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Correction of a bug in the augmented Lagrangian updating scheme, and inclusion of a field variable to control the maximum value for the penalization.
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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@@ -5,7 +5,7 @@ | |
| % [email protected] | ||
| % | ||
| % Originally programmed in: Jun 18, 2021 | ||
| % Last updated in: Aug 15, 2024 | ||
| % Last updated in: Dec 11, 2024 | ||
| % ----------------------------------------------------------------- | ||
| % This routine employs the Cross-entropy (CE) method to solve the | ||
| % following optimization problem: | ||
|
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@@ -74,6 +74,7 @@ | |
| % * NonlconAlgorithm : algorithm to handle nonlinear constraints | ||
| % * InitialPenalty : initial penalty value for the augmented Lagrangian | ||
| % * PenaltyFactor : factor by which the penalty parameter is increased | ||
| % * MaximumPenalty : maximum value for the penalty parameter | ||
| % * xmean : history of mean value over iterations | ||
| % * xmedian : history of median over iterations | ||
| % * xbest : history of best sample point over iterations | ||
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@@ -277,21 +278,22 @@ | |
| 'isVectorized' ,false , ... | ||
| 'Nvars' ,Nvars , ... | ||
| 'EliteFactor' ,0.05 , ... | ||
| 'Nsamp' ,200 , ... | ||
| 'Nsamp' ,100 , ... | ||
| 'MaxIter' ,100*Nvars , ... | ||
| 'MaxStall' ,50 , ... | ||
| 'MaxFcount' ,+Inf , ... | ||
| 'MinFval' ,-Inf , ... | ||
| 'TolAbs' ,1.0e-6 , ... | ||
| 'TolRel' ,1.0e-3 , ... | ||
| 'TolCon' ,1.0e-3 , ... | ||
| 'TolFun' ,1.0e-6 , ... | ||
| 'TolFun' ,1.0e-3 , ... | ||
| 'alpha' ,0.4 , ... | ||
| 'beta' ,0.4 , ... | ||
| 'q' ,10 , ... | ||
| 'NonlconAlgorithm','AugLagLog', ... | ||
| 'InitialPenalty' ,10 , ... | ||
| 'PenaltyFactor' ,100 ... | ||
| 'PenaltyFactor' ,100 , ... | ||
| 'MaximumPenalty' ,+Inf ... | ||
| ); | ||
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| % assign values for undefined fields in CEstr | ||
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@@ -511,10 +513,8 @@ function CheckCEstr(CEstr) | |
| CEstr.Fcount = Fcount; | ||
| CEstr.xmean(t,:) = xmean; | ||
| CEstr.xmedian(t,:) = xmedian; | ||
| %CEstr.xbest(t,:) = xbest; | ||
| CEstr.Fmean(t) = Fmean; | ||
| CEstr.Fmedian(t) = Fmedian; | ||
| %CEstr.Fbest(t) = Fbest; | ||
| CEstr.sigma(t,:) = sigma; | ||
| CEstr.ErrorS(t) = ErrorS; | ||
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@@ -569,15 +569,19 @@ function CheckCEstr(CEstr) | |
| ExitFlag = 0; % termination condition flag | ||
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| % initialize penalty parameters | ||
| Penalty = CEstr.InitialPenalty; | ||
| PenaltyFactor = CEstr.PenaltyFactor; | ||
| Penalty = CEstr.InitialPenalty; | ||
| PenaltyFactor = CEstr.PenaltyFactor; | ||
| MaximumPenalty = CEstr.MaximumPenalty; | ||
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| % initialize Lagrange multipliers | ||
| [G0,H0] = nonlcon(xmean0); | ||
| if isempty(G0), G0 = 0.0; end | ||
| if isempty(H0), H0 = 0.0; end | ||
| lambdaG = zeros(size(G0)); | ||
| lambdaH = zeros(size(H0)); | ||
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| % initialize constraint error | ||
| ErrorC = ComputeErrorC(G0,H0,lambdaG,lambdaH,Penalty,TolCon,1.0); | ||
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| % preallocate memory for design variables samples | ||
| X = zeros(Nsamp,Nvars); | ||
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@@ -620,16 +624,20 @@ function CheckCEstr(CEstr) | |
| % standard deviation error | ||
| [ErrorS,SmallErrorS] = ComputeErrorS(sigma,sigma0,TolAbs,TolRel); | ||
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| % update Lagrange multipliers | ||
| [lambdaG,lambdaH,G,H] = ... | ||
| UpdateLagrangeMult(xbest,nonlcon,lambdaG,lambdaH,Penalty); | ||
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| % constraint error | ||
| % evalute the constraints at xbest | ||
| [G,H] = nonlcon(xbest); | ||
