT.................................................................................................................................................................. 19

File Menu ...................................................................................................................................................... 20Constraints Menu ........................................................................................................................................ 21Optimization Menu..................................................................................................................................... 21



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Benchmarks menu........................................................................................................................................ 21Help menu...................................................................................................................................................... 22

DISPLAY CONTROL....................................................................................................................................................23Current Module ID ...................................................................................................................................... 23Next................................................................................................................................................................. 23Previous......................................................................................................................................................... 23Zoom All......................................................................................................................................................... 23Grid/Snap Size.............................................................................................................................................. 24

NEW MODULE ............................................................................................................................................................25MODULE TYPE...........................................................................................................................................................26RESIZING GRAPHICALLY...........................................................................................................................................27RESIZING NUMERICALLY..........................................................................................................................................28MODULE ORIENTATION...........................................................................................................................................29MODULE POSITION....................................................................................................................................................30MODULE DELETION..................................................................................................................................................31OTHER PROPERTIES ..................................................................................................................................................32COST AND FLOW MATRICES INPUT .......................................................................................................................33SOFT MODULE INPUT ...............................................................................................................................................34OPTIMIZATION PARAMETERS.................................................................................................................................35

Cost Function............................................................................................................................................... 35Optimization Seed........................................................................................................................................ 35Distance Norm.............................................................................................................................................. 36

OPTIMIZATION CONSTRAINTS................................................................................................................................37Module Padding .......................................................................................................................................... 37Boundary Shape........................................................................................................................................... 37Other Constraints ........................................................................................................................................ 37

OPTIMIZATION CONTROL .......................................................................................................................................38Optimize......................................................................................................................................................... 38Analyze Optimized Layout.......................................................................................................................... 38

OTHER INPUT....................................................................................................................................................................... 39

MODULE DEFAULTS WINDOW ...............................................................................................................................41How to Open ................................................................................................................................................. 41Notes............................................................................................................................................................... 41

DISCRETE ASPECT RATIOS WINDOW ....................................................................................................................42How to Open ................................................................................................................................................. 42Notes............................................................................................................................................................... 42

MATRIX INPUT WINDOW ........................................................................................................................................43How to Open ................................................................................................................................................. 43Notes............................................................................................................................................................... 43

ANCHORED MODULES PLACEMENT WINDOW ....................................................................................................46How to Open ................................................................................................................................................. 46Notes............................................................................................................................................................... 46

PICK-UP & DROP-OFF POINTS WINDOW ...............................................................................................................48How to Open ................................................................................................................................................. 48Notes............................................................................................................................................................... 48

MODULE PADDING WINDOW ..................................................................................................................................50How to Open ................................................................................................................................................. 50Notes............................................................................................................................................................... 50

BOUNDARY SHAPE WINDOW ..................................................................................................................................52How to Open ................................................................................................................................................. 52Notes............................................................................................................................................................... 52

OPTIMIZATION CONSTRAINTS WINDOW .............................................................................................................54How to Open ................................................................................................................................................. 54



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Notes............................................................................................................................................................... 55OPTIMAL LAYOUT ANALYSIS WINDOW ...............................................................................................................56

How to Open ................................................................................................................................................. 56Notes............................................................................................................................................................... 56

BENCHMARKPROBLEMS ................................................................................................................................................ 59

DATA FILES.................................................................................................................................................................59CHARACTERISTICS.....................................................................................................................................................60

PLANOPT Benchmark 1 (L3) .................................................................................................................... 60PLANOPT Benchmark 2 (L4B).................................................................................................................. 60PLANOPT Benchmark 3 (L8) .................................................................................................................... 60PLANOPT Benchmark 4 (L8FX) ............................................................................................................... 61PLANOPT Benchmark 5 (L12PD) ............................................................................................................ 61PLANOPT Benchmark 6 (L20).................................................................................................................. 61PLANOPT Benchmark 7 (L28).................................................................................................................. 61PLANOPT Benchmark 8 (L50).................................................................................................................. 62PLANOPT Benchmark 9 (L75).................................................................................................................. 62PLANOPT Benchmark 10 ( L100) ............................................................................................................ 62PLANOPT Benchmark 11 (L125A)........................................................................................................... 62PLANOPT Benchmark 12 (L125B)........................................................................................................... 63

SUMMARY ...................................................................................................................................................................64

Q & A ..................................................................................................................................................................................... 65

Q 1.................................................................................................................................................................................65Q 2.................................................................................................................................................................................66Q 3.................................................................................................................................................................................66Q 4.................................................................................................................................................................................68Q 5.................................................................................................................................................................................68Q 6.................................................................................................................................................................................69Q 7.................................................................................................................................................................................70Q 8.................................................................................................................................................................................70



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COPYRIGHT Copyright, 1996-2006, by Engineering Optimization Software. Worldwide rights of ownership and distribution of the computer programs PLANOPT,VIP-PLANOPT and VIP-PLANOPT 2006 rest with Engineering Optimization Software, 1386 Pritchett Industrial Drive, Austell, GA 30168, USA. Computer programs PLANOPT,VIP-PLANOPT and VIP-PLANOPT 2006 and all the associated documentation are proprietary products. Unlicensed use of the program or reproduction of the documentation in any form or by any means, without prior written permission from Engineering Optimization Software is explicitly prohibited. Note: All trademarks used in the manual are the property of their respective corporations.



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DISCLAIMER Considerable expenses, time and effort have gone into the development of PLANOPT and VIP-PLANOPT computer programs. In using the program, however, the user accepts and understands that no warranty is expressed or implied by the developers or the distributors on the accuracy or the reliability of the program. The authors and the distributors hereby disclaim any liability to any party for any loss or damage resulting from the installation or use of VIP-PLANOPT 2006. Engineering Optimization Software makes no representations or warranties with respect to the content hereof and specifically disclaim any implied warranties of merchantability or fitness for any particular purpose. The user must independently verify the results obtained by this program. Engineering Optimization Software also reserves the right to revise this publication and make changes from time to time in the content hereof without any obligation of Engineering Optimization Software to notify any person or organization of such revision or change.



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INTRODUCTION PLANOPT (floor-PLAN layout OPTimization) represents a general purpose layout optimization algorithm. VIP-PLANOPT (Visually Interfaced Package of PLANOPT) is a powerful software package developed to produce high-quality optimal layouts for small, medium and large-sized problems involving UNEQUAL-AREA rectangular blocks or modules. The term Layout Optimization implies the placement of a given number of such modules at their optimal locations in the Euclidean plane without any overlaps. It is a challenging area of research in various fields of engineering. In the field of industrial engineering the problem is usually referred to as Facility Layout problem. Several other terms like Plant Layout, Machine Layout, Floor-plan Layout, etc. refer basically to the same optimization problem.

