A hybrid evolutionary local search with depth first search split procedure for the heterogeneous vehicle routing problems

Routing Problems have been deeply studied over the last decades. Split procedures have proved their efficiency for those problems, especially within global optimization frameworks. The purpose is to build a feasible routing solution by splitting a giant tour into trips. This is done by computing a shortest path on an auxiliary graph built from the giant tour. One of the latest advances consists in handling extra resource constraints through the generation of labels on the nodes of the auxiliary graph. Lately, the development of a new generic split family based on a Depth First Search (DFS) approach during label generation has highlighted the efficiency of this new method for the routing problems, through extensive numerical evaluations on the location-routing problem.In this paper, we present a hybrid Evolutionary Local Search (hybrid ELS) for non-homogeneous fleet Vehicle Routing Problems (VRP) based on the application of split strategies. Experiments show our method is able to handle all known benchmarks, from Vehicle Fleet Mix Problems to Heterogeneous Fleet VRP (HVRP). We also propose a set of new realistic HVRP instances from 50 to more than 250 nodes coming from French counties. It relies on real distances in kilometers between towns. Since many classical HVRP instance sets are solved to optimality, this new set of instances could allow a fair comparative study of methods. The DFS split strategy shows its efficiency and attests the fact that it can be a promising line of research for routing problems including numerous additional constraints.     

The strong network orientation problem

This study presents models and heuristics for solving the strong network orientation problem (SNOP), which can model several tactical optimization problems of setting directions in urban networks. The objective is to set an orientation for each edge in an undirected graph such that the resulting digraph is strongly connected and the total travel distance between any pair of nodes is minimized (or maximized). Investigating tactical optimization problems such as SNOP is motivated by several challenges in urban networks due to the growth of population in urban areas, large number of daily trips, increasing price of maintaining urban networks, and the need to reduce air pollution and passive noise. Thus, a new trend is to utilize the urban networks better. In this context, we first use a multicommodity flow formulation to model the minimization problem. The maximization version is modeled by using the dual formulation of the shortest path problem. Then, scalable heuristic strategies for solving SNOP are investigated. For such purpose, we first propose basic components such as constructive heuristics, perturbations and local searches. They are combined into several metaheuristics based on local searches, multi-start and evolutionary schemes, i.e. Multistart Local Search, Iterated Local Search (ILS), Relaxed ILS, Evolutionary Local Search (ELS), Relaxed ELS, and Variable Neighborhood Search. Computational experiments have been performed to analyze the proposed methods in terms of efficiency and quality of solutions, using grid instances and a graph from downtown Clermont-Ferrand in France.