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基于栅格地图的遗传算法路径规划MATLAB实现

news 2025/11/6 7:46:07

一、算法框架设计

1. 栅格地图建模

编码方式：采用序号编码法，每个栅格对应唯一序号（从左到右、从上到下递增）
障碍物处理：自由栅格标记为0，障碍物标记为1
路径表示：路径由起点→中间节点→终点的栅格序号序列构成

2. 遗传算法流程

请添加图片描述

二、MATLAB核心代码实现

1. 环境建模与参数设置

%% 栅格地图参数
grid_size = [30,30]; % 地图尺寸
obs_ratio = 0.2;     % 障碍物比例
start_pos = [2,2];   % 起点坐标
goal_pos = [28,28];  % 终点坐标%% 遗传算法参数
pop_size = 100;      % 种群数量
max_gen = 200;       % 最大迭代次数
pc = 0.8;            % 交叉概率
pm = 0.15;           % 变异概率
elite_ratio = 0.1;   % 精英保留比例%% 生成栅格地图
[grid_map, num_nodes] = create_grid(grid_size, obs_ratio);
path_length = num_nodes - 2; % 路径节点数（含起点终点）

2. 种群初始化

function pop = init_population(pop_size, path_length)pop = zeros(pop_size, path_length);for i = 1:pop_sizepath = generate_path(path_length);pop(i,:) = path;end
endfunction path = generate_path(length)path = [1, randperm(length-2)+1, length]; % 起点+中间节点+终点
end

3. 适应度函数设计

function fitness = calc_fitness(pop, grid_map)[pop_size, path_len] = size(pop);fitness = zeros(pop_size,1);for i = 1:pop_sizepath = pop(i,:);% 路径有效性验证if ~is_valid_path(path, grid_map)fitness(i) = 0;continue;end% 多目标适应度计算path_length = calc_path_length(path);safety = calc_safety(path, grid_map);smoothness = calc_smoothness(path);% 加权适应度函数alpha = 0.5; beta = 0.3; gamma = 0.2;fitness(i) = alpha*(1/path_length) + ...beta*(1/safety) + ...gamma*(1/smoothness);end
end

4. 遗传操作实现

%% 选择操作（改进锦标赛选择）
function new_pop = selection(pop, fitness)[~, idx] = sort(fitness, 'descend');elite_num = round(elite_ratio * size(pop,1));new_pop = pop(idx(1:elite_num),:);while size(new_pop,1) < size(pop,1)candidates = randperm(size(pop,1),2);winner = candidates(1);if fitness(candidates(2)) > fitness(winner)winner = candidates(2);endnew_pop = [new_pop; pop(winner,:)];end
end%% 交叉操作（顺序交叉OX）
function offspring = crossover(parent1, parent2)path_len = length(parent1);cut1 = randi([2,path_len-1]);cut2 = randi([cut1+1,path_len]);offspring = zeros(1,path_len);offspring(cut1:cut2) = parent1(cut1:cut2);ptr = cut2+1;for i = 1:path_lenif ptr > path_lenptr = 1;endif ~ismember(parent2(i), offspring)offspring(ptr) = parent2(i);ptr = ptr+1;endend
end%% 变异操作（自适应扰动）
function mutated = mutation(path, grid_map, pm)if rand < pm[mutated, ~] = local_search(path, grid_map);elsemutated = path;end
end