Motivation Facility layout has profound effects on the organizational productivity and profitability. It is estimated that about 20-50% of operating costs in manufacturing relates to materials handling, a factor highly correlated to the quality of the facility layout design. Superior facility layouts reduce materials handling costs, help streamline all operations, and reduce energy bills. It is estimated that US businesses spend about a trillion dollars on new facilities, more than a quarter of it in re-designing the existing ones. Consequently, layout design remains an important issue for industrial facility planners with significant potential for research and automation.

Filling the Gap With the majority of the available software packages merely being CAD-based documentation or drawing tools, PLANOPT fills the gap with its robust hybrid proprietary optimization algorithm. The advent of this pioneering package, a decade ago, accompanied with a candid and uncontested claim: No other layout optimization software



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produces better-cost optimal layouts for any known set of benchmark problems. Since its first release, PLANOPT has a record of UNBEATEN PERFORMANCE with a money back guarantee. Now, advancing on its superiority for more expansive applications in industrial environment, PLANOPT has emerged as an excellent and affordable Teaching & Research aid with its enhanced version (VIP-PLANOPT). With the release of VIP-PLANOPT 2006, its guaranteed superiority on other algorithms for low-cost layouts has been reinforced. Now, it yields even better layouts for most problems. An improved optimization algorithm with double precision arithmetic has made the software more stable and almost crash-proof. Moreover the dependence of layout on a starting seed has been reduced. A host of new capabilities, introduced in this major update release of VIP-PLANOPT, increase its productivity for Industrial applications.

Unmatched Functionality VIP-PLANOPT has the capability of optimizing the layouts considering the user-specified pick-up and drop-off points. It also allows the user to specify any number of modules to be anchored at fixed locations. VIP-PLANOPT produces optimal layouts keeping these anchored modules strictly at the user-specified locations. The user can also specify the shape and the size of the boundary that must enclose the modules. This makes the program especially useful for consultants and layout designers interested in optimizing the layout designs for their projects. Some of its functionality is based on new concepts like Module Padding, Forbidden Area Module, No-flow Modules, etc which will be explained in this manual. Optimization Algorithm PLANOPT optimization algorithm is a research product. It is a robust hybrid proprietary optimization algorithm. It came into existence in 1995 when two University Professors working together in the areas of VLSI Layout design and Multi-disciplinary Facility Layout



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optimization developed a marvelous technique that could solve the Unequal Area QAP better than all published algorithms. They realized that the results were amazing. No researcher in the field could imagine (at that time) that it is at all possible to solve such a hard optimization problem better than all GAs, SA's and the conventional analytical or heuristic techniques. They decided not to publish the algorithm but to present the algorithm anonymously in the form of a software package as a challenge to other researchers. This is how PLANOPT software package came into existence. Since then, PLANOPT optimization algorithm has been a challenge to the researchers in the field. It becomes obvious from the review of published literature that researchers mostly shied away from comparing their techniques with PLANOPT using randomly generated benchmarks. I fact, published optimization algorithms don't even come close to PLANOPT algorithm. The optimization algorithm of VIP-PLANOPT 2006 program is now improved and advanced. It is based on a hybrid smart growth technique. It generates high quality solutions for large scale problems with minimal computational cost. This is due to the algorithm's embedded optimization philosophy of natural constructive growth while identifying, for each module, the feasible design space with the highest probability of local optima. The design space is then mapped onto a straight line. A pseudo-exhaustive search is then carried out for the optimum solution at each stage of a multi-stage optimization process. VIP-PLANOPT 2006 has specifically introduced the following improvements to the algorithm to reinforce its superiority over all known algorithms: 1) Double precision arithmetic has been introduced to control the instability of the algorithm that was observed in certain cases. 2) New techniques have been introduced to reduce the dependence on the user-specified starting seed that is used to generate random numbers for starting the optimization process. 3) Penalty functions have been introduced for obtaining optimal layouts within user-specified boundary of simple rectangular shape or complex composite shapes.



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TERMINOLOGY Since the terminology used for layout optimization differs in various applications, an effort has been made to adopt a generalized terminology that could be applicable to most layout optimization problems. It is briefly described in the following.

Module PLANOPT uses the term Module for the rectangular building block representing a functional unit like departments, machines, rooms, cells or spaces. Fig.1 shows a module and the notations used. The dimension of a module along x-axis is referred to as Length and is denoted by Li. Its dimension along y-axis is referred to as Width and is denoted by Wi. The subscript i refers to module identification number (module ID).

Fig. 1: Representation of a module



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Module Aspect Ratio The aspect ratio of a module is defined as the ratio of the dimension of the module along y-axis to its dimension along the x-axis. For a module i the aspect ratio Ri is given by:

Ri = Wi / Li (1)

Module Area For a module i its area Ai is given by:

Ai = Wi * Li (2)

Module Type PLANOPT has two basic types of modules. The user may specify a module type as Hard Soft.

Hard (Rigid) Module A module with fixed dimensions is called hard or rigid module. The user specifies the length and width of such modules. The dimensions of such modules are not modified during optimization.

Soft (Flexible) Module A module with variable aspect ratio but of constant area is called soft or flexible module. The user has to specify the area of a soft module with the upper and bounds on its aspect ratio. The user may also specify a set of permissible values of aspect ratios. The aspect ratios of all such modules are varied during optimization.

Module Position The position or location of a module, specified by the coordinates of their centroid, may be variable or fixed. A module with variable position must be specified by the user as Movable. Optimal location of such modules will be determined by PLANOPT. If the module position is fixed so it does not move, it must be specified by the user as Anchored. Anchored modules are strictly kept at their user-specified positions in the optimal layout.



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Module Placement Placement of module means locating it by specifying its centroid. Anchored modules are placed by the user. Movable modules are placed by PLANOPT to minimize the cost in an optimal layout.

Anchored Module A module whose position (location) is fixed and is not allowed to change during optimization is called an anchored module. PLANOPT produces optimal layouts with anchored modules located strictly at the user-specified position.

Forbidden Area Module (FAM) PLANOPT has introduced a new concept of Forbidden Area Module or FAM. It is used to model obstructions or areas that are not functional units of a facility. An example is a lake or hill inside the boundary of a facility that does not contribute to any processing. Only an anchored modules may be tagged as FAM. Any flow specified by the user for a FAM is ignored during optimization or any cost calculations.

Module Orientation The orientation of module may be fixed or may be allowed to vary so it may flip by rotating 90 degrees during optimization. PLANOPT finds the optimal orientation of all May flip orientation modules to minimize the cost.

