Python实现VRP常见求解算法——遗传算法（GA）_遗传算法求解vrptw python

基于python语言，实现经典遗传算法（GA）对车辆路径规划问题（CVRP）进行求解。

优质资源

• python实现6种智能算法求解CVRP问题
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• python实现7种智能算法求解MDVRPTW问题
• Python版MDHFVRPTW问题智能求解算法代码【TS算法】
• Python版MDHFVRPTW问题智能求解算法代码【SA算法】
• Python版MDHFVRPTW问题智能求解算法代码【GA算法】
• Python版MDHFVRPTW问题智能求解算法代码【DPSO算法】
• Python版MDHFVRPTW问题智能求解算法代码【DE算法】
• Python版MDHFVRPTW问题智能求解算法代码【ACO算法】
• Python版HVRP问题智能求解算法代码【GA算法】
• Python版HVRP问题智能求解算法代码【DPSO算法】

1. 适用场景

• 求解CVRP
• 车辆类型单一
• 车辆容量不小于需求节点最大需求
• 单一车辆基地

2. 求解效果

（1）收敛曲线

（2）车辆路径

3. 问题分析

CVRP问题的解为一组满足需求节点需求的多个车辆的路径集合。假设某物理网络中共有10个顾客节点，编号为1~10，一个车辆基地，编号为0，在满足车辆容量约束与顾客节点需求约束的条件下，此问题的一个可行解可表示为：[0-1-2-0,0-3-4-5-0,0-6-7-8-0,0-9-10-0]，即需要4个车辆来提供服务，车辆的行驶路线分别为0-1-2-0,0-3-4-5-0,0-6-7-8-0,0-9-10-0。由于车辆的容量固定，基地固定，因此可以将上述问题的解先表示为[1-2-3-4-5-6-7-8-9-10]的有序序列，然后根据车辆的容量约束，对序列进行切割得到若干车辆的行驶路线。因此可以将CVRP问题转换为TSP问题进行求解，得到TSP问题的优化解后再考虑车辆容量约束进行路径切割，得到CVRP问题的解。这样的处理方式可能会影响CVRP问题解的质量，但简化了问题的求解难度。

4. 数据格式

以xlsx文件储存网络数据，其中第一行为标题栏，第二行存放车辆基地数据。在程序中车辆基地seq_no编号为-1，需求节点seq_id从0开始编号。可参考github主页相关文件。

5. 分步实现

（1）数据结构
定义Sol()类，Node()类，Model()类，其属性如下表：

• Sol()类，表示一个可行解

• Node()类，表示一个网络节点

• Model()类，存储算法参数

def readXlsxFile(filepath,model):
    #It is recommended that the vehicle depot data be placed in the first line of xlsx file
    node_seq_no =-1 #the depot node seq_no is -1,and demand node seq_no is 0,1,2,...
    df = pd.read_excel(filepath)
    for i in range(df.shape[0]):
        node=Node()
        node.id=node_seq_no
        node.seq_no=node_seq_no
        node.x_coord= df['x_coord'][i]
        node.y_coord= df['y_coord'][i]
        node.demand=df['demand'][i]
        if df['demand'][i] == 0:
            model.depot=node
        else:
            model.node_list.append(node)
            model.node_seq_no_list.append(node_seq_no)
        try:
            node.name=df['name'][i]
        except:
            pass
        try:
            node.id=df['id'][i]
        except:
            pass
        node_seq_no=node_seq_no+1
    model.number_of_nodes=len(model.node_list)
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（3）初始解生成

def genInitialSol(model):
    nodes_seq=copy.deepcopy(model.node_seq_no_list)
    for i in range(model.popsize):
        seed=int(random.randint(0,10))
        random.seed(seed)
        random.shuffle(nodes_seq)
        sol=Sol()
        sol.nodes_seq=copy.deepcopy(nodes_seq)
        model.sol_list.append(sol)
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（4）适应度计算
适应度计算依赖" splitRoutes “函数对TSP可行解分割得到车辆行驶路线和所需车辆数，” calDistance "函数计算行驶距离。

