改进遗传算法求解VRP问题时的局部搜索能力

改进遗传算法求解VRP问题的局部搜索能力是提高算法性能的关键。

1. 局部搜索算子设计

1.1 2-opt局部搜索

matlab 复制代码

function new_route = two_opt(route, distance_matrix)
% 2-opt局部搜索：交换两条边来改进路径
    new_route = route;
    n = length(route);
    improved = true;
    
    while improved
        improved = false;
        for i = 1:n-2
            for j = i+2:n
                if j == n && i == 1
                    continue; % 避免首尾相连
                end
                
                % 计算当前距离
                current_dist = distance_matrix(route(i), route(i+1)) + ...
                              distance_matrix(route(j), route(mod(j,n)+1));
                
                % 计算交换后距离
                new_dist = distance_matrix(route(i), route(j)) + ...
                          distance_matrix(route(i+1), route(mod(j,n)+1));
                
                % 如果改进则交换
                if new_dist < current_dist
                    new_route(i+1:j) = new_route(j:-1:i+1);
                    improved = true;
                    break;
                end
            end
            if improved
                break;
            end
        end
    end
end

1.2 λ-interchange局部搜索

matlab 复制代码

function new_solution = lambda_interchange(solution, distance_matrix, lambda)
% λ-interchange局部搜索：交换不同路径间的客户
    new_solution = solution;
    num_routes = length(solution);
    improved = true;
    
    while improved
        improved = false;
        
        for i = 1:num_routes-1
            for j = i+1:num_routes
                route1 = solution{i};
                route2 = solution{j};
                
                if length(route1) < 2 || length(route2) < 2
                    continue;
                end
                
                % 尝试不同的交换组合
                for k = 1:min(lambda, length(route1)-1)
                    for m = 1:min(lambda, length(route2)-1)
                        % 交换k个客户从route1到route2，m个客户从route2到route1
                        [new_route1, new_route2, improvement] = ...
                            exchange_customers(route1, route2, k, m, distance_matrix);
                        
                        if improvement > 0
                            new_solution{i} = new_route1;
                            new_solution{j} = new_route2;
                            improved = true;
                        end
                    end
                end
            end
        end
    end
end

function [new_route1, new_route2, improvement] = exchange_customers(route1, route2, k, m, dist_mat)
% 执行客户交换
    best_improvement = 0;
    new_route1 = route1;
    new_route2 = route2;
    
    % 生成所有可能的交换组合
    combinations1 = nchoosek(2:length(route1)-1, k);
    combinations2 = nchoosek(2:length(route2)-1, m);
    
    for i = 1:size(combinations1, 1)
        for j = 1:size(combinations2, 1)
            customers1 = route1(combinations1(i, :));
            customers2 = route2(combinations2(j, :));
            
            % 创建新路径
            temp_route1 = route1;
            temp_route1(combinations1(i, :)) = [];
            insert_positions = find_insertion_positions(temp_route1, customers2, dist_mat);
            
            temp_route2 = route2;
            temp_route2(combinations2(j, :)) = [];
            insert_positions2 = find_insertion_positions(temp_route2, customers1, dist_mat);
            
            % 计算改进
            old_cost = calculate_route_cost(route1, dist_mat) + ...
                      calculate_route_cost(route2, dist_mat);
            new_cost = calculate_route_cost(temp_route1, dist_mat) + ...
                      calculate_route_cost(temp_route2, dist_mat);
            
            improvement = old_cost - new_cost;
            
            if improvement > best_improvement
                best_improvement = improvement;
                new_route1 = temp_route1;
                new_route2 = temp_route2;
            end
        end
    end
    
    improvement = best_improvement;
end

2. 混合遗传算法框架

2.1 主算法框架

matlab 复制代码

function [best_solution, best_cost, convergence] = hybrid_ga_vrp(customers, vehicle_capacity, pop_size, max_gen)
% 混合遗传算法求解VRP
    % 初始化参数
    num_customers = length(customers);
    distance_matrix = calculate_distance_matrix(customers);
    