Module Padding Many applications of layout optimization require the modules to be separated from each other with empty space around them for reasons related to environment, safety, logistics etc. PLANOPT has introduced this concept and allows the user to specify padding of empty space around any number of modules. Module padding implies additional constraints for optimization. Optimal layouts are always produced with empty spaces around the modules exactly as specified by the user. The padding may be same or different on all four sides. Only hard modules that have fixed dimensions may be padded.



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Pick-up & Drop-off Points PLANOPT allows the user to specify pick-up and drop-off points anywhere inside or on the boundary of the modules. Relative coordinates with respect to the lower left corner of the module are used to specify the pick-up and drop-off points. For example, if the pick-up and drop-off points for a module have to be as shown in Fig. 2, the user will specify the pick-up point coordinates as xP = 3, yP = 1 or (3,1) measured from the lower left corner of the module. Similarly the coordinates of the drop-off point will be specified as xD = 0 , yD = 2 or (0,2).

Fig. 2: Specifying the coordinates of pick-up & drop-off points

Boundary Shape Restricting the layout to be within a boundary of given shape is required in some applications. PLANOPT allows the user to impose this constraint. The user may specify any boundary shape. The only restriction is that the boundary shape is made of orthogonal line segments. All the user has to do is to point-and-click to specify the line segments. Optimizing inside a given boundary shape, however, is one of the most difficult issues in layout optimization and makes the hard problem even harder. It the toughest constraint to be imposed and results in degrading the quality of optimal layouts. The user must understand



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that trying to get an optimal layout in a tight space with little room for alternative placement of modules will mostly fail or will turn into a bin-packing problem rather than layout optimization. Therefore it is advised that this option be used only when really needed and the boundary area be specified as big as possible.

Enclosure The bounding rectangle enclosing all the modules in the optimized layout is termed as enclosure. Its dimensions along x and y axes are denoted by LB and WB respectively. Its aspect ratio, given by WB / LB, is denoted by RB and its area, given by WB * LB, is denoted by AB.

Fig. 3: Bounding rectangle enclosing the modules in a layout

Flow Matrix The flow matrix gives the flow of material, equipment or personnel between all pairs of modules. An element of this matrix, denoted by fij, is the flow between any two modules i and j. It is expressed in number of unit loads moved per unit time between the two modules. A unit load is defined as the unit to be moved or handled at one time. In some cases, the unit load is one item of production; in other situations the unit load is several cartons, each containing numerous items of



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production. The unit load includes the container, carrier, or support that will be used to move materials. PLANOPT allows the flow matrix to be either symmetric or non-symmetric. In some applications, this matrix is also referred to as the connectivity matrix.

Unit Cost Matrix The matrix representing the cost of transporting a unit load (as defined above) per unit distance between all pairs of modules is called unit cost matrix. An element of this matrix, denoted by uij, is defined as the cost of transporting a unit load of material per unit distance from module i to module j. In some applications, this matrix is referred to as the wire-weight matrix. Its individual elements are then referred to as wire-weights or simply weights.

Cost Matrix An element of this matrix, denoted by a ij, represents the total cost of flow per unit distance between any two modules i and j. In other words a ij = fij * uij. PLANOPT allows the cost matrix to be either symmetric or non-symmetric. PLANOPT gives the user the option of specifying either directly the values of a ij or instead the values of fij and uij separately. In effect, the cost matrix implies the same as the activity relationship matrix based on the closeness ratings as given in the activity relationship charts.



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DISTANCE NORMS

PLANOPT has the option of the following three norms for the distance dij between the centroids of any two modules i and j:

Rectilinear Norm It is also called Manhattan distance norm. The distance dij between two points using this norm is the sum of rectilinear distances along x and y axes.

dij = | | | |xi x j yi y j- + - (3)

Euclidean Norm The distance dij between two points, using this norm, is the shortest distance made by a straight line drawn between the two points.

dij = (( ) ( ) ) /xi x j yi y j- -+2 2 1 2 (4)

Squared Euclidean Norm The distance dij between two points, using this norm, is the square of the Euclidean norm distance.

dij = ( ) ( )xi x j yi y j- -+2 2 (5)



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COST FUNCTIONS

Layout optimization requires minimization of an objective function usually referred to as cost or cost function. Its definition may vary from one application to another. Since PLANOPT is a general purpose layout optimization program, a cost function definition has been adopted that suits most of the applications. Options for symmetric as well as non-symmetric flow matrices and composite cost functions have been provided. The cost function definition for a problem of n modules has four different forms as given below.

Cost Function F1 The cost function F1 has the following form:

F1 = fij uij dijj in

i

n

= +=

-

11

1 (6-a)

or,

F1 = aij dijj in

i

n

= +=

-

11

1 (6-b)

The function F1 is applicable only when the cost (relationship) matrix is symmetric.

Cost Function F2 The cost function F2 has the following form:

F2 = fij uij dijjn

i

n

==

11 (7-a)

or,

F2 = aij dijjn

i

n

==

11 (7-b)



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The function F2 may be used for both cases: symmetric as well as non-symmetric cost (relationship) matrix. Non-symmetric cost matrix is common in facilities/plant layout design. Note: For symmetric cost matrix : F2 = 2F1.

Cost Function F3 The composite cost function F3 has the following form:

F3 = fij uij dij Aj i

n

i

n

B= +=

- +

11

1w (8-a)

or,

F3 = a wij dij Aj i

n

i

n

B= +=

- +

11

1 (8-b)

where AB denotes the area of the bounding rectangle and w is the user-specified weight on this area. Note: The function F3 can be used only for symmetric cost (relationship) matrix. For non-symmetric cost (relationship) matrix use the function F4 as defined below.

Cost Function F4 The composite cost function F4 has the following form:

F4 = fij uij dij Aj

n

i

n

B== +

11w (9-a)

or,

F4 = a wij dij Aj

n

i

n

B== +

11 (9-b)



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PRIMARY INPUT

VIP-PLANOPT has a powerful visual interface with tips to help the user. Most users learn to use the program without any manual as they try VIP-PLANOPT on simple problems. Despite the efforts to make VIP-PLANOPT a self-learning tool supported by this manual, users may have questions while modeling a real-world problem. Technical support is available to all users of VIP-PLANOPT. They are encouraged to ask for assistance whenever they have any such questions. This chapter describes the primary input required to model a problem using the main input window of VIP-PLANOPT. The main input window of VIP-PLANOPT appears is shown below in Fig. 4.