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| % evaluate the constraint error | ||
| [ErrorC,SmallErrorC] = ... | ||
| ComputeErrorC(G,H,lambdaG,lambdaH,Penalty,TolCon); | ||
| ComputeErrorC(G,H,lambdaG,lambdaH,Penalty,TolCon,ErrorC); | ||
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| % update Lagrange multipliers | ||
| [lambdaG,lambdaH] = ... | ||
| UpdateLagrangeMult(G,H,lambdaG,lambdaH,Penalty); | ||
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| % update pentalty parameter | ||
| Penalty = UpdatePenalty(Penalty,PenaltyFactor,SmallErrorC); | ||
| Penalty = ... | ||
| UpdatePenalty(Penalty,PenaltyFactor,MaximumPenalty,SmallErrorC); | ||
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| % update old parameters | ||
| xmean0 = xmean; | ||
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@@ -654,10 +662,8 @@ function CheckCEstr(CEstr) | |
| CEstr.Fcount = Fcount; | ||
| CEstr.xmean(t,:) = xmean; | ||
| CEstr.xmedian(t,:) = xmedian; | ||
| %CEstr.xbest(t,:) = xbest; | ||
| CEstr.Fmean(t) = Fmean; | ||
| CEstr.Fmedian(t) = Fmedian; | ||
| %CEstr.Fbest(t) = Fbest; | ||
| CEstr.sigma(t,:) = sigma; | ||
| CEstr.ErrorS(t) = ErrorS; | ||
| CEstr.ErrorC(t) = ErrorC; | ||
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@@ -833,11 +839,10 @@ function CheckCEstr(CEstr) | |
| % ----------------------------------------------------------------- | ||
| % UpdateLagrangeMult - update Lagrange multipliers | ||
| % ----------------------------------------------------------------- | ||
| function [lambdaG,lambdaH,G,H] = ... | ||
| UpdateLagrangeMult(x,nonlcon,lambdaG,lambdaH,Penalty) | ||
| function [lambdaG,lambdaH] = ... | ||
| UpdateLagrangeMult(G,H,lambdaG,lambdaH,Penalty) | ||
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| % nonlinear constraints at x | ||
| [G,H] = nonlcon(x); | ||
| % check the nonlinear constraints | ||
| if isempty(G), G = 0.0; end | ||
| if isempty(H), H = 0.0; end | ||
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@@ -853,28 +858,33 @@ function CheckCEstr(CEstr) | |
| % ComputeErrorC - compute constraint error | ||
| % ----------------------------------------------------------------- | ||
| function [ErrorC,SmallErrorC] = ... | ||
| ComputeErrorC(G,H,lambdaG,lambdaH,Penalty,TolCon) | ||
| ComputeErrorC(G,H,lambdaG,lambdaH,Penalty,TolCon,ErrorC0) | ||
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| % check the nonlinear constraints | ||
| if isempty(G), G = 0.0; end | ||
| if isempty(H), H = 0.0; end | ||
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| % constraints violation metrics | ||
| ViolationEq = max(abs(H)); | ||
| ViolationIn = max(min(-G,lambdaG/Penalty)); | ||
| ViolationEqNorm = norm(H,Inf); | ||
| ViolationInNorm = norm(min(-G,lambdaG/Penalty),Inf); | ||
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| % constraints violation error | ||
| ErrorC = max(ViolationIn,ViolationEq); | ||
| ErrorC = max(ViolationEqNorm,ViolationInNorm); | ||
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| % convergence indicator for constraint violation | ||
| SmallErrorC = abs(ErrorC) <= TolCon; | ||
| SmallErrorC = ErrorC <= TolCon*ErrorC0; | ||
| end | ||
| % ----------------------------------------------------------------- | ||
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| % ----------------------------------------------------------------- | ||
| % UpdatePenalty - update penalty parameter | ||
| % ----------------------------------------------------------------- | ||
| function Penalty = UpdatePenalty(Penalty,PenaltyFactor,SmallErrorC) | ||
| function Penalty = ... | ||
| UpdatePenalty(Penalty,PenaltyFactor,MaximumPenalty,SmallErrorC) | ||
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| % update penalty parameter | ||
| if ~SmallErrorC | ||
| Penalty = PenaltyFactor*Penalty; | ||
| Penalty = min(PenaltyFactor*Penalty,MaximumPenalty); | ||
| end | ||
| end | ||
| % ----------------------------------------------------------------- | ||
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