    % 初始化种群
    population = initialize_population(pop_size, num_customers, customers, vehicle_capacity);
    
    % 评估初始种群
    costs = zeros(pop_size, 1);
    for i = 1:pop_size
        costs(i) = calculate_total_cost(population{i}, distance_matrix);
    end
    
    [best_cost, best_idx] = min(costs);
    best_solution = population{best_idx};
    
    convergence = zeros(max_gen, 1);
    
    % 遗传算法主循环
    for gen = 1:max_gen
        % 选择
        selected_indices = tournament_selection(costs, pop_size);
        
        % 交叉
        offspring = cell(pop_size, 1);
        for i = 1:2:pop_size
            parent1 = population{selected_indices(i)};
            parent2 = population{selected_indices(i+1)};
            
            [child1, child2] = order_crossover(parent1, parent2, vehicle_capacity);
            offspring{i} = child1;
            offspring{i+1} = child2;
        end
        
        % 变异
        for i = 1:pop_size
            if rand() < 0.1
                offspring{i} = swap_mutation(offspring{i});
            end
        end
        
        % 局部搜索（关键改进）
        for i = 1:pop_size
            % 自适应局部搜索概率
            ls_probability = 0.3 + 0.5 * (gen / max_gen);
            
            if rand() < ls_probability
                % 多种局部搜索算子轮换使用
                if mod(gen, 3) == 0
                    offspring{i} = two_opt_multiple_routes(offspring{i}, distance_matrix);
                elseif mod(gen, 3) == 1
                    offspring{i} = lambda_interchange(offspring{i}, distance_matrix, 2);
                else
                    offspring{i} = relocation_search(offspring{i}, distance_matrix);
                end
            end
        end
        
        % 评估子代
        offspring_costs = zeros(pop_size, 1);
        for i = 1:pop_size
            offspring_costs(i) = calculate_total_cost(offspring{i}, distance_matrix);
        end
        
        % 精英选择
        combined_pop = [population; offspring];
        combined_costs = [costs; offspring_costs];
        
        [sorted_costs, sorted_indices] = sort(combined_costs);
        for i = 1:pop_size
            population{i} = combined_pop{sorted_indices(i)};
            costs(i) = sorted_costs(i);
        end
        
        % 更新最优解
        if costs(1) < best_cost
            best_cost = costs(1);
            best_solution = population{1};
        end
        
        convergence(gen) = best_cost;
        
        fprintf('Generation %d: Best Cost = %.2f\n', gen, best_cost);
    end
end

3. 高级局部搜索技术

3.1 变邻域搜索(VNS)

matlab 复制代码

function improved_solution = vns_search(solution, distance_matrix, max_iter)
% 变邻域搜索
    improved_solution = solution;
    current_cost = calculate_total_cost(solution, distance_matrix);
    
    % 定义邻域结构
    neighborhood_structures = {@swap_neighborhood, @relocation_neighborhood, @two_opt_neighborhood};
    
    for iter = 1:max_iter
        k = 1;
        while k <= length(neighborhood_structures)
            % 抖动：在当前邻域中随机移动
            shaken_solution = shaking(improved_solution, k);
            
            % 局部搜索
            candidate_solution = local_search_vns(shaken_solution, distance_matrix, k);
            candidate_cost = calculate_total_cost(candidate_solution, distance_matrix);
            
            if candidate_cost < current_cost
                improved_solution = candidate_solution;
                current_cost = candidate_cost;
                k = 1; % 回到第一个邻域
            else
                k = k + 1; % 移动到下一个邻域
            end
        end
    end
end

function shaken_solution = shaking(solution, k)
% 抖动过程
    shaken_solution = solution;
    num_routes = length(solution);
    
    switch k
        case 1
            % 交换两个随机客户
            shaken_solution = random_swap(shaken_solution);
        case 2
            % 随机重定位一个客户
            shaken_solution = random_relocation(shaken_solution);
        case 3
            % 2-opt随机交换
            route_idx = randi(num_routes);
            if length(shaken_solution{route_idx}) > 3
                shaken_solution{route_idx} = random_two_opt(shaken_solution{route_idx});
            end
    end
end

