Error in using parallel computing with gamultiobj

Hello,

I have a problem using the parallel computing in 'gamultiobj' function. I call the optimization algorithm by using:

ObjFun = @(x)FitnessFunction(x, Data);
options = optimoptions("gamultiobj","UseParallel",true,"UseVectorized",false,'PopulationSize',30,'MaxGenerations',60, 'MaxStallGenerations', 10);
[pareto,fval,exitflag,output,population,scores]  = gamultiobj(ObjFun,n_vars,[],[],[],[],lb,ub,[],intcon,options);

The function work perfectly if "UseParallel" is set as "false" but if it is set as "true" I get diffent errors.

If I use "Parallel Preferences"->"Parallel environment"->"Default profile" = Threads, I get this error:

Error using linprog
LINPROG has stopped because it encountered an internal error. We are sorry for the inconvenience.

Please contact technical support for assistance with your problem, quoting the code "-1000@-1000".

Error in CuttingBinProblem (line 32)
    [values,nLogs,exitflag,~,lambda] = linprog(f,A,b,[],[],lb,[],lpopts);

Error in FitnessFunction (line 64)
    n_bin = CuttingBinProblem(cnt_unique, unique_l, logLength);

Error in main_Opt_GA>@(x)FitnessFunction(x,Data) (line 77)
ObjFun = @(x)FitnessFunction(x, Data);

Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)
fcn_handle = @(x) fcn(x,FcnArgs{:});

Error in objAndConVectorizer (line 37)
        parfor (i = 1:popSize)

Error in gamultiobjMakeState (line 93)
        [Score,C,Ceq,isFeas] = objAndConVectorizer(state.Population(initScoreProvided+1:end,:), ...

Error in gamultiobjsolve (line 20)
state = gamultiobjMakeState(GenomeLength,FitnessFcn,ConstrFcn,output.problemtype,options);

Error in gamultiobj (line 338)
[x,fval,exitFlag,output,population,scores,residuals] = gamultiobjsolve(FitnessFcn,nvars, ...

Error in main_Opt_GA (line 81)
[pareto,fval,exitflag,output,population,scores]  = gamultiobj(ObjFun,n_vars,[],[],[],[],lb,ub,[],intcon,options);

Caused by:
    Failure in user-supplied fitness function evaluation. Cannot continue.

In this case the function CuttingBinProblem is the function available on mathworks website (https://it.mathworks.com/help/optim/ug/cutting-stock-problem-solver-based.html) that I have slightly modified as follows:

    function logsUsed = CuttingBinProblem(quantity,lengthlist,logLength) 

%% Cutting bin problem

% https://it.mathworks.com/help/optim/ug/cutting-stock-problem-solver-based.html

% logLength = 12; % Length of the bins
% lengthlist = [1.5; 1.78; 1.30; 2.0; 3.2];
% quantity = [200; 42; 55; 30; 60];
nLengths = length(lengthlist);

patterns = diag(floor(logLength./lengthlist));
nPatterns = size(patterns,2);

lb2 = zeros(nLengths,1);
A2 = lengthlist';
b2 = logLength;

lpopts = optimoptions('linprog','Display','off');
ipopts = optimoptions('intlinprog',lpopts);

reducedCost = -Inf;
reducedCostTolerance = -0.0001;
exitflag = 1;

while reducedCost < reducedCostTolerance && exitflag > 0
    lb = zeros(nPatterns,1);
    f = lb + 1;
    A = -patterns;
    b = -quantity;
    
    [values,nLogs,exitflag,~,lambda] = linprog(f,A,b,[],[],lb,[],lpopts); 
    if exitflag > 0
%         fprintf('Using %g logs\n',nLogs);
        % Now generate a new pattern, if possible
        f2 = -lambda.ineqlin;
        [values,reducedCost,pexitflag] = intlinprog(f2,1:nLengths,A2,b2,[],[],lb2,[],ipopts);
        reducedCost = 1 + reducedCost; % continue if this reducedCost is negative
        newpattern = round(values);
        if pexitflag > 0 && reducedCost < reducedCostTolerance
            patterns = [patterns newpattern];
            nPatterns = nPatterns + 1;
        end
    end
end


if exitflag <= 0 
    disp('Error in column generation phase')
else
    [values,logsUsed,exitflag] = intlinprog(f,1:length(lb),A,b,[],[],lb,[],[],ipopts);
    if exitflag > 0
        values = round(values);
        logsUsed = round(logsUsed);
    else 
        disp('Error in final optimization')
    end
end

If I use "Parallel Preferences"->"Parallel environment"->"Default profile" = Processes, I get this error:

    Error using StructuralAnalysis
Index in position 1 exceeds array bounds.

Error in AreaCalculation (line 16)
    Verified = StructuralAnalysis(DataStru,index);

Error in FitnessFunction (line 67)
    [A, indexTable] =  AreaCalculation(DataStru);

Error in main_Opt_GA>@(x)FitnessFunction(x,Data) (line 77)
ObjFun = @(x)FitnessFunction(x, Data);

Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)
fcn_handle = @(x) fcn(x,FcnArgs{:});

Error in objAndConVectorizer (line 37)
        parfor (i = 1:popSize)

Error in gamultiobjMakeState (line 93)
        [Score,C,Ceq,isFeas] = objAndConVectorizer(state.Population(initScoreProvided+1:end,:), ...

Error in gamultiobjsolve (line 20)
state = gamultiobjMakeState(GenomeLength,FitnessFcn,ConstrFcn,output.problemtype,options);

Error in gamultiobj (line 338)
[x,fval,exitFlag,output,population,scores,residuals] = gamultiobjsolve(FitnessFcn,nvars, ...

