Constraint-based local search for solving non-simple paths problems on graphs: application to the routing for network covering problem

Routing problems have been considered as central problems in the fields of transportation, distribution and logistics. LS(Graph) is a generic framework allowing to model and solve constrained optimum paths problems on graphs by local search where paths are known to be elementary (i.e., edges, vertices cannot be repeated on paths). In many real-world situations, the paths to be determined are not known to be neither simple nor elementary. In this paper, we extend the LS(Graph) framework by designing and implementing abstractions that allow to model and solve constrained paths problem where edges, vertices can be repeated on paths (call non-simple paths). We also propose an instance of such problem class: the routing for network covering (RNC) problem which arises in the context of rescue after a natural disaster in which we have to route a fleet of identical vehicles with limited capacity on a transportation network in order to collect the informations of the disaster. Given an undirected weighted graph G = (V, E) representing a transportation network and a vertex v0 ∈ V representing the depot, the RNC problem consists of routing a fleet of unlimited number of identical vehicles with limited capacity that cannot perform a path of length > L such that each vehicle starts from and teminates at the depot and all the edges of a given set S (S ⊆ E) must be visited. The objective of the routing plan is to minimize the number of vehicles used. This paper discusses the challenge around this problem and applies the constructed framework to the resolution of this problem. The proposed model is generic; it allows to solve some variants of the problem where side constraints are required to be added.