Global Optimization Toolbox User's Guide - MathWorks

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2 Write Files for Optimization Functions 2-8 As an example, suppose your nonlinear constraints for a three-dimensional problem are x 4 x + 9 x + ≤ 6 25 x3 ≥ cosh x + x xxx = 2. 1 2 2 2 3 2 1 2 3 ( ) 1 2 The following code gives these nonlinear constraints in a vectorized fashion, assuming that the rows of your input matrix x are your population or input vectors: function [c ceq] = nlinconst(x) c(:,1) = x(:,1).^2/4 + x(:,2).^2/9 + x(:,3).^2/25 - 6; c(:,2) = cosh(x(:,1) + x(:,2)) - x(:,3); ceq = x(:,1).*x(:,2).*x(:,3) - 2; For example, minimize the vectorized quadratic function function y = vfun(x) y = -x(:,1).^2 - x(:,2).^2 - x(:,3).^2; over the region with constraints nlinconst using patternsearch: options = psoptimset('CompletePoll','on','Vectorized','on'); [x fval] = patternsearch(@vfun,[1,1,2],[],[],[],[],[],[],... @nlinconst,options) Optimization terminated: mesh size less than options.TolMesh and constraint violation is less than options.TolCon. x = 0.2191 0.7500 12.1712 fval = -148.7480 Using ga: options = gaoptimset('Vectorized','on');
Write Constraints [x fval] = ga(@vfun,3,[],[],[],[],[],[],@nlinconst,options) Optimization terminated: maximum number of generations exceeded. x = -1.4098 -0.1216 11.6664 fval = -138.1066 For this problem patternsearch computes the solution far more quickly and accurately. 2-9
Page 1 and 2: Global Optimization Toolbox User’
Page 3: Revision History January 2004 Onlin
Page 6 and 7: vi Contents 3 How to Write a Functi
Page 8 and 9: viii Contents An Unsuccessful Poll
Page 10 and 11: x Contents 6 Genetic Algorithm Usin
Page 12 and 13: xii Contents 8 9 Bibliography .....
Page 14 and 15: 11 12 A Getting Started xiv Content
Page 16 and 17: 1 Introducing Global Optimization T
Page 44 and 45: 2 Write Files for Optimization Func
Page 54 and 55: 3 Using GlobalSearch and MultiStart
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3 Using GlobalSearch and MultiStart
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4 Using Direct Search 4-2 What Is D
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4 Using Direct Search 4-4 Choose so
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4 Using Direct Search 4-6 Optimize
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4 Using Direct Search 4-8 The reaso
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4 Using Direct Search 4-10 Pattern
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4 Using Direct Search 4-12 The algo
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4 Using Direct Search 4-14 The prob
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4 Using Direct Search 4-16 Note By
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4 Using Direct Search 4-18 8*[0 -1]
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4 Using Direct Search 4-20 2 1.5 1
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4 Using Direct Search 4-22 The dist
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4 Using Direct Search 4-24 Update c
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4 Using Direct Search 4-26 Search T
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4 Using Direct Search 4-28 3 Set th
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4 Using Direct Search 4-30 Referenc
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4 Using Direct Search 4-32 Pattern
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4 Using Direct Search 4-34 - Set Ae
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4 Using Direct Search 4-36 The uppe
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4 Using Direct Search 4-38 if optim
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4 Using Direct Search 4-40 Now, whe
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4 Using Direct Search 4-42 Custom P
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4 Using Direct Search 4-44 x = -4.7
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4 Using Direct Search 4-46 MaxFunEv
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4 Using Direct Search 4-48 You can
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4 Using Direct Search 4-50 [-100...
