Matlab simulation of solving multi-objective optimal value based on PSO optimization

Catalog

1. Algorithm description

2. Partial procedure

3. Preview of some simulation drawings

4. Source code acquisition method

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1. Algorithm description

        stay PSO in , Each particle in a group is represented as a vector . In the context of portfolio optimization , This is a weight vector , Represents the allocated capital of each asset . The vector is transformed into a position in the multidimensional search space . Each particle will also remember its best historical position . about PSO Every iteration of , Find the global optimal location . This is the best position in the group . Once the global optimal location is found , Each particle will be closer to its local optimal position and global optimal position . When executed in multiple iterations , The process produces a good solution to the problem , Because the particles converge on the near optimal solution .

       Ray Wait for someone to pass PSO Algorithm and Pareto The sorting mechanism wants to be combined . use Pareto Sorting method to select a group of elite solutions , The global optimal particle is selected by roulette . In actual operation , Only a few individuals have a high probability of selection , The population diversity is not maintained well .Coello Wait in PSO In the algorithm, the best position of the group is selected by introducing Pareto Competition mechanism and particle knowledge base . This knowledge base is used to store the flight experience of particles after each flight cycle , The knowledge base is updated by considering a geography based system , The system is defined in terms of the objective function value of each particle . This knowledge base is used by particles to identify a leader who guides the search . At the same time, the non inferior solution is determined by comparing the candidate individuals with the comparison set randomly selected from the population , Therefore, the parameters of the comparison set have a crucial impact on the success of the algorithm . If the parameter is too large , Is prone to premature convergence , And the parameter is too small , Then the number of non inferior solutions selected in the population may be too small .

2. Partial procedure

for it=1:MaxIt
    for i=1:nPop
        rep_h=SelectLeader(rep,beta);

        particle(i).Velocity=w*particle(i).Velocity ...
                             +c1*rand*(particle(i).Best.Position - particle(i).Position) ...
                             +c2*rand*(rep_h.Position -  particle(i).Position);

        particle(i).Velocity=min(max(particle(i).Velocity,-VelMax),+VelMax);

        particle(i).Position=particle(i).Position + particle(i).Velocity;

        flag=(particle(i).Position<VarMin | particle(i).Position>VarMax);
        particle(i).Velocity(flag)=-particle(i).Velocity(flag);
        
        particle(i).Position=min(max(particle(i).Position,VarMin),VarMax);

        particle(i).Cost=CostFunction(particle(i).Position);

        if Dominates(particle(i),particle(i).Best)
            particle(i).Best.Position=particle(i).Position;
            particle(i).Best.Cost=particle(i).Cost;
            
        elseif ~Dominates(particle(i).Best,particle(i))
            if rand<0.5
                particle(i).Best.Position=particle(i).Position;
                particle(i).Best.Cost=particle(i).Cost;
            end
        end

    end
    
    particle=DetermineDomination(particle);
    nd_particle=GetNonDominatedParticles(particle);
    
    rep=[rep
         nd_particle];
    
    rep=DetermineDomination(rep);
    rep=GetNonDominatedParticles(rep);
    
    for i=1:numel(rep)
        [rep(i).GridIndex rep(i).GridSubIndex]=GetGridIndex(rep(i),G);
    end
    
    if numel(rep)>nRep
        EXTRA=numel(rep)-nRep;
        rep=DeleteFromRep(rep,EXTRA,gamma);
        
        rep_costs=GetCosts(rep);
        G=CreateHypercubes(rep_costs,nGrid,alpha);
        
    end
   
    disp(['Iteration ' num2str(it) ': Number of Repository Particles = ' num2str(numel(rep))]);
    
    w=w*wdamp;
end

3. Preview of some simulation drawings

 

 

 

4. Source code acquisition method

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