Fig. 4: Main Input Window of VIP-PLANOPT



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Menu Bar

File Menu The items on this menu are New, Open, Save, Save As, Export and Exit. Export, when clicked, opens a window called Data Export Window and lets the user select data for export. The user may export the module dimensions and the matrices in CSV format for text editing or spread sheets. This menu item also lets the user export the optimal layout to AutoCAD. Export window is shown in Fig. 5 below:

Fig. 5: Data Export Window of VIP-PLANOPT



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Constraints Menu The items on this menu are namely Module Padding, Boundary Constraints and Optimization Constraints. The same has been duplicated by the command buttons in the Optimization Constraints frame on the right. The windows that open when these items are clicked, are described in the next chapter.

Optimization Menu This menu has three items related to optimization. This menu duplicates the functionality of the controls available on the right side of the main input window. The menu item Set Optimization Parameters opens a window that lets the user set optimization parameters like Distance Norm, Optimization Seed and the type of Cost Function. The next menu item is Optimize. Clicking it will start the optimization process. The third menu item on this menu is Analyze Optimize Layout. It opens a window that displays the optimal layout and lets the user to modify the layout for comparing the cost with the optimized layout. The windows that open when these items are clicked, are described in the next chapter.

Benchmarks menu Clicking a menu item on this menu opens the project file for the particular benchmark problem. Data will be displayed. Optimization results may be viewed by clicking the Analyze Optimized Layout button in the bottom right corner of the screen.



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Help menu The first item on this menu About VI-PLANOPT. It displays the copyright information and a disclaimer. The next item is License Information. When clicked, it shows you licensees name, license type, license ID, date of issue and date of expiry. The third item on this menu is Authorize that lets you search for the license on your system and installs it so that optimization is enabled for all problems. The Authorize window is shown below in Fig. 6.

Fig. 6: License Authorization Window of VIP-PLANOPT



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Display Control The Display Control frame on the top left corner of the screen has the controls to display any of the modules for editing. This frame is shown in Fig. 7. Its components are described in the following:

Fig. 7: Display Control frame

Current Module ID This control displays ID of the current module i.e. the module on display. Any modifications to the properties and data apply to the current module. Clicking the down arrow displays a drop-down list of all modules. User may select any module from the list.

Next This command-button displays the next module from the list of modules.

Previous This command-button displays the previous module from the list of modules.

Zoom All This command-button refreshes the graphic display. It is needed when the user resizes the module by dragging the mouse in the graphic area.



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Grid/Snap Size Enter a value in the text box for the grid size of the graphic display area. The snap size will be set the same as the grid size. The value entered here determines the accuracy of the graphical input while dragging the mouse to resize the module. This does not affect the optimization accuracy. Optimization always takes place in continuous design space.



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New Module The New Module frame on the top right corner of the screen has the controls to create a new module and specify its properties. It is shown in Fig. 8.

Fig. 8: New module creation control frame

At the beginning of new project, a module will be automatically created with default size and properties. Only some of the properties of the module have to be modified to make it as required by the user. This is due to the philosophy of input used in PLANOPT which is: Never leave the user with an empty screen. PLANOPT always creates a module and leaves only the modifications to the user.

When Module 1 is created, Create Module 2 title for the frame will appear indicating that the Module2 has not been created and will be created when Create button is clicked. The user may choose to create a module of default size or the of the same size as any one of the existing modules. The default size is set when a new project is started by clicking New from the File menu.. However the user may modify the defaults any time by clicking the Reset button in this frame.



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Module Type The New Module frame on the top right corner of the screen has the controls to create a new module and specify its properties. It is shown in Fig. 9.

Fig. 9: Module Type frame

By default, each new module is created as a hard module. When a module type is Hard, the data entry panel to the right of the module display appears as shown in Fig. 10 and when the user chooses Soft, the display panel appears as shown in Fig. 17 later in this chapter.



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Resizing Graphically A hard module on display can be resized graphically. There are two ways as follows:

1) Move the mouse pointer to locate the upper right corner in the graphics area and then click.

2) Move the mouse pointer to a boundary line of the module. Sizing icon with up and down arrows or right and left arrows will appear. Click and drag to make it to the required size.

Set a proper grid size to suit your problem. Mouse pointer will snap to the grid points. You may set any value for the grid size. Decimal fractions are allowed for example you may set a grid size of 0.5

Fig. 10: Graphic display for resizing of modules



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Resizing Numerically While most users will do the resizing using the graphic input as described above, data entry boxes have been provided for entering the data numerically using the key board. The Dimensions frame next to the graphic display has the data entry boxes showing the length and width of the current module. This frame is shown in Fig. 11.

Fig. 11: Numerical data entry frame for module resizing The user may type in the values in the data entry boxes to resize the module. The Import button in this frame when clicked will lets you open a text file for importing the dimensions of hard modules.



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Module Orientation The user may choose module orientation for optimization purpose from the options in the Orientation frame as shown in Fig. 12. As described earlier a hard module may be either of Fixed orientation or of variable orientation allowing to flip or rotate by 90 degrees. For all modules in a problem that are allowed to flip May flip must be chosen.

Fig. 12: Module Orientation frame



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Module Position A modules position may be specified as Movable or Anchored. The Position frame shown in Fig. 13 has the options for the user to choose between the two. In the optimal layout generated by VIP-PLANOPT, the anchored modules will remain strictly at their user-specified location whereas the movable modules will be placed at optimal locations to minimize the cost.

Fig. 13: Module Position frame



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Module Deletion To delete any module it must be selected and displayed as the current module. Select the module either from the Display Control frame or from the data grid display. The title of the Delete Module frame, as shown in Fig. 14, will indicate the ID of the current module. Click the Delete button to delete the module. Whenever a module is deleted, an automatic re-numbering takes place.

Fig. 14: Module deletion frame



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Other Properties Fig 15 shows the frame titled Other Properties. This frame provides two command buttons to the user. One for the placement of the fixed module and the other for specifying the PD points (Pick-up an drop-off points). Each of these command buttons opens a new window. The user-specified Placement is only possible for hard moles that are anchored. PD points are applicable to all hard modules. For soft modules, the module centroid is assumed to be the pick-up as well as the drop-off point.

Fig. 15: Other Properties frame



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Cost and Flow Matrices Input VIP-PLANOPT gives the user two ways to input the Flow and Cost matrices. Flow and Cost matrices may be input element by element on this main input window using the controls in the frame shown in Fig 16. Alternatively the user may click Show All button. A window for complete matrix input will appear with option to import from a pre-edited text file. In the context of flow and cost matrices, the current module (the module on display) will be called the Source module. Initially the Destination module ID will be set to be the same as the Source module. In this situation, the user may not enter any values for flow and the Flow and Cost both are set to zero.

