1. CVRP模型
CVRP指的是有容量（capacity）限制的VRP模型，是最常见的VRP模型。
2. 示例
依旧用上一章节的点，不同的是每个点多了一个送货需求。每辆车的最大容量是15，最小化总运输距离。
dimension可以使用AddDimensionWithVehicleCapacity方法，和AddDimension唯一的区别就是，第三个参数从一个固定值变成了一个列表，表示每一辆车有自己单独的最大容量限制。
from __future__ import print_functionfrom ortools.constraint_solver import pywrapcpfrom ortools.constraint_solver import routing_enums_pb2############################ Problem Data Definition ############################def create_data_model(): """Stores the data for the problem""" data = {} # Locations in block units _locations = [(4, 4), # depot (2, 0), (8, 0), # locations to visit (0, 1), (1, 1), (5, 2), (7, 2), (3, 3), (6, 3), (5, 5), (8, 5), (1, 6), (2, 6), (3, 7), (6, 7), (0, 8), (7, 8)] demands = [0, # depot 1, 1, # row 0 2, 4, 2, 4, 8, 8, 1, 2, 1, 2, 4, 4, 8, 8] capacities = [15, 15, 15, 15] # Multiply coordinates in block units by the dimensions of an average city block, 114m x 80m, # to get location coordinates. data["locations"] = [(l[0] * 114, l[1] * 80) for l in _locations] data["num_locations"] = len(data["locations"]) data["num_vehicles"] = 4 data["depot"] = 0 data["demands"] = demands data["vehicle_capacities"] = capacities return data######################## Problem Constraints ########################def manhattan_distance(position_1, position_2): """Computes the Manhattan distance between two points""" return ( abs(position_1[0] - position_2[0]) + abs(position_1[1] - position_2[1]))def create_distance_callback(data): """Creates callback to return distance between points.""" _distances = {} for from_node in range(data["num_locations"]): _distances[from_node] = {} for to_node in range(data["num_locations"]): if from_node == to_node: _distances[from_nodefzdpkqto_node] = 0 else: _distances[from_nodefzdpkqto_node] = ( manhattan_distance(data["locations"fzdpkqfrom_node], data["locations"fzdpkqto_node])) def distance_callback(from_node, to_node): """Returns the manhattan distance between the two nodes""" return _distances[from_nodefzdpkqto_node] return distance_callbackdef create_demand_callback(data): """Creates callback to get demands at each location.""" def demand_callback(from_node, to_node): return data["demands"fzdpkqfrom_node] return demand_callbackdef add_capacity_constraints(routing, data, demand_callback): """Adds capacity constraint""" capacity = "Capacity" routing.AddDimensionWithVehicleCapacity( demand_callback, 0, # null capacity slack data["vehicle_capacities"], # vehicle maximum capacities True, # start cumul to zero capacity)############ Printer ############def print_solution(data, routing, assignment): """Print routes on console.""" total_dist = 0 for vehicle_id in range(data["num_vehicles"]): index = routing.Start(vehicle_id) plan_output = 'Route for vehicle {0}:n'.format(vehicle_id) route_dist = 0 route_load = 0 while not routing.IsEnd(index): node_index = routing.IndexToNode(index) next_node_index = routing.IndexToNode(assignment.Value(routing.NextVar(index))) route_dist += manhattan_distance( data["locations"fzdpkqnode_index], data["locations"fzdpkqnext_node_index]) route_load += data["demands"fzdpkqnode_index] plan_output += ' {0} Load({1}) -> '.format(node_index, route_load) index = assignment.Value(routing.NextVar(index)) node_index = routing.IndexToNode(index) total_dist += route_dist plan_output += ' {0} Load({1})n'.format(node_index, route_load) plan_output += 'Distance of the route: {0}mn'.format(route_dist) plan_output += 'Load of the route: {0}n'.format(route_load) print(plan_output) print('Total Distance of all routes: {0}m'.format(total_dist))######### Main #########def main(): """Entry point of the program""" # Instantiate the data problem. data = create_data_model() # Create Routing Model routing = pywrapcp.RoutingModel( data["num_locations"], data["num_vehicles"], data["depot"]) # Define weight of each edge distance_callback = create_distance_callback(data) routing.SetArcCostEvaluatorOfAllVehicles(distance_callback)# Add Capacity constraint demand_callback = create_demand_callback(data) add_capacity_constraints(routing, data, demand_callback) # Setting first solution heuristic (cheapest addition). search_parameters = pywrapcp.RoutingModel.xsdxg() search_parameters.first_solution_strategy = ( routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC) # Solve the problem. assignment = routing.SolveWithParameters(search_parameters) if assignment: print_solution(data, routing, assignment)if __name__ == '__main__': main()
结果如下图：