def splitRoutes(nodes_seq,model):
    num_vehicle = 0
    vehicle_routes = []
    route = []
    remained_cap = model.vehicle_cap
    for node_no in nodes_seq:
        if remained_cap - model.node_list[node_no].demand >= 0:
            route.append(node_no)
            remained_cap = remained_cap - model.node_list[node_no].demand
        else:
            vehicle_routes.append(route)
            route = [node_no]
            num_vehicle = num_vehicle + 1
            remained_cap =model.vehicle_cap - model.node_list[node_no].demand
    vehicle_routes.append(route)
    return num_vehicle,vehicle_routes
def calDistance(route,model):
    distance=0
    depot=model.depot
    for i in range(len(route)-1):
        from_node=model.node_list[route[i]]
        to_node=model.node_list[route[i+1]]
        distance+=math.sqrt((from_node.x_coord-to_node.x_coord)**2+(from_node.y_coord-to_node.y_coord)**2)
    first_node=model.node_list[route[0]]
    last_node=model.node_list[route[-1]]
    distance+=math.sqrt((depot.x_coord-first_node.x_coord)**2+(depot.y_coord-first_node.y_coord)**2)
    distance+=math.sqrt((depot.x_coord-last_node.x_coord)**2+(depot.y_coord - last_node.y_coord)**2)
    return distance
def calFit(model):
    #calculate fit value：fit=Objmax-obj
    Objmax=-float('inf')
    best_sol=Sol()#record the local best solution
    best_sol.obj=float('inf')
    #计算目标函数
    for sol in model.sol_list:
        nodes_seq=sol.nodes_seq
        num_vehicle, vehicle_routes = splitRoutes(nodes_seq, model)
        if model.opt_type==0:
            sol.obj=num_vehicle
            sol.routes=vehicle_routes
            if sol.obj>Objmax:
                Objmax=sol.obj
            if sol.obj<best_sol.obj:
                best_sol=copy.deepcopy(sol)
        else:
            distance=0
            for route in vehicle_routes:
                distance+=calDistance(route,model)
            sol.obj=distance
            sol.routes=vehicle_routes
            if sol.obj>Objmax:
                Objmax=sol.obj
            if sol.obj < best_sol.obj:
                best_sol = copy.deepcopy(sol)
    #calculate fit value
    for sol in model.sol_list:
        sol.fit=Objmax-sol.obj
    #update the global best solution
    if best_sol.obj<model.best_sol.obj:
        model.best_sol=best_sol
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（5）优良个体选择
采用二元锦标赛法进行优良个体选择。

def selectSol(model):
    sol_list=copy.deepcopy(model.sol_list)
    model.sol_list=[]
    for i in range(model.n_select):
        f1_index=random.randint(0,len(sol_list)-1)
        f2_index=random.randint(0,len(sol_list)-1)
        f1_fit=sol_list[f1_index].fit
        f2_fit=sol_list[f2_index].fit
        if f1_fit<f2_fit:
            model.sol_list.append(sol_list[f2_index])
        else:
            model.sol_list.append(sol_list[f1_index])
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（6）交叉
采用OX交叉法。

def crossSol(model):
    sol_list=copy.deepcopy(model.sol_list)
    model.sol_list=[]
    while True:
        f1_index = random.randint(0, len(sol_list) - 1)
        f2_index = random.randint(0, len(sol_list) - 1)
        if f1_index!=f2_index:
            f1 = copy.deepcopy(sol_list[f1_index])
            f2 = copy.deepcopy(sol_list[f2_index])
            if random.random() <= model.pc:
                cro1_index=int(random.randint(0,model.number_of_nodes-1))
                cro2_index=int(random.randint(cro1_index,model.number_of_nodes-1))
                new_c1_f = []
                new_c1_m=f1.nodes_seq[cro1_index:cro2_index+1]
                new_c1_b = []
                new_c2_f = []
                new_c2_m=f2.nodes_seq[cro1_index:cro2_index+1]
                new_c2_b = []
                for index in range(model.number_of_nodes):
                    if len(new_c1_f)<cro1_index:
                        if f2.nodes_seq[index] not in new_c1_m:
                            new_c1_f.append(f2.nodes_seq[index])
                    else:
                        if f2.nodes_seq[index] not in new_c1_m:
                            new_c1_b.append(f2.nodes_seq[index])
                for index in range(model.number_of_nodes):
                    if len(new_c2_f)<cro1_index:
                        if f1.nodes_seq[index] not in new_c2_m:
                            new_c2_f.append(f1.nodes_seq[index])
                    else:
                        if f1.nodes_seq[index] not in new_c2_m:
                            new_c2_b.append(f1.nodes_seq[index])
                new_c1=copy.deepcopy(new_c1_f)
                new_c1.extend(new_c1_m)
                new_c1.extend(new_c1_b)
                f1.nodes_seq=new_c1
                new_c2=copy.deepcopy(new_c2_f)
                new_c2.extend(new_c2_m)
                new_c2.extend(new_c2_b)
                f2.nodes_seq=new_c2
                model.sol_list.append(copy.deepcopy(f1))
                model.sol_list.append(copy.deepcopy(f2))
            else:
                model.sol_list.append(copy.deepcopy(f1))
                model.sol_list.append(copy.deepcopy(f2))
            if len(model.sol_list)>model.popsize:
                break
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（7）突变
采用二元突变。