Fig. 16: Element by element cost and flow input To input the relevant element of Flow, Unit Cost or Cost matrix, a Destination module other than the Source module must be selected as shown in Fig.16. Whenever the user clicks the text boxes, the values are automatically incremented by 1. To input any other value, the user must select the text in a data box and then type in any desired number. When a value is entered in any of the three data entry boxes, the other two are automatically updated so that the product of flow and unit cost is equal to the cost. Normally, the matrices are assumed to be symmetric. To work with non-symmetric matrices, click Show All button. A window for complete matrix input will appear. Set the matrix type on this window to Non-symmetric. Input may be then be continued in the Matrix Input window or the main input window.



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Soft Module Input If the user modifies the type of a module to Soft, the frames for Dimensions, Orientation and Position pertaining to the hard module disappear. Instead Soft Module Data and Aspect Ratio Set frames appear as shown in Fig. 17.

Fig. 17: Soft module properties input

The required data for Soft module consists of its area and the bounds on the aspect ratio i.e. the minimum and maximum aspect ratios. PLANOPT will determine the best aspect ratio for the module within the upper and lower bounds specified by the user. The user may choose Continuous or Discrete aspect ratio option. The Discrete Set ID and Generate controls become activated only when the user selects Discrete option. Enter a value for the set ID by using the up-down arrow. Clicking the Generate button displays the window for discrete aspect ratio input.



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Optimization Parameters There are three optimization parameters namely the Cost Function, Optimization Seed and Distance Norm that the user can modify as shown in Fig. 18.

Fig. 18: Optimization parameters input

Cost Function The user may choose between a Simple and Composite cost function. A simple cost function does not include the area of the enclosure. It is only a function of cost of flow and the inter-module distances. A composite function has an additional term for the enclosure area with a user-specified weight on the area. When the user chooses a composite cost function, the Weight on area data entry box is enabled for the user to enter the required weight.

Optimization Seed VIP-PLANOPT has an optimization algorithm requiring a seed to start the optimization process. Unlike other algorithms, the



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dependence of the optimal layout on the seed has been minimized. For this reason, there are only 2N seeds where N is the number of modules. All other seeds will produce the same result so they are included in the list of user-specified seeds. When the user choose the User-specified seed option, the down arrow when clicked will display all the available seeds for the particular problem. In addition, VIP-PLANOPT finds the best value of seed based on a predefined criterion which is part of the proprietary algorithm. However, it is not necessary that the default value of the seed produces the best layout. The user may experiment with both: the default seed value found by VIP-PLANOPT for a particular problem or any other value of seed between 1 and 2N.

Distance Norm The Distance Norm control frame gives the user the option to choose any of the three distance norms. These have been described in chapter 4.



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Optimization Constraints There are three types of optimization constraints that can be applied. These constraints can be specified using the command buttons available in Optimization Constraints frame as shown in Fig. 19.

Fig. 19: Optimization constraints input

Module Padding Module Padding imposes empty area around a module so two modules may not come closer than a specified distance. This control when clicked opens a window. The user may apply the padding to any module simply by click an drag operations of the mouse pointer..

Boundary Shape Boundary Shape constraint forces the optimal layout to remain within a user-specified boundary. This control when clicked opens a window where the user can click to specify the points that make the enclosing boundary.

Other Constraints Other Constraints control when clicked opens a window for input of two other constraints: 1) constraint on the maximum distance between any two modules and 2) constraint on the enclosure aspect ratio.



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Optimization Control The Optimization Control frame has two command buttons has shown in Fig. 20. They are described as follows:

Fig. 20: Optimization Control frame

Optimize Optimize control, when clicked, starts optimization. The data file must have been saved before starting optimization. Also, all modules must have flow assigned to them. No user interaction is required during the optimization and in this sense the optimization is fully automated. A plot of the optimized layout with important data will be displayed as soon as the optimization process comes to an end.

Analyze Optimized Layout Analyze Optimal Layout control, when clicked, displays the optimal layout in a separate window and lets the user move around any module by dragging the mouse pointer to see how the cost varies when a module is moved from its optimal location.



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OTHER INPUT The Main Input Window of VIP-PLANOPT is supported by 10 other input windows. The basic and primary input with no special properties or constraints may be completed on the Main Input window. Whenever the user wants to associate special properties to the modules like anchoring, pick-up and drop-off points, discrete aspect ratio sets, module padding, boundary shape and other constraints, the input will be done through of one of these windows. These input windows are described in this chapter. A list of these input windows is given below:

Table 1: List of supporting windows of VIP-PLANOPT

S/N Window Name Functionality

1 Module Defaults Window Set default dimensions for automatic creation of Hard and Soft modules.

2 Discrete Aspect Ratios Window Input aspect ratios for discrete aspect ratio set for Soft modules.

3 Matrix Input Window Input or import the Flow, Unit Cost and Cost cost matrices.

4 Anchored Modules Placement Window Specify location of Anchored modules and tag as Forbidden Area.

5 Pick-up and Drop-off Points Window Specify pick-up and drop-off points for Hard modules.

6 Module Padding Constraint Window Impose constraints of empty spaces around Hard modules.

7 Boundary Shape Constraint Window Specify a boundary shape to enclose the optimal layout.

8 Optimization Constraints Window Specify Enclosure Aspect Ratio and bounds on inter-module distances.

9 Optimal Layout Analysis Window Display optimal layout and evaluate the optimality by moving around modules.



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10 Data Export Window Export modules and matrices to text files and optimal layout to AutoCAD.



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Module Defaults Window

Fig. 21: Module Defaults Window

How to Open Click Reset button in Create Module frame of the Main Input Window.

Notes 1) For hard modules, set the default length and width that you will need most frequently. 2) If you have Soft modules in your problem, set the default area, the minimum aspect ratio and the maximum aspect ratio that you will need to input most frequently. 3) This window also opens when a new project is started by clicking New on the File menu.



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Discrete Aspect Ratios Window

Fig. 22: Discrete Aspect Ratio Window

How to Open Select module Type to Soft. Aspect Ratio Set frame will be visible. In this frame select Discrete option. Click Generate button.

Notes 1) Select Automatic Generation if you have values at regular

intervals. Enter the Minimum Value, Maximum Value and Increment in the data entry boxes. Click Generate button. The numbers as shown in column 1 of the table in Fig 22 will be generated.

2) Select Manual Input if an aspect ratio set has values that have no regular increment. Type in the values in the column for the particular set. See column 2 of the table in Fig. 22.



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Matrix Input Window

Fig. 23: Matrix Input Window

How to Open Click Show All button. This button is located in the Flow from source to destination frame of the Main Input window. It is used for entry of elements of the cost and flow matrices.

Notes 1) The grid that displays the matrix has data entry boxes (called

cells) for each element. 2) By default Auto Cell Increment option is on as shown in the

frame under the matrix display. Set an increment value to suit your data. With this option, the cell value is incremented each time the user clicks (left-click) inside a cell. Right-click causes



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the cell value to decrement and the new value becomes cell value the increment set by the user.