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4 Using Direct Search 4-52 0 −5
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4 Using Direct Search 4-54 mesh and
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4 Using Direct Search 4-56 Example:
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4 Using Direct Search 4-58 2 Choose
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4 Using Direct Search 4-60 Algorith
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4 Using Direct Search 4-62 The most
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4 Using Direct Search 4-64 To see t
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4 Using Direct Search 4-66 With the
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4 Using Direct Search 4-68 3 Run th
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4 Using Direct Search 4-70 The firs
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4 Using Direct Search 4-72 When you
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4 Using Direct Search 4-74 Note For
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4 Using Direct Search 4-76 Iter f-c
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4 Using Direct Search 4-78 3 Run th
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4 Using Direct Search 4-80 This tim
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4 Using Direct Search 4-82 The patt
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4 Using Direct Search 4-84 Best Obj
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4 Using Direct Search 4-86 If x0 is
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4 Using Direct Search 4-88 The same
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4 Using Direct Search 4-90 The init
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4 Using Direct Search 4-92 ylabel('
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4 Using Direct Search 4-94 distance
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4 Using Direct Search 4-96 if nargi
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4 Using Direct Search 4-98 You can
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4 Using Direct Search 4-100 outpt =
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5 Using the Genetic Algorithm 5-2 W
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5 Using the Genetic Algorithm 5-4 U
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5 Using the Genetic Algorithm 5-6 T
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5 Using the Genetic Algorithm 5-8 G
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5 Using the Genetic Algorithm 5-10
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6 Using Simulated Annealing 6-2 Wha
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6 Using Simulated Annealing 6-4 Usi
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6 Using Simulated Annealing 6-6 To
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6 Using Simulated Annealing 6-8 Man
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6 Using Simulated Annealing 6-10 Si
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6 Using Simulated Annealing 6-12 Ho
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6 Using Simulated Annealing 6-14 T
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6 Using Simulated Annealing 6-16 Us
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6 Using Simulated Annealing 6-18 op
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6 Using Simulated Annealing 6-20 x,
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6 Using Simulated Annealing 6-22
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7 Multiobjective Optimization 7-2 W
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7 Multiobjective Optimization 7-4 F
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7 Multiobjective Optimization 7-6 U
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7 Multiobjective Optimization 7-8 3
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7 Multiobjective Optimization 7-10
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8 Parallel Processing 8-2 Backgroun
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8 Parallel Processing 8-4 Suppose,
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8 Parallel Processing 8-6 reaches a
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8 Parallel Processing 8-8 Implement
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8 Parallel Processing 8-10 Run gamu
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8 Parallel Processing 8-12 MultiSta
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8 Parallel Processing 8-14 After yo
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8 Parallel Processing 8-16 Parallel
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8 Parallel Processing 8-18
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9 Options Reference 9-2 GlobalSearc
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9 Options Reference 9-4 run when th
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9 Options Reference 9-6 If you spec
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9 Options Reference 9-8 If MaxWaitC
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9 Options Reference 9-10 In this se
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9 Options Reference 9-12 - TolX —
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9 Options Reference 9-14 the number
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9 Options Reference 9-16 Note If yo
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9 Options Reference 9-18 The search
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9 Options Reference 9-20 Off or On
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9 Options Reference 9-22 Specify
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9 Options Reference 9-24 - TolFun
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9 Options Reference 9-26 When Evalu
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9 Options Reference 9-28 Option Ava
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9 Options Reference 9-30 Option Ava
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9 Options Reference 9-32 See “Set
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9 Options Reference 9-34 To display
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9 Options Reference 9-36 Selection
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9 Options Reference 9-38 The functi
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9 Options Reference 9-40 - Set Scal
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9 Options Reference 9-42 The input
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9 Options Reference 9-44 options =
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9 Options Reference 9-46 - Selects
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9 Options Reference 9-48 Your cross
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9 Options Reference 9-50 space (gen
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9 Options Reference 9-52 Enter @myf
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9 Options Reference 9-54 Max Constr
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9 Options Reference 9-56 Simulated
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9 Options Reference 9-58 optimvalue
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9 Options Reference 9-60 - @anneali
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9 Options Reference 9-62 Stopping C
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9 Options Reference 9-64 - 'iter'
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9 Options Reference 9-66
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10 Function Reference 10-2 GlobalSe
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10 Function Reference 10-4 Genetic
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10 Function Reference 10-6 Simulate
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11 Class Reference 11-2
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createOptimProblem 12-2 Purpose Cre
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createOptimProblem 12-4 Output Argu
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CustomStartPointSet 12-6 Get the fo
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ga 12-8 x = ga(fitnessfcn,nvars,A,b
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ga 12-10 If the problem has m linea
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ga 12-12 where constraintfile.m is
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ga 12-14 Exit Flag Meaning 1 Withou
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ga 12-16 Examples Given the followi
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gamultiobj 12-18 Purpose Find minim
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gamultiobj 12-20 rngstate Optional
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gamultiobj 12-22 end y(i,1) = x(i)
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gamultiobj 12-24 See Also ga | gaop
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gaoptimset 12-26 Purpose Create gen
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gaoptimset 12-28 Option Description
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GlobalOptimSolution 12-34 Copy Sema
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GlobalSearch 12-36 'off' —Nodispl
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GlobalSearch 12-38 Default: [] Star
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CustomStartPointSet.list 12-40 Purp
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RandomStartPointSet.list 12-42 Algo
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MultiStart 12-44 OutputFcns A funct
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MultiStart 12-46 Methods Copy Seman
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patternsearch 12-48 Ax ≤ b Aeq
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patternsearch 12-50 Exit Flag 1 Mea
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patternsearch 12-52 x = 0.6667 1.33
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psoptimget 12-54 Purpose Obtain val
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psoptimset 12-56 Option Description
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psoptimset 12-58 Option Description
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GlobalSearch.run 12-60 Purpose Find
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GlobalSearch.run 12-62 funcCount Nu
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MultiStart.run 12-64 Purpose Run lo
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MultiStart.run 12-66 output 2 At le
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RandomStartPointSet 12-68 Purpose R
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saoptimget 12-70 Purpose Values of
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saoptimset 12-72 AnnealingFcn: @ann
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saoptimset 12-74 Option Description
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simulannealbnd 12-76 solver 'simula
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simulannealbnd 12-78 x = 0.0392 -31
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simulannealbnd 12-80 See Also ga |
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A Examples A-2 GlobalSearch and Mul
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A Examples A-4 Genetic Algorithm
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A Examples A-6
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Index global 5-97 local 5-97 minimi
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