Error in main_Opt_GA (line 81)
[pareto,fval,exitflag,output,population,scores]  = gamultiobj(ObjFun,n_vars,[],[],[],[],lb,ub,[],intcon,options);

Caused by:
    Failure in user-supplied fitness function evaluation. Cannot continue.

In this case the function AreaCalculation is the following:

function [A,index] = AreaCalculation(DataStru)

global CrossSecTable


% Assign initial value to index and
index = 0;

Verified = 1;

while Verified == 1
    index = index+1;
    if index > length(CrossSecTable)
        Verified = 2;
    end
    Verified = StructuralAnalysis(DataStru,index);
end

A = 0.0001*CrossSecTable(index,4);

end

StructuralAnalysis is the following:

    function Verified1 = StructuralAnalysis(DataStru,index)

global CrossSecTable


n_vinc = DataStru.n_vinc; 

load = [0;0;-10;0;0;0];  % [kN]



% Initialize 
% (ns=number of sections; nn=number of nodes; ne=number of elements)
ns=1; nn=size(DataStru.u_end,1); ne=size(DataStru.link,1);
stru=InitializeStructure(ns,nn,ne);

% Cross sections and material
s=1;
stru.sec(s).nome='C 88.9 x 3.2';
A=0.0001*CrossSecTable(index,4);        % [m^2]
J=(10^(-8))*CrossSecTable(index,6);     % [m^4]
rho = 78.5;                             % [kN/m^3] peso per unità di volume acciaio
fy = 355;                               % [MPa]
E=2.1e8;                                % [kN/m^2]
G=E/2.4;
stru.sec(s).Ks=[E*J 0 0 0; 0 E*J 0 0; 0 0 E*A 0; 0 0 0 2*G*J];

% Nodes
for n = 1: nn
    stru.node(n).x=DataStru.u_end(n,:)';
    if n<=n_vinc
        stru.node(n).v=[1;1;1;1;1;1];
    else
        stru.node(n).f=load;
    end
end

% Elements
for e = 1: ne
    stru.elem(e).nodes=DataStru.link(e,:)';
    stru.elem(e).nz = 3;
end



for e=1:ne
    stru.elem(e).form='EBBeam3D';
    stru.elem(e).sec=1;
    stru.elem(e).vr=[0;0;1];
    stru.elem(e).qg = [0;0;-A*rho;0;0;0];
end

%% Analysis
stru.Analysis='Static';
stru=AnalyzeStructure(stru);

%% Verifications
Verified1 = 0;
% Max displacement

for iii = 1:ne
    Ncr = -(pi^2)*E*J/(stru.elem(iii).L^2);
    ymax = CrossSecTable(index,1)/1000/2;
    N = max(stru.elem(iii).f(3,1:3));
    M = max(stru.elem(iii).f(5,1:3));
    Sigma_max = abs((N/A + M/J*ymax)/1000);  % [MPa]
    if Sigma_max > fy
        Verified1 = 1;
        break;
    elseif N < Ncr
        Verified1 = 1;
        break;
    end
end



% Max stress and linear buckling

if Verified1 == 0
    for jjj = n_vinc+1:nn
        Disp = abs(stru.node(jjj).d(3));
        if Disp > 15/250
            Verified1 = 1;
            break;
        end
    end
end


toc
end

I cannot understand why the code works without the parallel computing but it is not able to run in parallel.

Answer 1

[Walter Roberson]

You cannot use global with parallel. Or to be more accurate, no global variables will be passed between processes so they will start out empty in the workers.

[Jonathan]

I eliminated the global and now it is running with "Parallel Preferences"->"Parallel environment"->"Default profile" = Processes but still not with "Parallel Preferences"->"Parallel environment"->"Default profile" = Threads. The error is:

Error using linprog
LINPROG has stopped because it encountered an internal error. We are sorry for the inconvenience.

Please contact technical support for assistance with your problem, quoting the code "-1000@-1000".

Error in CuttingBinProblem (line 32)
    [values,nLogs,exitflag,~,lambda] = linprog(f,A,b,[],[],lb,[],lpopts);

Error in FitnessFunction (line 65)
    n_bin = CuttingBinProblem(cnt_unique, unique_l, logLength);

Error in main_Opt_GA>@(x)FitnessFunction(x,Data) (line 77)
ObjFun = @(x)FitnessFunction(x, Data);

Error in createAnonymousFcn>@(x)fcn(x,FcnArgs{:}) (line 11)
fcn_handle = @(x) fcn(x,FcnArgs{:});

Error in objAndConVectorizer (line 37)
        parfor (i = 1:popSize)

Error in gamultiobjMakeState (line 93)
        [Score,C,Ceq,isFeas] = objAndConVectorizer(state.Population(initScoreProvided+1:end,:), ...

Error in gamultiobjsolve (line 20)
state = gamultiobjMakeState(GenomeLength,FitnessFcn,ConstrFcn,output.problemtype,options);

Error in gamultiobj (line 338)
[x,fval,exitFlag,output,population,scores,residuals] = gamultiobjsolve(FitnessFcn,nvars, ...

Error in main_Opt_GA (line 81)
[pareto,fval,exitflag,output,population,scores]  = gamultiobj(ObjFun,n_vars,[],[],[],[],lb,ub,[],intcon,options);

Caused by:
    Failure in user-supplied fitness function evaluation. Cannot continue.