運籌系列15：routing模型之TSP問題
阿新 • • 發佈：2018-11-24
1. 問題模型
TSP問題是旅行商問題的簡寫，問題非常簡單：從原點出發經過所有需求點並回到原點，使得途經的距離最短。
ortools可以使用RoutingModel來進行求解。
2. 求解程式碼
首先建立RoutingModel模型：
routing = pywrapcp.RoutingModel(tsp_size, num_routes, depot)
為SetArcCostEvaluatorOfAllVehicles方法傳入一個計算距離的回撥函式，然後使用預設的引數pywrapcp.RoutingModel.DefaultSearchParameters()，就可以使用SolveWithParameters進行求解了。注意使用這個引數的話，給出的是一個可行初始解，而不是最優解。
程式碼如下
from ortools.constraint_solver import pywrapcp
from ortools.constraint_solver import routing_enums_pb2
# Cities
city_names = ["New York", "Los Angeles", "Chicago", "Minneapolis", "Denver", "Dallas", "Seattle",
"Boston", "San Francisco", "St. Louis", "Houston", "Phoenix", "Salt Lake City" 輸出為：
Total distance: 7293 miles
Route:
New York -> Boston -> Chicago -> Minneapolis -> Denver -> Salt Lake City -> Seattle -> San Francisco -> Los Angeles -> Phoenix -> Houston -> Dallas -> St. Louis -> New York
可以手動設定初始可行解的求解演算法：
search_parameters.first_solution_strategy = (routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
清單如下：
| Option | Description |
|---|---|
| AUTOMATIC | Lets the solver detect which strategy to use according to the model being solved. |
| PATH_CHEAPEST_ARC | Starting from a route “start” node, connect it to the node which produces the cheapest route segment, then extend the route by iterating on the last node added to the route. |
| PATH_MOST_CONSTRAINED_ARC | Similar to PATH_CHEAPEST_ARC, but arcs are evaluated with a comparison-based selector which will favor the most constrained arc first. To assign a selector to the routing model, use the method ArcIsMoreConstrainedThanArc(). |
| EVALUATOR_STRATEGY | Similar to PATH_CHEAPEST_ARC, except that arc costs are evaluated using the function passed to SetFirstSolutionEvaluator(). |
| SAVINGS | Savings algorithm (Clarke & Wright). Reference: Clarke, G. & Wright, J.W.: “Scheduling of Vehicles from a Central Depot to a Number of Delivery Points”, Operations Research, Vol. 12, 1964, pp. 568-581. |
| SWEEP | Sweep algorithm (Wren & Holliday). Reference: Anthony Wren & Alan Holliday: Computer Scheduling of Vehicles from One or More Depots to a Number of Delivery Points Operational Research Quarterly (1970-1977), Vol. 23, No. 3 (Sep., 1972), pp. 333-344. |
| CHRISTOFIDES | Christofides algorithm (actually a variant of the Christofides algorithm using a maximal matching instead of a maximum matching, which does not guarantee the 3/2 factor of the approximation on a metric travelling salesman). Works on generic vehicle routing models by extending a route until no nodes can be inserted on it. Reference: Nicos Christofides, Worst-case analysis of a new heuristic for the travelling salesman problem, Report 388, Graduate School of Industrial Administration, CMU, 1976. |
| ALL_UNPERFORMED | Make all nodes inactive. Only finds a solution if nodes are optional (are element of a disjunction constraint with a finite penalty cost). |
| BEST_INSERTION | Iteratively build a solution by inserting the cheapest node at its cheapest position; the cost of insertion is based on the global cost function of the routing model. As of 2/2012, only works on models with optional nodes (with finite penalty costs). |
| PARALLEL_CHEAPEST_INSERTION | Iteratively build a solution by inserting the cheapest node at its cheapest position; the cost of insertion is based on the the arc cost function. Is faster than BEST_INSERTION. |
| LOCAL_CHEAPEST_INSERTION | Iteratively build a solution by inserting each node at its cheapest position; the cost of insertion is based on the the arc cost function. Differs from |
| GLOBAL_CHEAPEST_ARC | Iteratively connect two nodes which produce the cheapest route segment. |
| LOCAL_CHEAPEST_ARC | Select the first node with an unbound successor and connect it to the node which produces the cheapest route segment. |
| FIRST_UNBOUND_MIN_VALUE | Select the first node with an unbound successor and connect it to the first available node. This is equivalent to the CHOOSE_FIRST_UNBOUND strategy combined with ASSIGN_MIN_VALUE (cf. constraint_solver.h). |
返回值的清單如下：
| Value | Description |
|---|---|
| 0 | ROUTING_NOT_SOLVED: Problem not solved yet. |
| 1 | ROUTING_SUCCESS: Problem solved successfully. |
| 2 | ROUTING_FAIL: No solution found to the problem. |
| 3 | ROUTING_FAIL_TIMEOUT: Time limit reached before finding a solution. |
| 4 | ROUTING_INVALID: Model, model parameters, or flags are not valid. |
3. 第二階段演算法：local search
使用local search可以在初始可行解的基礎上進行優化，如下：
search_parameters.local_search_metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
search_parameters.time_limit_ms = 30000 # 30s
可使用的清單如下：
| Option | Description |
|---|---|
| AUTOMATIC | Lets the solver select the metaheuristic. |
| GREEDY_DESCENT | Accepts improving (cost-reducing) local search neighbors until a local minimum is reached. |
| GUIDED_LOCAL_SEARCH | Uses guided local search to escape local minima (cf. http://en.wikipedia.org/wiki/Guided_Local_Search); this is generally the most efficient metaheuristic for vehicle routing. |
| SIMULATED_ANNEALING | Uses simulated annealing to escape local minima (cf. http://en.wikipedia.org/wiki/Simulated_annealing). |
| TABU_SEARCH | Uses tabu search to escape local minima (cf. http://en.wikipedia.org/wiki/Tabu_search). |
| OBJECTIVE_TABU_SEARCH | Uses tabu search on the objective value of solution to escape local minima |