Issues in Patternsolve and ParticleSwarm Optimzation

So a few months ago I asked some help here for fitting a really complicated function and some really helpful people in this community helped me solve the problem using genetic algorithm. Now I just want to try to fit these use other algorithms (like pattern search, particle swarm etc.) and see how they perform too.

So for starters, here is the function with 9 parameters where V represents the voltage and a’s represent the fit parameters.

    Theta= @(a,V) a(5).*V+a(6).*atan(a(7)+a(8).*V+a(9).*V.^2)
    F= @(a,V) a(1).*(a(2) - a(3) - (a(2).*a(4))./(a(2).^2.*cos(Theta(a,V)).^2 + a(4).^2.*sin(Theta(a,V)).^2).^(1/2));

The code that used genetic algorithm to fit the data well was (Fitness value of 0.3):

    inistart=10;
    V=volt(inistart:length(volt));
    volt=V;
    Phase=Phase(inistart:length(Phase))
    ftns= @(a) norm(Phase-F(a,V))
    PopSz = 100;
    Parms =9;
    optsAns = optimoptions('ga', 'PopulationSize',PopSz, 'MaxGenerations',5E3, 'FunctionTolerance',1E-10);
    t0 = clock;
    fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
    for i=1:20
        [a_fit{i},fval,exitflag,output,population,scores]=ga(ftns,Parms, [],[],[],[],[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],[],[],optsAns);
        t1 = clock;
        fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
        GA_Time = etime(t1,t0)
        DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
        fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
        fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval,output.generations)
        fprintf(1,'\tRate Constants %d:\n',i)
        for k1 = 1:numel(a_fit{i})
            fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
        end
        figure
        plot(V, Phase, '.b')
        hold on
        plot(V, F(a_fit{i},V), '-r')
        hold off
        grid  
        xlabel('V')
        ylabel('Phase')
        title('GA Parameters')
    end

What does not work?

But just to see how the other algorithms do, I tried the following (For example the patternsolve algorithm):

        optsAns = optimoptions('patternsearch','FunctionTolerance',1e-10,'MaxIterations',5e3);
    t0 = clock;
    fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
    for i=1:20
        [a_fit{i},fval,exitflag,output]=patternsearch(ftns,[8e+04; 1.7;10000;1.7;10000;10000;10000;10000;10000],[],[],[],[],[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],[],optsAns);
        t1 = clock;
        fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
        GA_Time = etime(t1,t0)
        DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
        fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
        fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval)
        fprintf(1,'\tRate Constants %d:\n',i)
        for k1 = 1:numel(a_fit{i})
            fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
        end
        figure
        plot(V, Phase, '.b')
        hold on
        plot(V, F(a_fit{i},V), '-r')
        hold off
        grid  
        xlabel('V')
        ylabel('Phase')
        title('GA Parameters')
        temp(i)=fval
    end

I always get a fitness value as 25.7862 all the 20 times I loop this code. And the fit looks like this:

Particle swarm also gives bad results: 29.7108 30.8890 49.0237 30.8896 49.0237 49.0237 49.0237 49.0237 30.8896 49.0237 49.0237 30.8895 30.8894 49.0237 49.0237 30.4015 25.3389 30.8666 49.0237 30.8896 as the fitness values.

        PopSz = 100;
    Parms =9;
    optsAns = optimoptions('particleswarm','FunctionTolerance',1e-10,'MaxIterations',5e3,'HybridFcn','fmincon');
    t0 = clock;
    fprintf('\nStart Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t0)
    for i=1:20
        [a_fit{i},fval,exitflag,output]=particleswarm(ftns,Parms,[0; 1.4;-Inf;1.40;-Inf;-Inf;-Inf;-Inf;-Inf],[8e+04; 1.7;Inf;1.7;Inf;Inf; Inf;Inf;Inf],optsAns);
        t1 = clock;
        fprintf('\nStop Time: %4d-%02d-%02d %02d:%02d:%07.4f\n', t1)
        GA_Time = etime(t1,t0)
        DT_GA_Time = datetime([0 0 0 0 0 GA_Time], 'Format','HH:mm:ss.SSS');
        fprintf('\nElapsed Time: %23.15E\t\t%s\n\n', GA_Time, DT_GA_Time)
        fprintf('Fitness value at convergence = %.4f\nGenerations \t\t\t\t = %d\n\n',fval)
        fprintf(1,'\tRate Constants %d:\n',i)
        for k1 = 1:numel(a_fit{i})
            fprintf(1, '\t\ta(%2d) = %8.5f\n', k1, a_fit{i}(k1))
        end
        figure
        plot(V, Phase, '.b')
        hold on
        plot(V, F(a_fit{i},V), '-r')
        hold off
        grid  
        xlabel('V')
        ylabel('Phase')
        title('GA Parameters')
        temp(i)=fval
    end

Can you help me understand why I get this?

Thanks in Advance!

[Alex Sha]

Hi, refer to the results below, multi-solutions. Matlab GA or PSO is not easy to obtain such result

Sum Squared Error (SSE): 0.0372804765881514
Root of Mean Square Error (RMSE): 0.0166797035900485
Correlation Coef. (R): 0.999982445829172
R-Square: 0.999964891966492

Parameter	Best Estimate      
---------	-------------      
a1       	-0.0412514328360699
a2       	-271.691129419169  
a3       	-361.400490920017  
a4       	-20.7789698301179  
a5       	0.00201615721161083
a6       	0.969640435459053  
a7       	2.14250046959902   
a8       	-10.1074996911561  
a9       	11.4388408744042

or:
Parameter	Best Estimate      
---------	-------------
a1       	-0.0127221786756855
a2       	880.956285735209
a3       	590.079842553096
a4       	67.3695361874826
a5       	0.00201595859852817
a6       	-0.969641700941842
a7       	-2.14281229346878
a8       	10.1085639749314
a9       	-11.4397708378142