给出已知十四个地点之间的距离矩阵，求经过十四个地点的最短路劲，每个地点有且仅经过一次。用mtalab语言求解

这个问题可以用MATLAB语言中的遗传算法来求解，下面是MATLAB代码示例：

% 输入距离矩阵
dist_matrix = [
    0 2 3 4 5 6 7 8 9 10 11 12 13 14;
    2 0 3 4 5 6 7 8 9 10 11 12 13 14;
    3 3 0 4 5 6 7 8 9 10 11 12 13 14;
    4 4 4 0 5 6 7 8 9 10 11 12 13 14;
    5 5 5 5 0 6 7 8 9 10 11 12 13 14;
    6 6 6 6 6 0 7 8 9 10 11 12 13 14;
    7 7 7 7 7 7 0 8 9 10 11 12 13 14;
    8 8 8 8 8 8 8 0 9 10 11 12 13 14;
    9 9 9 9 9 9 9 9 0 10 11 12 13 14;
    10 10 10 10 10 10 10 10 10 0 11 12 13 14;
    11 11 11 11 11 11 11 11 11 11 0 12 13 14;
    12 12 12 12 12 12 12 12 12 12 12 0 13 14;
    13 13 13 13 13 13 13 13 13 13 13 13 0 14;
    14 14 14 14 14 14 14 14 14 14 14 14 14 0
];

% 定义遗传算法参数
pop_size = 100; % 种群大小
num_generations = 500; % 迭代次数
mutation_rate = 0.01; % 变异率

% 定义适应度函数，计算路径长度
fitness_func = @(path) path_length(path, dist_matrix);

% 初始化种群
population = init_population(pop_size, size(dist_matrix, 1));

% 迭代遗传算法
for i = 1:num_generations
    % 计算适应度
    fitness = arrayfun(fitness_func, population);

    % 选择
    parents = select_parents(population, fitness);

    % 杂交
    offspring = crossover(parents, pop_size);

    % 变异
    mutated_offspring = mutate(offspring, mutation_rate);

    % 合并父代和子代
    combined_population = [population; mutated_offspring];

    % 计算适应度
    combined_fitness = arrayfun(fitness_func, combined_population);

    % 选择下一代种群
    population = select_population(combined_population, combined_fitness, pop_size);
end

% 打印最优解
best_path = population(1, :);
fprintf('Best path: ');
fprintf('%d ', best_path);
fprintf('\nPath length: %f\n', path_length(best_path, dist_matrix));

% 定义初始化种群函数
function pop = init_population(pop_size, num_nodes)
    pop = zeros(pop_size, num_nodes);
    for i = 1:pop_size
        pop(i, :) = randperm(num_nodes);
    end
end

% 定义选择函数（锦标赛选择）
function selected = select_parents(population, fitness)
    num_parents = size(population, 1);
    selected = zeros(num_parents, size(population, 2));
    for i = 1:num_parents
        % 随机选择两个个体进行比较
        idx1 = randi(size(population, 1));
        idx2 = randi(size(population, 1));
        if fitness(idx1) < fitness(idx2)
            selected(i, :) = population(idx1, :);
        else
            selected(i, :) = population(idx2, :);
        end
    end
end

% 定义杂交函数（顺序交叉）
function offspring = crossover(parents, num_offspring)
    num_parents = size(parents, 1);
    offspring = zeros(num_offspring, size(parents, 2));
    for i = 1:num_offspring
        % 随机选择两个父代进行杂交
        idx1 = randi(num_parents);
        idx2 = randi(num_parents);
        parent1 = parents(idx1, :);
        parent2 = parents(idx2, :);
        % 随机选择杂交点
        crossover_point = randi(size(parent1, 2));
        % 进行杂交
        offspring(i, :) = [parent1(1:crossover_point), parent2(crossover_point+1:end)];
    end
end

% 定义变异函数（随机交换两个节点）
function mutated_offspring = mutate(offspring, mutation_rate)
    mutated_offspring = offspring;
    num_mutations = ceil(mutation_rate * size(offspring, 1) * size(offspring, 2));
    for i = 1:num_mutations
        idx1 = randi(size(offspring, 1));
        idx2 = randi(size(offspring, 2));
        idx3 = randi(size(offspring, 2));
        temp = mutated_offspring(idx1, idx2);
        mutated_offspring(idx1, idx2) = mutated_offspring(idx1, idx3);
        mutated_offspring(idx1, idx3) = temp;
    end
end

% 定义选择下一代种群函数（精英保留）
function selected = select_population(population, fitness, pop_size)
    [~, idx] = sort(fitness);
    selected = population(idx(1:pop_size), :);
end

% 定义计算路径长度函数
function length = path_length(path, dist_matrix)
    length = 0;
    for i = 1:length(path)-1
        length = length + dist_matrix(path(i), path(i+1));
    end
end

在这个示例代码中，我们定义了一个适应度函数，它计算遗传算法中的路径长度。然后，我们使用遗传算法进行迭代优化，找到经过所有节点的最短路径。最后，我们输出最优解和路径长度。

注意，这只是一个示例代码，你需要根据你的具体问题来修改代码。