Solving the large‐scale min–max K‐rural postman problem for snow plowing

Abstract

International audienceThis article studies the snow plow routing problem, which is a modified version of the min–max problem with k-vehicles for arc routing on a mixed graph with hierarchy. Each arc or edge is given a priority and instead of minimizing the overall finishing time, we minimize the latest finishing time for each priority class. We consider turn restrictions, route balancing, and variable vehicle speeds in a real large-scale network. To solve the problem, we present a graph transformation from a directed rural postman problem with turn penalties to an asymmetric traveling salesman problem. We then make the following modifications to the metaheuristics to better handle the constraints: development of new neighborhood operators, several applications of the same destruction operators before repair of the solution, and a dynamic arc-grouping procedure when links are removed or inserted. We tested our methodology on three real networks with 1,626 to 2,146 street segments and 613 to 723 intersections. The results show that our approach can improve the solution, and the grouping procedure is helpful. The results also show that some operators perform better than others; the network topology seems to explain these variations. Finally, we validated our methodology by comparing to some routes planned in the past and to some routes obtained from a commercial solver

A rolling horizon framework for the time‐dependent multi‐visit dynamic safe street snow plowing problem

“…ALNS is a renowned metaheuristic that was introduced by Pisinger and Ropke [14]. It has been applied to a multitude of related problems (e.g., [15][16][17]). To the best of our knowledge, we are the first to apply it to the introduced dynamic stochastic snow plowing problem.…”

“…They use ALNS to solve it for varying fleet compositions and deduce bottlenecks. Quirion et al [16] focus on a hierarchical rural postman problem with turn penalties, variable speeds, and heterogeneous vehicles with the objective to minimize a weighted sum of the makespan for each subset of streets of the same priority. The problem is transformed into an asymmetric traveling salesman problem and is solved using ALNS.…”

Optimization of Snow Removal in Cities

“…The snow plow routing problem considering partial area coverage, the service hierarchy, the workload balance, the vehicle dependence, and turning restrictions is studied in [35] and [36]. In [35], an ALNS metaheuristic is implemented and the algorithm is used to design new routes in large-scale mixed rural and urban network of a city located in the north of Quebec in Canada and to measure the impact of having fewer vehicles.…”

“…In [35], an ALNS metaheuristic is implemented and the algorithm is used to design new routes in large-scale mixed rural and urban network of a city located in the north of Quebec in Canada and to measure the impact of having fewer vehicles. In [36], the problem is formulated as a modified version of the min-max problem with k-vehicles for arc routing on a mixed graph with hierarchy. In order to solve the problem, a graph transformation from a directed rural postman problem with turn penalties to an ATSP is presented.…”

“…Turning penalties in snow removal problem have been studied in [36], [35] and [37]. Precedence of clearing a street to transportation on that street is studied in [8], precedence of different lanes and precedence of streets to sidewalks are discudded in [12], and precedence of street classes is studied in [30].…”