def muSol(model):
    sol_list=copy.deepcopy(model.sol_list)
    model.sol_list=[]
    while True:
        f1_index = int(random.randint(0, len(sol_list) - 1))
        f1 = copy.deepcopy(sol_list[f1_index])
        m1_index=random.randint(0,model.number_of_nodes-1)
        m2_index=random.randint(0,model.number_of_nodes-1)
        if m1_index!=m2_index:
            if random.random() <= model.pm:
                node1=f1.nodes_seq[m1_index]
                f1.nodes_seq[m1_index]=f1.nodes_seq[m2_index]
                f1.nodes_seq[m2_index]=node1
                model.sol_list.append(copy.deepcopy(f1))
            else:
                model.sol_list.append(copy.deepcopy(f1))
            if len(model.sol_list)>model.popsize:
                break
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（8）绘制收敛曲线

def plotObj(obj_list):
    plt.rcParams['font.sans-serif'] = ['SimHei'] #show chinese
    plt.rcParams['axes.unicode_minus'] = False  # Show minus sign
    plt.plot(np.arange(1,len(obj_list)+1),obj_list)
    plt.xlabel('Iterations')
    plt.ylabel('Obj Value')
    plt.grid()
    plt.xlim(1,len(obj_list)+1)
    plt.show()
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（9）输出结果

def outPut(model):
    work=xlsxwriter.Workbook('result.xlsx')
    worksheet=work.add_worksheet()
    worksheet.write(0,0,'opt_type')
    worksheet.write(1,0,'obj')
    if model.opt_type==0:
        worksheet.write(0,1,'number of vehicles')
    else:
        worksheet.write(0, 1, 'drive distance of vehicles')
    worksheet.write(1,1,model.best_sol.obj)
    for row,route in enumerate(model.best_sol.routes):
        worksheet.write(row+2,0,'v'+str(row+1))
        r=[str(i)for i in route]
        worksheet.write(row+2,1, '-'.join(r))
    work.close()
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（10）主函数

def run(filepath,epochs,pc,pm,popsize,n_select,v_cap,opt_type):
    """
    :param filepath:Xlsx file path
    :param epochs:Iterations
    :param pc:Crossover probability
    :param pm:Mutation probability
    :param popsize:Population size
    :param n_select:Number of excellent individuals selected
    :param v_cap:Vehicle capacity
    :param opt_type:Optimization type:0:Minimize the number of vehicles,1:Minimize travel distance
    :return:
    """
    model=Model()
    model.vehicle_cap=v_cap
    model.opt_type=opt_type
    model.pc=pc
    model.pm=pm
    model.popsize=popsize
    model.n_select=n_select

    readXlsxFile(filepath,model)
    genInitialSol(model)
    history_best_obj = []
    best_sol=Sol()
    best_sol.obj=float('inf')
    model.best_sol=best_sol
    for ep in range(epochs):
        calFit(model)
        selectSol(model)
        crossSol(model)
        muSol(model)
        history_best_obj.append(model.best_sol.obj)
        print("%s/%s， best obj: %s" % (ep,epochs,model.best_sol.obj))
    plotObj(history_best_obj)
    outPut(model)
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6. 完整代码

代码和数据文件获取【私信】：

https://download.csdn.net/download/python_n/37357242

参考

1. 汪定伟. 智能优化方法[M]. 高等教育出版社, 2007.
2. https://www.cnblogs.com/shankun/p/Vehicle_Routing_Problem.html
3. https://blog.csdn.net/u012750702/article/details/54563515
4. https://blog.csdn.net/xinbolai1993/article/details/79458929
5. https://blog.csdn.net/weixin_30239361/article/details/101686764