Non-linear constraints format for GA using solve function

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Jarek
Jarek 2025-3-4
编辑： Torsten 2025-3-4
I am trying to optimize integer variables with non-linear constraints using GA optimization. Specifically, the constraint is meant to make sure that each integer variable is unique (see example_2). I used to the following code to ensure that each integer is unique
-size(unique(x),2) + size(x,2)
when I include this in the solve function with ga, it gives me error stating:
% Error using optim.problemdef.OptimizationProblem.checkValidConstraints
% Constraints must be an OptimizationConstraint or a struct containing OptimizationConstraints.
%
% Error in indexing
%
% Error in indexing
%
% Error in example_2 (line 34)
% problem.Constraints.c1 = -size(unique(Pos_Input_mtx),2) + size(Pos_Input_mtx,2)<=0;%const_2(Pos_Input_mtx);
I tried couple of different ways to format this without any success. The work around I had was to use ga function directly with the same constraint function (see example_1). This demostrates that the GA function is able to intepret my constraint function. I would prefer to use solve function as it is more versatile and was wondering how I can format the constraint properly without the error shown above.
I have included two sets of code as example.
  1. example_1.m uses const_1.m and calcResistance.m. Example_1 is the format using ga function directly that runs.
  2. example_2.m uses const_2.m and calcResistance.m. Example_2 is the format using solve function that does not run.