3) If the data entry involves numbers that cannot be generated easily by incrementing, turn the option off. With this option turned off, click inside a cell to select the cell. Cursor will appear inside the cell. Select the existing value inside the cell by dragging the mouse pointer over it and then type in any desired value.

4) Choose matrix type and symmetry or non-symmetry before starting the input.

5) All elements of the unit cost matrix are pre-set to 1 and all elements of flow and cost matrices are pre-set to 0. If you have entered any values for cost or flow on the main input window, the non-zero values will be shown here.

6) Any change made to Flow matrix automatically updates the Cost matrix and similarly the Flow matrix is updated automatically when the Cost matrix is modified. Any modification to Unit-cost matrix automatically update the Cost matrix. All the updating is based on : a ij = fij * uij

7) The user may choose to import the matrices in various

different forms from a text data file. Input data file must be a text file and must have an extension VPM. The following options are available:

a) Full Matrix Option: Using this option the user may import complete matrix from an existing data file. Data input is row by row. The diagonal element (which is always zero) is required. The numbers in the input file may be separated by commas or by blank spaces. A row of matrix may be split in more than one line. b) Upper Triangle Option: Using this option the user may import the upper triangle of the matrix from an existing data file. This option is used only for symmetric matrices. Data input is row by row without the diagonal element. Last row of the upper triangle containing only one zero element must not be included.



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The numbers in the input file may be separated by commas or by blank spaces c) Lower Triangle Option: Using this option the user may import the lower triangle of the matrix from an existing data file. This option is used only for symmetric matrices. First row of the lower triangle containing only one zero element must not be included. Data is input row by row starting from the element in the first column. The numbers may be separated by commas or by blank spaces d) Element by Element Option: Using this option the user may import the non-zero elements of the matrix in any order from an existing data file. Each data element must be on a separate line. The data required for each element are: Row Number, Column Number, and Value (of the element of the matrix).



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Anchored Modules Placement Window

Fig. 24: Anchored Modules Placement Window

How to Open Click Placement button in Other Properties frame of the Main Input Window. This window can open only when at least one of the modules is anchored.

Notes 1) On the top right corner of this window, a list is displayed.

This list shows all the modules that have been marked as Anchored in the main input window. The status of the module whether it is placed or unplaced is also indicated.

2) To place an unplaced module, select it from the list shown on the top right and then click at the desired location.

3) Once a module is placed, it can be moved. Left click inside a module and drag to any desired location.



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4) To modify the dimensions of a placed module, right-click inside and drag.

5) In the bottom of the list there is a check box. When this check box is checked he selected module is tagged as Forbidden Area Module (FAM). All flow from a FAM is suppressed and is considered just an obstruction in the layout. It does not contribute directly to the cost but occupies a fixed position in the layout blocking other modules to occupy the area.

6) The user may choose to modify the dimensions and place the modules by entering data using the keyboard. Enter the data in the data entry boxes and then click Modify button to modify the dimensions or enter the data in the placement data entry boxes and then click Place button.

7) There is a button labeled Undo previous operation. This button, when clicked cancels the previous operation of placing or modifying the dimensions.

8) On the top left, this window has a display controls frame with buttons to zoom in, zoom out and zoom all. The Zoom all button (with a plus sign) when clicked, zooms in around the selected module after bringing it in the center of the display. The Zoom out button (with a minus sign) zooms out such that the selected module is in the center of the display. The Zoom all button (blank) shows the placed modules with wide area around to let the user place other modules.

9) The user may specify any grid size. When a placed module is dragged and placed with Snap to grid checked, its lower left corner will snap to a grid point.



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Pick-up & Drop-off Points Window

Fig. 25: Pick-up & Drop-off Points Window

How to Open Click PD Points button in Other Properties frame of the Main Input Window.

Notes 1) The pick-up point symbol is green color triangle pointing

upward and the drop-off symbol is red color triangle pointing downward.

2) Pick-up and drop-off points for a module may be selected from the data entry panel (on the left).

3) Pick-up and drop-off points may also be input graphically using the mouse pointer.

4) Move the mouse pointer to green or red triangle. Click inside the triangle and then drag it to any desired location.



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5) Set a proper snap size. The pick-up and drop-off points always snap to the nearest grid point.



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Module Padding Window

Fig. 26: Module Padding Window

How to Open Click Module Padding button in Optimization Constraints frame of the Main Input Window. Alternatively, click Constraints on the menu bar then select Module Padding from the drop down menu.

Notes 1. Padding of empty space can be applied only to hard

modules.

2. Padding size may be different on all 4 sides of a module.

3. To apply padding, select it from the drop-down list in the Display Control frame on the right. The selected module will be displayed. Move the mouse pointer towards an



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outside boundary of the module until the mouse pointer changes to a sizing icon. Click and drag to pad the module.

4. Alternatively, enter the values for padding for one or more sides in the data entry panel and then click the button labeled Pad this module.

5. Click the button Pad all modules if the same padding has to be applied to all modules.

6. Set a grid size to suit the problem. During graphic click and drag input, the padding snaps to the nearest grid point.



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Boundary Shape Window

Fig. 27: Boundary Shape Window

How to Open Click Boundary Shape button in Optimization Constraints frame of the Main Input window. Alternatively, click Constraints on the menu bar then select Boundary Shape from the drop down menu.

Notes 1) The first thing to do on this window is to select type of shape

from Shape Type frame on the right. There are two options: Composite Shape and Simple Rectangle.

2) When Simple Rectangle is selected, the data entry cells labeled Rectangle Width and Rectangle Length are enabled with default values of (100, 100). Enter the required



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values and the rectangle will be shown drawn in the graphics area.

3) When Composite Shape is selected, the data entry cells are disabled. Click at the desired points in the graphics area to create the required shape. Points snap to the grid so the grid spacing must be set to a proper value to suit the problem. As the points are drawn, orthogonal lines join each point to the previous point. Once all the required points to define the boundary are drawn, click Close Boundary button. The shape will be automatically closed by joining the last point created to the first point.

4) Only non-intersecting orthogonal line segments may be used to define a boundary.

5) Click Delete previous point button to undo the previous point. If the boundary was closed the deletion of the point erases two previous line segments.

6) Total area of all the modules and the area of the enclosure are displayed on the top right corner of the window when the boundary is closed by the user.

7) If there are Anchored modules that have already been placed by the user, the anchored modules are shown highlighted on the screen to help user create a boundary that keeps the Anchored modules inside it.



