1 内容介绍
蚁群算法是继模拟退火、遗传算法、禁忌搜索等之后的又一启发式智能优化算法,它是由意大利学者M.Dorigo等人首次提出,并广泛应用于求解一系列组合优化问题,如:旅行商问题,二次分配问题,车辆路径问题和图着色问题等,这些应用充分显示了它在解决复杂离散优化问题方面的优越性。连续空间函数优化问题也是蚁群算法的研究课题之一,多峰函数优化又是函数优化的一个重要方面,但目前蚁群算法对该问题的研究主要是集中在求解函数的最大(小)值,对求解函数所有极值方面的研究却很少。
2 部分代码
clear
close all
clc
% Set ABC Control Parameters
ABCOpts = struct( 'ColonySize', 100, ... % Number of Employed Bees+ Number of Onlooker Bees 种群规模
'MaxCycles', 500,... % Maximum cycle number in order to terminate the algorithm 循环次数，即全部蚂蚁走几遍
'ErrGoal', 1e-20, ... % Error goal in order to terminate the algorithm (not used in the code in current version)
'Dim', 20 , ... % Number of parameters of the objective function 维数
'Limit', 100, ... % Control paramter in order to abandone the food source 放弃食物源的阈值
'lb', -5.12, ... % Lower bound of the parameters to be optimized 函数值下限
'ub', 5.12, ... %Upper bound of the parameters to be optimized 函数值上限
'ObjFun' , 'rastrigin', ... %Write the name of the objective function you want to minimize 选择函数
'RunTime',3); % Number of the runs 迭代次数
GlobalMins=zeros(ABCOpts.RunTime,ABCOpts.MaxCycles);
GlobalMins_WABC=zeros(ABCOpts.RunTime,ABCOpts.MaxCycles);
for r=1:ABCOpts.RunTime
% Initialise population
Range = repmat((ABCOpts.ub-ABCOpts.lb),[ABCOpts.ColonySize ABCOpts.Dim]);
Lower = repmat(ABCOpts.lb, [ABCOpts.ColonySize ABCOpts.Dim]);
Colony = rand(ABCOpts.ColonySize,ABCOpts.Dim) .* Range + Lower;
Employed=Colony(1:(ABCOpts.ColonySize/2),:);
GlobalMins(r,:) = ABCbee(ABCOpts,Employed); % ABC算法
GlobalMins_WABC(r,:) = WABCbee(ABCOpts,Employed); % WABC-ABC算法
end; %end of runs
%----------------------------- 画图、记录最优均值和方差 --------------------------
dd=ABCOpts.MaxCycles;
if ABCOpts.RunTime==1
semilogy((1:10:dd),GlobalMins(1:10:end));
hold on
semilogy((1:10:dd),GlobalMins_WABC(1:10:end),'-*g');
else
semilogy((1:10:dd),mean(GlobalMins(:,1:10:end)));%若多次执行，求均值
hold on
semilogy((1:10:dd),mean(GlobalMins_WABC(:,1:10:end)),'-*g');%若多次执行，求均值
end
grid on
title('Mean of Best function values');
xlabel('cycles');
ylabel('fitness');
legend('ABC','WABC');
fprintf('Mean =%g Std=%g\n',mean(GlobalMins(:,end)),std(GlobalMins(:,end)));
fprintf('Mean =%g Std=%g\n',mean(GlobalMins_WABC(:,end)),std(GlobalMins_WABC(:,end)));
3 运行结果
4 参考文献
[1]刘卉. 应用蚁群算法求解函数所有极值[D]. 四川师范大学, 2011.