3.2 模拟退火局部搜索

matlab 复制代码

function improved_solution = sa_local_search(solution, distance_matrix, initial_temp, cooling_rate)
% 模拟退火局部搜索
    current_solution = solution;
    current_cost = calculate_total_cost(solution, distance_matrix);
    best_solution = current_solution;
    best_cost = current_cost;
    
    temperature = initial_temp;
    
    while temperature > 1e-6
        for i = 1:100 % 内循环次数
            % 生成邻域解
            neighbor = generate_neighbor(current_solution);
            neighbor_cost = calculate_total_cost(neighbor, distance_matrix);
            
            % 计算代价差
            delta_cost = neighbor_cost - current_cost;
            
            % 接受准则
            if delta_cost < 0 || rand() < exp(-delta_cost / temperature)
                current_solution = neighbor;
                current_cost = neighbor_cost;
                
                if current_cost < best_cost
                    best_solution = current_solution;
                    best_cost = current_cost;
                end
            end
        end
        
        % 降温
        temperature = temperature * cooling_rate;
    end
    
    improved_solution = best_solution;
end

4. 自适应局部搜索策略

4.1 自适应算子选择

matlab 复制代码

function operator_weights = adaptive_operator_selection(operator_weights, improvements, learning_rate)
% 自适应调整局部搜索算子的权重
    total_improvements = sum(improvements);
    if total_improvements > 0
        success_rates = improvements / total_improvements;
        
        % 更新权重
        for i = 1:length(operator_weights)
            operator_weights(i) = (1 - learning_rate) * operator_weights(i) + ...
                                 learning_rate * success_rates(i);
        end
        
        % 归一化
        operator_weights = operator_weights / sum(operator_weights);
    end
end

function selected_operator = select_operator_by_weight(operator_weights)
% 根据权重选择局部搜索算子
    r = rand();
    cumulative_weights = cumsum(operator_weights);
    selected_operator = find(cumulative_weights >= r, 1);
end

5. 记忆和引导策略

5.1 路径重连(Path Relinking)

matlab 复制代码

function improved_solution = path_relinking(initial_solution, guiding_solution, distance_matrix)
% 路径重连：从初始解向引导解移动
    current_solution = initial_solution;
    best_solution = initial_solution;
    best_cost = calculate_total_cost(initial_solution, distance_matrix);
    
    % 计算解之间的差异
    differences = calculate_solution_differences(initial_solution, guiding_solution);
    
    while ~isempty(differences)
        % 选择最佳的移动
        best_move = [];
        best_improvement = inf;
        
        for i = 1:length(differences)
            candidate_solution = apply_move(current_solution, differences(i));
            candidate_cost = calculate_total_cost(candidate_solution, distance_matrix);
            improvement = candidate_cost - calculate_total_cost(current_solution, distance_matrix);
            
            if improvement < best_improvement
                best_improvement = improvement;
                best_move = differences(i);
            end
        end
        
        % 应用最佳移动
        current_solution = apply_move(current_solution, best_move);
        current_cost = calculate_total_cost(current_solution, distance_matrix);
        
        % 更新最优解
        if current_cost < best_cost
            best_solution = current_solution;
            best_cost = current_cost;
        end
        
        % 更新差异
        differences = calculate_solution_differences(current_solution, guiding_solution);
    end
    
    improved_solution = best_solution;
end

参考代码改进遗传算法求解VRP问题时的局部搜索能力 www.3dddown.com/csa/82193.html

6. 实施建议

分层局部搜索：
- 第一层：快速局部搜索（2-opt）
- 第二层：中等强度搜索（λ-interchange）
- 第三层：高强度搜索（VNS、模拟退火）
自适应控制：
- 根据搜索进度调整局部搜索强度
- 早期：较弱局部搜索，保持多样性
- 后期：较强局部搜索，精细调优
计算资源分配：
- 对优质个体施加更强局部搜索
- 限制每次局部搜索的计算时间
混合策略：
- 结合多种局部搜索算子的优点
- 使用自适应机制选择最有效的算子