# Introduction to particle swarm optimization 03: with Matlab and python code (PSO)

## VIII:

Inertia weight w reflects the ability of particles to inherit the previous velocity. Shi Y first introduced inertia weight w into PSO algorithm, and analyzed and pointed out that a larger inertia weight value is conducive to global search, while a smaller inertia weight value is more conducive to local search. In order to balance the two, a linear decreasing inertia weight (LDIW) is proposed.

Equation (13-4) is wrong. The denominator is only k, and Tmax is removed-

Without inertia weight, let the program run 100 times, and the average value is the optimal result. Improve on the previous code: the function code is the same as the previous section.

%% Double emptying+Close drawing clc,clear,close all; %% Perform 100 operations on the program for k = 1:100 %% PSO Parameter calibration. ***Note: inertia weight is missing here w And dimensions D*** c1 = 1.49445; %Individual learning factor c2 = 1.49445; %Social learning factor maxgen = 300; %Number of iterations sizepop = 20; %Population size Vmax = 0.5; %Upper and lower limits of speed Vmin = -0.5; popmax = 2; %Upper and lower limit of position popmin = -2; %% Initialize the position and velocity of each particle in the particle swarm, and calculate the fitness value for j = 1:sizepop %Self reference for loop pop(j,:) = 2*rands(1,2); %Self reference rands V(j,:) = 0.5*rands(1,2); fitness(j) = fun(pop(j,:)); %Self reference function end %% Search for initial individual extremum and group extremum %{ ***be careful: pop Is a matrix of 20 rows and 2 columns, of which the first column is X1，The second column is X2；V Also fitness If there is a great God who understands, please explain in the comment area. What I understand is a matrix with 20 rows and 1 column, so as to find the position of the extreme value of the group, But the program does give a matrix of 1 row and 20 columns*** -------------------------------------------------------------------------------------------- There are many things to pay attention to here matlab Medium max The reference blog doesn't say that Through experiments, it is found that when the matrix A Is a row vector,[maxnumber maxindex] = max(A)in maxindex The column of the maximum value is returned This explains the question just now! A=[1,2,3,4,8,6,75,9,243,25] A = 1 2 3 4 8 6 75 9 243 25 [maxnumber maxindex] = max(A) maxnumber = 243 maxindex = 9 -------------------------------------------------------------------------------------------- %} [bestfitness bestindex] = max(fitness); %Self reference max Function usage zbest = pop(bestindex,:); %Group extreme position gbest = pop; %The individual extreme position is initialized, so the individual extreme position of each particle is its own random position fitnessgbest = fitness; %Individual extreme fitness value fitnesszbest = bestfitness; %Population extreme fitness value %% Optimization iteration for i = 1:maxgen %Speed update for j = 1:sizepop V(j,:)=V(j,:)+c1*rand*(gbest(j,:)-pop(j,:))+c2*rand*(zbest-pop(j,:)); %Inertia weight is not added V(j,find(V(j,:)>Vmax)) = Vmax; %find The function returns the index here. There are three cases: 1; 2； 1 2； V(j,find(V(j,:)<Vmin)) = Vmin; %Location update pop(j,:)=pop(j,:)+V(j,:); pop(j,find(pop(j,:)>popmax)) = popmax; pop(j,find(pop(j,:)<popmin)) = popmin; %Update fitness value fitness(j)=fun(pop(j,:)); end %Individual extremum update for j = 1:sizepop if fitness(j)>fitnessgbest(j) gbest(j,:)=pop(j,:); fitnessgbest(j)=fitness(j); end %Population extremum update if fitness(j)>fitnesszbest zbest=pop(j,:); fitnesszbest=fitness(j); end end %Each generation records to the optimal extreme value result in result(i)=fitnesszbest; end G(k) = max(result); end GB = max(G); %The largest optimal solution among all the optimal solutions after 100 runs Average = sum(G)/100; %Average of all optimal solutions Fnumber =length(find(G>1.0054-0.01&G<1.0054+0.01));%Number of optimal solutions within the error range FSnumber =length(find(G>1.0054+0.01|G<1.0054-0.01));%Number of optimal solutions outside the error range precision = Fnumber/100 %Solution accuracy

It can be found that the evaluation of the optimal solution is very unstable:

There are only 79 times to find the optimal solution, and there are 21 times left. Thus, inertia weight is very important. Here is a direct conclusion:

It can be seen that the effect of the second inertia weight is the best, that is, formula (13-5). Here, I tested it later and found that no matter what kind of inertia weight, I can't get the above conclusion.

Reference: analysis of 30 cases of matlab intelligent algorithm (Second Edition)

My experimental conclusions are as follows:

On the whole, formula 4 is the best, but after many experiments, you will find that each w has a wide range of accuracy (the number of experiments with the optimal solution / the number of experiments),

Therefore, there is no best choice for inertia weight here. For specific problems, you can increase the number of code runs for specific experiments, and finally take the best value.

The code is divided into two parts. The original code of some references has errors in its inertia weight and lacks w

The other part is to modify the code for myself

Connection source code

https://download.csdn.net/download/weixin_42212924/18839919

Previous PSO articles

https://blog.csdn.net/weixin_42212924/article/details/116808786

https://blog.csdn.net/weixin_42212924/article/details/116947153