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
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% 参数设置/ Q s: Y; S& o
numParticles = 30; % 粒子数量
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numDimensions = 2; % 问题维度* L! u! m/ y( M) \. t" Y
maxIterations = 100; % 最大迭代次数
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bounds = [-10, 10]; % 搜索边界5 `/ ?! B6 C: z/ ]$ y* ]
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% 初始化粒子位置和速度; O% [9 c! R; D, K# a
positions = rand(numParticles, numDimensions) * (bounds(2) - bounds(1)) + bounds(1);
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velocities = rand(numParticles, numDimensions) * 2 - 1;
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% 适应度值预分配) E' r1 ~9 U- Q5 E! G! e+ g: ?
fitness = ones(numParticles, 1) * Inf; j q7 l$ _5 ^+ i% H
personalBestPositions = positions; : s' }7 t# O7 ]% @/ r
personalBestFitness = fitness; 2 j+ A1 ~, u5 T; S$ L
globalBestPosition = zeros(1, numDimensions);
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globalBestFitness = Inf;
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% 目标函数 (Rosenbrock函数)& ^% `7 X+ L8 u) M" _. d9 X: L
objectiveFunction = @(x) sum(100*(x(:,2) - x(:,1).^2).^2 + (1 - x(:,1)).^2);8 V: w# h$ V" G. O
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% PSO主循环/ L' c0 J8 D0 Q5 G* `
for iter = 1:maxIterations
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% 计算适应度
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fitness = objectiveFunction(positions);( ~7 n: ?* W% F b
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% 更新个人最佳和全局最佳$ v& [8 n) b' M
for i = 1:numParticles
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if fitness(i) < personalBestFitness(i)
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personalBestFitness(i) = fitness(i);
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personalBestPositions(i, :) = positions(i, :);% R9 c* p; ]5 [- K- [
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end
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[minFitness, minIndex] = min(personalBestFitness);" l U, P6 b5 N1 y5 b( q
if minFitness < globalBestFitness' _- w8 I1 j$ s5 F( G4 H2 V0 c2 Z/ U T7 O: K
globalBestFitness = minFitness;
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globalBestPosition = personalBestPositions(minIndex, :);
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end
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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
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socialWeight = 1.5; % 社会学习因子; P* x1 ]( _/ a8 _
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for i = 1:numParticles* ~: V4 f2 W0 o: W
r1 = rand(1, numDimensions);7 n+ {% q+ z2 X3 ?5 T
r2 = rand(1, numDimensions); `) {& _4 {5 ]
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% 更新速度
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velocities(i, :) = inertiaWeight * velocities(i, :) + ...$ V8 L7 H; B6 w- k6 n4 X
cognitiveWeight * r1 .* (personalBestPositions(i, :) - positions(i, :)) + ...6 B1 Q, m: V& {: o6 {5 O! I
socialWeight * r2 .* (globalBestPosition - positions(i, :)); l6 @0 ^8 |3 V7 M' j, Z$ D
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% 更新位置
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positions(i, :) = positions(i, :) + velocities(i, :);
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% 限制在边界内. W1 Y) s$ k2 O- u* R3 {
positions(i, :) = max(min(positions(i, :), bounds(2)), bounds(1));
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end
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% 可选的日志输出
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disp(['Iteration ' num2str(iter) ': Best Fitness = ' num2str(globalBestFitness)]);
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end! A/ h2 T! P/ G/ c
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% 输出结果% |' u- `* f `* H
disp(['全局最佳位置: ', num2str(globalBestPosition)]);
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disp(['全局最佳适应度: ', num2str(globalBestFitness)]);; @+ V* v$ I! N
```

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