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Optimization Constraints Window

Fig. 28: Optimization Constraints Window

How to Open Click Other Constraints button in Optimization Constraints frame of the Main Input window. Alternatively, click Constraints on the menu bar then select Optimization Constraints from the drop down menu.



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Notes 1) This window is used to impose two different constraints. First

one is the Enclosure Aspect Ratio and the second is the Upper Bounds on distance between any pair of modules.

2) When Enclosure Aspect Ratio is selected the data entry cell is enabled. Type in the desired value. Like all other constraints, VIP-PLANOPT attempts to satisfy the constraints while minimizing the cost.

3) Upper bounds on distances may be imposed on any pair of modules. Select Module I from the list of modules that appears when the down arrow is clicked. Select Module J in a similar way. Enter the desired value of the upper bound on the distance between the two modules in the data entry cell under the label Upper Bound. Click Add to List button.

4) The upper bounds may be modified for any of the constraints added to the list. To modify a given constraint, select it from the list. It will appear in blue color and the data will be copied to the data entry cells above. Modify the values as required and then click Modify button. The constraint will be updated.

5) To delete a constraint select it from the list then click the Delete button.



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Optimal Layout Analysis Window

Fig. 29: Optimal Layout Analysis Window

How to Open There are three ways to open this window:

a) Click Analyze Optimized Layout button in Optimization Control frame at the bottom right corner of the Main Input window.

b) Click Optimization on the menu bar then select Analyze Optimized Layout from the drop down menu.

c) Click anywhere on the graphic display of the optimal layout on the Main Input window. This display appears only after the user clicks Optimize button and optimization finishes successfully.

Notes 1) This window can only open when the optimized layout file

exists from a previous optimization of the same problem. If



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the problem has not been optimized or if the plot data file has been deleted or modified then this window will not open.

2) The main purpose of this window is to analyze the optimal layout and compare it with user-modified layouts or other imported layouts.

3) The user may move any module by clicking inside it and then by dragging the mouse pointer to any desired location. This operation results in a modified layout with a modified value of the cost and other parameters. The user may compare the two and evaluate the optimality of the layout generated by VIP-PLANOPT. Any anchored modules may not be moved.

4) Restore button (in the lower right region of the window), when clicked will restore the optimal layout after any modifications by the user.

5) The data for the layout is displayed on the right side. They are organized in three frames. First frame labeled Optimization Parameters has values of the users input parameters for optimization. The second frame labeled Enclosing rectangle has values of area, aspect ratio, length and width of the layout on display. The third frame has the label has the label Cost of Layout. It contains the cost of the optimized layout and the cost of the modified layout currently on display.

6) Any user-modified layout must be free from any overlaps between modules. If the user moves a module and relocates it at a position that causes overlap then the cost cannot be calculated for the modified layout and the cost value under User modified layout label is displayed as Invalid.

7) Once an overlap has been created by the user, it is not possible to move any other module unless the overlapping modules are moved so that there are no over laps. The user may click Restore button any time to undo the changes and display the optimal layout.

8) When the Snap Centroid is checked on the centroid of any module when dragged snap to the nearest grid point.

9) Since it is difficult and time consuming to move around a large number of modules to obtain a desired layout, an option



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to import a layout for the problem is available on this window. The user must have a text file in CSV format (Comma Separated Values) created for this purpose. When the Import Layout button in the bottom right corner of the window is clicked a small window will appear that will have the options of import as show in the figure below.

Fig. 30: Layout import options



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BENCHMARKPROBLEMS

Benchmark problems with the number of modules ranging from small to large and cost matrices of varying sparseness and randomness are required for a realistic evaluation of a layout optimization program. Such a set of completely documented benchmark problems involving unequal-area modules does not exist in the published literature. For this reason a set of 12 benchmark problems, used for evaluating the performance of the PLANOPT program, has been integrated with the software package. These problems may be used for comparison with other layout optimization programs.

Data Files

S/N Benchmark No. of Modules

Input File

Output File

1 L3 3 L003.VIP L003.OUT 2 L4B 5 L004B.VIP L004B.OUT 3 L8 8 L008.VIP L008.OUT 4 L8FX 8 L008FX.VIP L008FX.OUT 5 L12PD 12 L012PD.VIP L012PD.OUT 6 L20 20 L020.VIP L020.OUT 7 L28 28 L028.VIP L028.OUT 8 L50 50 L050.VIP L050.OUT 9 L75 75 L075.VIP L075.OUT 10 L100 100 L100.VIP L100.OUT

11 L125A 125 L125A.VIP L125A.OUT

12 L125B 125 L125B.VIP L125B.OUT



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Characteristics The characteristics of the benchmark problems are briefly described in the following:

PLANOPT Benchmark 1 (L3) This problem of only three modules has been selected as a benchmark problem because its global optimum solution is known. It also serves as a good test problem for the accuracy of the program. The cost matrix is symmetric and fully populated with each module having a functional relationship with the other two modules.

PLANOPT Benchmark 2 (L4B) This problem of only 4 modules has been selected as a benchmark problem. It has been taken from the famous book on Facilities Planning [Tompkins et al, Facilities Planning, 3rd Ed., John Wiley Inc., NY, 2002. (Problem 6.7)] Since there are only four modules to be placed in a specified rectangular boundary of the same area as the total area of the modules, the number of feasible solutions is very small. Its global optimum solution can be found by exhaustive enumeration. It also serves as a good test problem for the accuracy of the program. The cost matrix is non-symmetric. All modules are functionally connected to each other. There is only one-way flow between modules 2 and 3.

PLANOPT Benchmark 3 (L8) This problem has been taken from the Ref. [Imam, M. H. & Mir, M., Nonlinear programming approach to automated topology optimization, Computer-Aided Design, 21(2), 107-115, 1989]. About 15 years ago when research on PLANOPT software development was started, this was one of the very few published problems used for layout optimization with complete data given in the paper. This problem of 8 Hard modules of unequal areas has all dimensions and cost matrix elements as integer valued numbers ranging between 1 and 6. The cost matrix is symmetric and moderately sparse indicating that there are several pairs of modules with no flow between them.



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PLANOPT Benchmark 4 (L8FX) All data for this benchmark are the same as for PLANOPT Benchmark 3 (L8) except that 3 of the modules have been anchored.

PLANOPT Benchmark 5 (L12PD) This problem of 12 modules has been taken from the Ref. [Welgama & Gibson, A construction algorithm for the machine layout problem with fixed pick-up and drop-off points, Int. J Prod Res., 31(11), 2575-2590, 1993]. All the 12 modules are hard modules with specified pick-up and drop-off points. All the modules in this problem are allowed to flip.

