[Optimization solution] Function optimization analysis based on matlab gravitational search algorithm [Contains Matlab source code 218]

1. Introduction

Gravitational Search Algorithm (Gravitational Search Algorithm, GSA) is a new heuristic optimization algorithm proposed by Esmat Rashedi et al. of Kerman University in Iran in 2009. It is derived from the population generated by simulating the gravitation in physics. Intelligent optimization algorithm. The principle of the gravitational search algorithm GSA is to treat the search particles as a group of objects moving in space. The objects are attracted by the gravitational interaction, and the movement of the objects follows the law of dynamics. A particle with a moderately large value has a larger inertial mass, so the universal gravitation will cause the objects to move toward the most massive object, thereby gradually approaching the optimal solution of the optimization problem. The universal gravitation search algorithm GSA has a strong global search capability and convergence speed. With the progress of GSA theoretical research, its application has become more and more extensive, gradually attracting the attention of domestic and foreign scholars. However, the universal gravitation search algorithm GSA, like other global algorithms, has problems such as being easy to fall into local solutions and the solution accuracy is not quotient. There are many things to be improved. This chapter will focus on introducing the most basic gravitational algorithm to the majority of programming enthusiasts. Each programming researcher can improve on the algorithm in this chapter and apply it to actual cases.
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1 Inertial mass calculation

2 Gravitation calculation

3 Position update

4 Parameter analysis

5 Universal gravitation algorithm implementation process

Second, the source code

% 万有引力搜索算法
clc,clear,close all
warning off
feature jit off
 N=50;           % 粒子数量（智能个体）
 max_it=1000;    % 最大迭代次数
 ElitistCheck=1; % ElitistCheck: 算法执行次数选择
 Rpower=1;       % Rpower: 'R'的次方
 min_flag=1;     % 1: 求函数最小值，0：求函数最大值
 F_index=1;      % 带求解函数选择
 [Fbest,Lbest,BestChart,MeanChart]=GSA(F_index,N,max_it,ElitistCheck,min_flag,Rpower);
 %  输出:
% Fbest: 最优适应度值.
% Lbest: 最优解向量
% BestChart: 适应度变化值.
% MeanChart: 平均适应度变化值
 Fbest,  % 最优适应度值
 Lbest,  % 最优解
%% 绘制适应度曲线
figure('color',[1,1,1])
plot(BestChart,'linewidth',2),
xlabel('\fontsize{12}\bf Iteration');ylabel('\fontsize{12}\bf 最优适应度值');
legend('\fontsize{10}\bf GSA',1);
grid on
% 万有引力搜索算法
function [Fbest,Lbest,BestChart,MeanChart]=GSA(F_index,N,max_it,ElitistCheck,min_flag,Rpower)
%V:   速度
%a:   加速度
%M:   质量.  Ma=Mp=Mi=M;
%dim: 待求解未知量维数
%N:   智能粒子个数
%X:   种群个体位置. dim-by-N matrix.
%R:   种群之间的距离
%[low-up]: 取值范围
%Rnorm:  范数
%Rpower: Power of R 
Rnorm=2;  % 2阶范数，即欧氏距离
% 获取待求解目标方程的未知数个体以及取值范围
[low,up,dim]=test_functions_range(F_index); 
% 随机的初始化个体
X=initialization(dim,N,up,low); 
% 适应度值数组初始化
BestChart=[];
MeanChart=[];
V=zeros(N,dim); % 速度初始化
for iteration=1:max_it  % 迭代开始
%     iteration
    
    % 检查x个体是否在取值范围内
    X=space_bound(X,up,low); 
    % 计算适应度值
    fitness=evaluateF(X,F_index); 
    
    if min_flag==1
        [best best_X]=min(fitness); %minimization.
    else
        [best best_X]=max(fitness); %maximization.
    end        
    
    if iteration==1
       Fbest=best;Lbest=X(best_X,:);
    end
    if min_flag==1
      if best<Fbest  % 极小值求解
       Fbest=best;Lbest=X(best_X,:);
      end
    else 
      if best>Fbest  % 极大值求解
       Fbest=best;Lbest=X(best_X,:);
      end

Three, running results

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Four, remarks

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