粒子群优化算法 - 数学建模社区-数学中国

% 粒子群优化算法 (PSO) 示例( B8 R) c" K+ y
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% 参数设置$ I/ n/ d& D0 R0 z9 _" v
numParticles = 30; % 粒子数量
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numDimensions = 2; % 问题维度0 s7 q! Z8 R! m9 @ H6 f
maxIterations = 100; % 最大迭代次数4 |% V- {9 b* W! W1 A5 v
bounds = [-10, 10]; % 搜索边界
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% 初始化粒子位置和速度2 z* p3 c+ Y# l! B3 X! m9 V' H
positions = rand(numParticles, numDimensions) * (bounds(2) - bounds(1)) + bounds(1);
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velocities = rand(numParticles, numDimensions) * 2 - 1;4 V0 C) Y- ^3 _5 }
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% 适应度值预分配
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fitness = ones(numParticles, 1) * Inf;8 R4 I2 [- n# {3 N* \1 g& x. `
personalBestPositions = positions;
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personalBestFitness = fitness; ' f7 @, y) F7 X
globalBestPosition = zeros(1, numDimensions);+ o1 v* o2 c8 `$ m
globalBestFitness = Inf;2 F" d2 m, a# w+ L
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% 目标函数 (Rosenbrock函数)" n5 ?' t; w. {. _8 y8 S( k$ `0 h- [
objectiveFunction = @(x) sum(100*(x(:,2) - x(:,1).^2).^2 + (1 - x(:,1)).^2);
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% PSO主循环
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for iter = 1:maxIterations- q( q: S/ o( k& S1 t U
% 计算适应度
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fitness = objectiveFunction(positions);7 N6 m6 X ~' V9 G/ a9 Z
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% 更新个人最佳和全局最佳0 }# r' u" s; U$ A8 H
for i = 1:numParticles
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if fitness(i) < personalBestFitness(i)
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personalBestFitness(i) = fitness(i);# n; j. w' r- {' E& U, f# _
personalBestPositions(i, :) = positions(i, :);) D- y- n7 w- c, N6 v* u
end; z8 F: \! ?7 t. j
end+ ^9 M* L: D5 p' p& a& r, }
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[minFitness, minIndex] = min(personalBestFitness);+ |$ O9 n% \; R2 z( t0 K% z
if minFitness < globalBestFitness
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globalBestFitness = minFitness;+ h, K- N0 G' d
globalBestPosition = personalBestPositions(minIndex, :);
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end( ?/ M8 \6 a. y* V5 X5 c# O
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% 更新速度和位置
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inertiaWeight = 0.7; % 惯性权重
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cognitiveWeight = 1.5; % 个体学习因子+ p# T4 {& h$ w0 M8 b
socialWeight = 1.5; % 社会学习因子- N0 \- P' M/ h- d) u- F4 Z9 W
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for i = 1:numParticles
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r1 = rand(1, numDimensions);
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r2 = rand(1, numDimensions);
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% 更新速度
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velocities(i, :) = inertiaWeight * velocities(i, :) + ...- C" P5 w6 W( f
cognitiveWeight * r1 .* (personalBestPositions(i, :) - positions(i, :)) + ...# \1 W# ^0 W" X/ h& E6 N! j. X8 _
socialWeight * r2 .* (globalBestPosition - positions(i, :));
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% 更新位置" ~& h# [+ @+ K
positions(i, :) = positions(i, :) + velocities(i, :);
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% 限制在边界内* P9 T4 |: n: Z8 i+ R$ }/ [. o. y
positions(i, :) = max(min(positions(i, :), bounds(2)), bounds(1)); Y% L9 r$ ~. c; U! K# b% X
end; |: h9 W4 @; d/ g8 h, O( H( v% `
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% 可选的日志输出. w# h8 [0 @0 y! ^
disp(['Iteration ' num2str(iter) ': Best Fitness = ' num2str(globalBestFitness)]);
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end4 `+ T6 J/ X9 g
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% 输出结果$ A+ G( ` M' E$ [
disp(['全局最佳位置: ', num2str(globalBestPosition)]);5 ], J- ^: n2 f+ f' ]1 k$ t
disp(['全局最佳适应度: ', num2str(globalBestFitness)]);
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```

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