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采纳的回答

Matt J
Matt J 2025-3-4
编辑：Matt J 2025-3-4
I would formulate it as,
N=numel(Pos_Input_mtx);
problem.Constraints.c1=abs(Pos_Input_mtx(:)-Pos_Input_mtx(:)') >= (1-eye(N))*0.5;
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Jarek
Jarek 2025-3-4
编辑：Jarek 2025-3-4
This worked! I'm wondering what is preventing my code from working? Is it because the use of unique function? Why does it work for the GA direct method?
I am using 2024b.
Torsten
Torsten 2025-3-4
编辑：Torsten 2025-3-4
Ran in:
Both versions work with the solver-based approach. For the problem-based approach, I guess you have to use "fcn2optimexpr" to make the constraint work in your formulation.
R1 = 2;
R2 = 1;
Pos_Input_init = [1 3 2 4 6 5];
r_stator = calcResistance(Pos_Input_init, R1, R2);
%% Optimization Problem
LB = 1;
UB = 6;
fun = @(x)calcResistance(x, R1,R2);
nvars = 6;
A = [];
b = [];
Aeq = [];
beq = [];
lb = ones(1,6)*LB;
ub = ones(1,6)*UB;
nonlcon = @(x)const_1(x);
intcon = 1:6;
options = optimoptions('ga','Display','diagnose');
[x,fval,exitflag,output,population,scores] = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon,options);
Diagnostic information. Fitness function: @(x)calcResistance(x,R1,R2) Nonlinear constraint function: @(x)const_1(x) 6 Variables 6 Integer variables 36 Nonlinear inequality constraints Options: CreationFcn: @gacreationuniformint CrossoverFcn: @crossoverlaplace SelectionFcn: @selectiontournament MutationFcn: @mutationpower Display: 'diagnose' End of diagnostic information. Best Mean Stall Generation Func-count Penalty Penalty Generations 1 120 0.2222 0.7312 0 2 177 0.2222 0.6111 1 3 234 0.2222 10.96 2 4 291 0.2222 11.06 3 5 348 0.2222 10.91 4 6 405 0.2222 10.93 5 7 462 0.2222 14.81 6 8 519 0.2222 14.82 7 9 576 0.2222 10.33 8 10 633 0.2222 10.46 9 11 690 0.2222 10.43 10 12 747 0.2222 14.73 11 13 804 0.2222 10.39 12 14 861 0.2222 11.05 13 15 918 0.2222 10.43 14 16 975 0.2222 10.41 15 17 1032 0.2222 10.37 16 18 1089 0.2222 10.34 17 19 1146 0.2222 10.4 18 20 1203 0.2222 10.49 19 21 1260 0.2222 9.209 20 22 1317 0.2222 9.165 21 23 1374 0.2222 9.18 22 24 1431 0.2222 14.72 23 25 1488 0.2222 12.32 24 26 1545 0.2222 9.187 25 27 1602 0.2222 9.076 26 28 1659 0.2222 9.113 27 29 1716 0.2222 9.146 28 Best Mean Stall Generation Func-count Penalty Penalty Generations 30 1773 0.2222 9.154 29 31 1830 0.2222 9.146 30 32 1887 0.2222 9.128 31 33 1944 0.2222 9.128 32 34 2001 0.2222 9.124 33 35 2058 0.2222 12.85 34 36 2115 0.2222 9.139 35 37 2172 0.2222 9.072 36 38 2229 0.2222 9.146 37 39 2286 0.2222 9.109 38 40 2343 0.2222 9.146 39 41 2400 0.2222 10.41 40 42 2457 0.2222 9.031 41 43 2514 0.2222 9.131 42 44 2571 0.2222 14.72 43 45 2628 0.2222 11.61 44 46 2685 0.2222 10.97 45 47 2742 0.2222 9.143 46 48 2799 0.2222 9.128 47 49 2856 0.2222 14.79 48 50 2913 0.2222 9.128 49 51 2970 0.2222 9.791 50 ga stopped because the average change in the penalty function value is less than options.FunctionTolerance but constraints are not satisfied to within options.ConstraintTolerance.
x
x = 1×6
6 2 5 3 4 2
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fval
fval = 14.3333
nonlcon = @(x)const_2(x);
[x,fval,exitflag,output,population,scores] = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon,options);
Diagnostic information. Fitness function: @(x)calcResistance(x,R1,R2) Nonlinear constraint function: @(x)const_2(x) 6 Variables 6 Integer variables 1 Nonlinear inequality constraints Options: CreationFcn: @gacreationuniformint CrossoverFcn: @crossoverlaplace SelectionFcn: @selectiontournament MutationFcn: @mutationpower Display: 'diagnose' End of diagnostic information. Best Mean Stall Generation Func-count Penalty Penalty Generations 1 120 13.67 14.09 0 2 180 10.33 13.97 0 3 240 10.33 13.98 1 4 300 10.33 13.91 2 5 360 10.33 11.36 3 6 420 10.33 13.3 4 7 480 10.33 11.4 5 8 540 10.33 11.35 6 9 600 10.33 11.36 7 10 660 10.33 11.35 8 11 720 10.33 14.44 9 12 780 10.33 10.76 10 13 840 10.33 13.18 11 14 900 10.33 10.73 12 15 960 10.33 10.74 13 16 1020 9.667 13.22 0 17 1080 9.667 10.72 1 18 1140 9.667 12.62 2 19 1200 9 10.7 0 20 1260 9 12.6 1 21 1320 9 10.69 2 22 1380 9 10.69 3 23 1440 9 11.33 4 24 1500 9 11.31 5 25 1560 8.333 11.27 0 26 1620 8.333 15.08 1 27 1680 8.333 12.55 2 28 1740 8.333 10.03 3 29 1800 8.333 10.05 4 Best Mean Stall Generation Func-count Penalty Penalty Generations 30 1860 8.333 10.04 5 31 1920 8.333 12.5 6 32 1980 8.333 9.401 7 33 2040 8.333 9.394 8 34 2100 8.333 10.63 9 35 2160 7.667 9.372 0 36 2220 7.667 8.716 1 37 2280 7.667 8.726 2 38 2340 7.667 8.716 3 39 2400 7 13.03 0 40 2460 7 14.84 1 41 2520 7 8.67 2 42 2580 7 14.4 3 43 2640 7 8.707 4 44 2700 7 9.947 5 45 2760 7 11.13 6 46 2820 7 13.75 7 47 2880 7 8.707 8 48 2940 7 11.25 9 49 3000 7 8.73 10 50 3060 7 8.697 11 51 3120 7 8.693 12 52 3180 7 8.667 13 53 3240 7 8.693 14 54 3300 7 8.69 15 55 3360 7 8.677 16 56 3420 7 10.55 17 57 3480 7 8.693 18 58 3540 7 10.51 19 59 3600 7 8.039 20 Best Mean Stall Generation Func-count Penalty Penalty Generations 60 3660 7 8.056 21 61 3720 7 9.944 22 62 3780 7 10.56 23 63 3840 7 8.069 24 64 3900 7 11.23 25 65 3960 7 8.046 26 66 4020 7 11.84 27 67 4080 7 8.042 28 68 4140 7 8.056 29 69 4200 7 8.086 30 70 4260 7 9.942 31 71 4320 7 9.308 32 72 4380 7 8.039 33 73 4440 7 8.042 34 74 4500 7 11.19 35 75 4560 7 8.036 36 76 4620 7 9.299 37 77 4680 7 9.914 38 78 4740 7 8.066 39 79 4800 7 8.039 40 80 4860 7 9.914 41 81 4920 7 9.269 42 82 4980 7 12.45 43 83 5040 7 8.652 44 84 5100 7 13.73 45 85 5160 7 11.82 46 86 5220 7 8.042 47 87 5280 7 8.039 48 88 5340 7 8.076 49 89 5400 7 8.046 50 ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and the constraint violation is less than options.ConstraintTolerance.
x
x = 1×6
1 2 3 4 5 6
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<mw-icon class=""></mw-icon>
fval
fval = 7
function [c,ceq] = const_1(x)
N = numel(x);
c = (1-eye(N))*0.5 - abs(x(:)-x(:)');
c = c(:);
ceq = [];
end
function [c,ceq] = const_2(x)
c = -size(unique(x),2) + size(x,2);
ceq = [];
end
function [R_all] = calcResistance(R_pos_input, R1,R2)
parallel = @(varargin)1/sum(1./[varargin{:}]);
R_group = zeros(3,3);
R_phase = zeros(3,1);
for ph = 1:3
ind = (ph - 1) * 2 + 1;
R_out(ind) = (R_pos_input(ind)-1) *R1;
R_out(ind + 1) = abs((R_pos_input(ind) - R_pos_input(ind+1))) *R1;
for i = 1:3
R_group(i,ph) = R_out(ind) + R_out(ind + 1) + R2 ;
end
R_phase(ph) = parallel(R_group(1,ph),R_group(2,ph),R_group(3,ph));
end
R_all = sum(R_phase);
end

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