【优化选址】基于精英保留策略遗传算法校园快递驿站选址优化（目标函数：最小化加权距离）附Matlab代码

✅作者简介热爱科研的Matlab仿真开发者擅长毕业设计辅导、数学建模、数据处理、算法改进、程序设计科研仿真。完整代码获取 定制创新 论文复现私信个人信条做科研博学之、审问之、慎思之、明辨之、笃行之是为博学慎思明辨笃行。 内容介绍一、研究背景与问题描述1. 研究背景高校校园面积大、学生宿舍、教学楼、食堂、操场等人群分布分散现有快递点存在布局混乱、取件步行距离过长、人流聚集拥堵、配送成本高等问题。校园驿站选址属于带权重多设施平面选址问题需求点宿舍楼、教学楼、实训楼每个点位赋予人流量权重代表取件需求规模决策变量k 个快递驿站平面坐标优化目标所有需求点到最近驿站的加权总距离最小约束驿站不可布置在禁建区道路、湖泊、教学楼内部、驿站数量固定、坐标限定校园地理边界内。二、精英保留遗传算法 (Elitist GA) 基础原理标准 GA 存在优秀个体丢失、后期收敛缓慢、最优解震荡问题精英保留策略直接将每一代最优个体不参与交叉变异完整复制到下一代保证全局最优解不退化收敛速度与稳定性大幅提升。完整迭代流程种群初始化适应度计算目标函数取倒数越小距离对应越高适应度精英保存筛选前 Ne 个最优个体直接保留选择操作轮盘赌 / 锦标赛选择剩余父代交叉、变异生成子代子代 精英合并形成新种群迭代直至最大迭代次数。三、整体选址优化模型搭建步骤 1校园数据采集与预处理需求点位采集标记全部宿舍楼、教学楼、商业街坐标 (xi,yi)统计日均快递取件人数归一化得到权重 wi。校园地理约束建模划定校园坐标上下限多边形顶点描述湖泊、主干道、教学区等禁建区域参数初始化驿站数量 k、种群规模、迭代次数、交叉概率、变异概率、精英个体比例、最小驿站间距。⛳️ 运行结果 部分代码​% 问题数据points [5,12,120; 10,25,180; 15,8,100; 18,20,150; 22,5,80;25,18,160; 30,10,140; 32,28,110; 38,15,170; 42,25,190];x_i points(:,1); y_i points(:,2); w_i points(:,3);​% 参数N 100; k_tour 2; eta_c 2; p_m 0.1;sigma_m [5,3]; max_stagnation 50; epsilon 0.001;num_runs 20;​% 存储结果results_with_elite zeros(num_runs, 1);results_without_elite zeros(num_runs, 1);​%% 有精英策略fprintf(\n1. 有精英策略\n);for run 1:num_runsrng(shuffle);population [050*rand(N,1), 030*rand(N,1)];fitness zeros(N,1);for i1:Nfitness(i) -sum(w_i.*sqrt((population(i,1)-x_i).^2(population(i,2)-y_i).^2));endstagnation 0; prev_best -inf;for gen 1:500[sorted_fit, idx] sort(fitness,descend);elites population(idx(1:10),:);n_off N-10;parents zeros(n_off,2);for i1:n_offcand randi(N,2,1);[~,best_c] max(fitness(cand));parents(i,:) population(cand(best_c),:);endoffspring zeros(n_off,2);shuff randperm(n_off);parents parents(shuff,:);for i1:2:n_off-1p1parents(i,:); p2parents(i1,:);for d1:2urand();if u0.5; beta(2*u)^(1/(eta_c1));else beta(1/(2*(1-u)))^(1/(eta_c1)); endc1(d)0.5*((1beta)*p1(d)(1-beta)*p2(d));c2(d)0.5*((1-beta)*p1(d)(1beta)*p2(d));endc1(1)max(0,min(50,c1(1))); c1(2)max(0,min(30,c1(2)));c2(1)max(0,min(50,c2(1))); c2(2)max(0,min(30,c2(2)));offspring(i,:)c1; offspring(i1,:)c2;endfor i1:n_offif rand()p_moffspring(i,1)max(0,min(50,offspring(i,1)sigma_m(1)*randn()));offspring(i,2)max(0,min(30,offspring(i,2)sigma_m(2)*randn()));endendoff_fit zeros(n_off,1);for i1:n_offoff_fit(i) -sum(w_i.*sqrt((offspring(i,1)-x_i).^2(offspring(i,2)-y_i).^2));endnew_pop [elites; offspring];new_fit [sorted_fit(1:10); off_fit];[new_fit, new_idx] sort(new_fit,descend);population new_pop(new_idx(1:N),:);fitness new_fit(1:N);if gen1 abs(fitness(1)-prev_best)/abs(prev_best)epsilonstagnation stagnation1;if stagnationmax_stagnation; break; endelse; stagnation0; endprev_best fitness(1);endresults_with_elite(run) -fitness(1);fprintf(第%d次: %.4f\n, run, results_with_elite(run));end​%% 无精英策略fprintf(\n2. 无精英策略\n);for run 1:num_runsrng(shuffle);population [050*rand(N,1), 030*rand(N,1)];fitness zeros(N,1);for i1:Nfitness(i) -sum(w_i.*sqrt((population(i,1)-x_i).^2(population(i,2)-y_i).^2));endstagnation 0; prev_best -inf;for gen 1:500parents zeros(N,2);for i1:Ncand randi(N,2,1);[~,best_c] max(fitness(cand));parents(i,:) population(cand(best_c),:);endoffspring zeros(N,2);shuff randperm(N);parents parents(shuff,:);for i1:2:N-1p1parents(i,:); p2parents(i1,:);for d1:2urand();if u0.5; beta(2*u)^(1/(eta_c1));else beta(1/(2*(1-u)))^(1/(eta_c1)); endc1(d)0.5*((1beta)*p1(d)(1-beta)*p2(d));c2(d)0.5*((1-beta)*p1(d)(1beta)*p2(d));endc1(1)max(0,min(50,c1(1))); c1(2)max(0,min(30,c1(2)));c2(1)max(0,min(50,c2(1))); c2(2)max(0,min(30,c2(2)));offspring(i,:)c1; offspring(i1,:)c2;endfor i1:Nif rand()p_moffspring(i,1)max(0,min(50,offspring(i,1)sigma_m(1)*randn()));offspring(i,2)max(0,min(30,offspring(i,2)sigma_m(2)*randn()));endendoff_fit zeros(N,1);for i1:Noff_fit(i) -sum(w_i.*sqrt((offspring(i,1)-x_i).^2(offspring(i,2)-y_i).^2));endpopulation offspring;fitness off_fit;if gen1 abs(fitness(1)-prev_best)/abs(prev_best)epsilonstagnation stagnation1;if stagnationmax_stagnation; break; endelse; stagnation0; endprev_best fitness(1);endresults_without_elite(run) -fitness(1);fprintf(第%d次: %.4f\n, run, results_without_elite(run));end​​%% 输出对比结果表格​ 参考文献[1]胥杰馨,柴俊霖,董志明,等.基于动态自适应遗传算法的电动轮矿车储能系统多目标协同优化[J].煤炭科学技术, 2026, 54(S1):492.DOI:10.12438/cst.2025-1123.更多免费数学建模和仿真教程关注领取