PLANOPT Benchmark 6 (L20) This problem has been taken from the Ref. [Imam, M. H., Mir, M., Automated layout of facilities of unequal area, Computers Ind. Engng, 24(3), 355-366 (1993)]. The paper reports complete data and optimal layouts for this problem. The data for this problem of 20 unequal area modules consist of only integer values between 1 and 3 for the dimensions of the modules. The cost matrix is symmetric and sparse. There are a number of pairs of modules with no flow between them. The non-zero elements of the cost matrix are integers between 1 and 5. This problem has been used as a test problem in some other publications. The best published result for this problem has a cost of 1264 whereas VIP-PLANOPT produces the optimal layout with a cost of 1157 only.

PLANOPT Benchmark 7 (L28) This problem has been taken from the Ref. [Mir, M. & Imam, M. H., Topology optimization of arbitrary sized blocks using a bivariate formulation, Computer-Aided Design, 24(10), 556-564, 1992]. At the time PLANOPT development work started. this was another of the very few published problems in the area of facility layout optimization of unequal area departments. For this problem complete data were given in the paper. This was a randomly generated problem as reported by the authors. It is a



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medium size unequal area layout optimization problem. The dimensions of the modules are all real numbers between 2.0 and 4.0. The cost matrix has quite a large number of zeroes with non-zero values ranging between 1 and 4.

PLANOPT Benchmark 8 (L50) This is a problem of 50 modules randomly generated as a PLANOPT benchmark problem. A problem of 50 or more modules was not presented in the literature on layout optimization until the first release of PLANOPT. The dimensions of the modules are decimal numbers between 1.0000 to 6.0000 with five significant digits. The elements of the cost matrix are all integers between 1 and 10. There are no zeroes in the cost matrix indicating that each module is functionally connected to all other modules.

PLANOPT Benchmark 9 (L75) This is a randomly generated problem of 75 modules. The problem has modules with both fixed and variable aspect ratios. The elements of the cost matrix are all integers between 1 and 5. As compared to L50 the cost matrix of this problem is quite sparse.

PLANOPT Benchmark 10 ( L100) This is a randomly generated large size problem of 100 modules. The dimensions of the module are decimal numbers between 1.0000 to 6.0000 with five significant digits. The cost matrix is symmetric and its elements are integers between 1 and 10 such that each module is functionally connected to all other modules.

PLANOPT Benchmark 11 (L125A) Since VIP-PLANOPT can now handle problems with up to 500 modules or more, this problem of 125 modules is no more the largest size problem that can be solved with this version of PLANOPT. The cost matrix for this problem is non-symmetric. Its elements are randomly generated integers between 1 and 5. The cost matrix is sparse. The problem has both hard and soft modules. The dimension of the hard modules and the areas of the



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soft modules and bounds on their aspect ratios are randomly generated real numbers.

PLANOPT Benchmark 12 (L125B) This problem of 125 modules is different from L125A in three respects: a) the cost matrix is symmetric, b) the cost matrix is not sparse and c) it consists of hard modules only. Elements of the cost matrix are randomly generated integers between 1 and 10.



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Summary The following table gives a summary of the results for the benchmark problems. The run-times based on Pentium 1 (120 MHz) and for Pentium 4 (2.4 GHz) are given only for comparison. The actual run-times depend upon the system configuration and the available resources at the time the program is executing.

Computer Run Time (Seconds)

Problem Name

Cost Function

Type

Distance Norm

Seed Optimum Cost

120 MHz Pentium 1

2.4 GHz Pentium 4

L3 F1 Rectilinear 1 270.0 0.5 0.05

L8 F1 Square Euc. 6 692.5 1 0.10

L8FX F1 Square Euc. 7 763.5 3 0.15

L12PD F2 Rectilinear 20 5384.4 8 0.27

L20 F1 Rectilinear 7 1157.0 3 0.30

L28 F1 Square Euc. 9 6447.2 12 1.5

L50 F1 Euclidean 12 78224.7 50 7

L75 F1 Rectilinear 26 34396.4 420 13

L100 F1 Rectilinear 96 538193.1 480 14

L125A F2 Rectilinear 36 288774.6 3000 110

L125B F1 Rectilinear 183 1,84450.7 2400 70



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Q & A

VIP-PLANOPT was developed initially as a benchmark program with the sole purpose of presenting an algorithm that could be used by researchers in the related fields to compare their algorithms and the available software packages. However, gradually the feedback from the users converted it into a practical tool for facility layout optimization. Since some of the questions helped many users, we are including them here in the manual. This part of the manual is new and will be gradually enhanced by additions of more questions and answers.

Q 1 How an enclosing shape for the facility representing the building or the land is specified in VIP-PLANOPT? A 1 This is one of the most difficult issues in layout optimization and makes the hard problem even harder. The answer is not straightforward because, specifying a fixed bounding rectangle or enclosure which may represent the building or the land enclosing all departments is one of the toughest constraints which results in degrading the quality of optimal layouts. The user must understand that trying to get an optimal layout in a tight space with little room for alternative placement of modules will mostly fail or will turn into a bin-packing problem rather than layout optimization. Therefore it is advised that this option be used only when you really need it and when trying to enclose, make sure you have the enclosing area as big as possible. In the previous versions of VIP-PLANOPT, the user could impose this constraint artificially by making a boundary of any desired shape with the help of the Anchored modules. Now, in VIP-PLAOPT 2006, a boundary of any shape can be specified using the Boundary



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Shape Constraint. As described in this manual, the user has to click and create points that are connected with orthogonal line segments. A penalty function approach is used to impose the constraint and obtain optimal layouts.

Q 2 How new departments to an existing facility can be added without moving the departments in the existing facility but still getting optimal layout by optimal placement of the new departments? A 2 VIP-PLANOPT has been quite effective in handling such problems. With VIP-PLANOPT, it is quite simple to add new cells because VIP-PLANOPT has the option of specifying the Position of any number cells (modules) as Fixed or Movable. Fixed modules are anchored in place and do not move during the optimization. So, the best way to handle the problem of adding new departments to an existing facility is to tag all existing cells as Fixed in position and let all new modules be Movable. To anchor a module, you just have to click the option Fixed in the Position frame on the main input window. To specify its position, click the Placement button. VIP-PLANOPT allows you to position the fixed modules either graphically by dragging the mouse or by entering coordinates for the lower left corners.

Q 3 How can the position of aisles be defined in a layout? A 3 Aisles can be specified as modules of fixed position. Create a module in VIP-PLANOPT and then modify its dimensions to the dimensions of the actual aisles in your problem and tag them as fixed in position. All aisles must have flow from all modules in the problem. If the flow does not exist, specify a very small value. This will not affect the optimization. Once you have created all modules, place them to construct the aisle system you want. Click the Placement button in the Other Proper

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Vip Planopt Manual