Memetic algorithm for solving one-to-one shortest path problem

Abstract : The shortest path problem (SPP) is widely applied in different fields of application such as transportation, telecommunication and networks. It aims at determining the path between two points with the minimum associated/allocated resource (distance, time, cost…) in a directed or undirected graph. SPP has been well studied over the last 60 years, graph theory experts still endeavor to extract new variants of the basic problem in order to model and provide efficient solutions for several real life issues. Important forms of the SPP may be considered such as finding the shortest paths in a dynamic graph where the arcs’ weights vary as functions of time. Moreover, finding shortest paths subject to some additional constraints like fixing the maximum number of visited nodes or precising the nodes’ types, colors, etc. To deal with the SPP and its different variants, several algorithms have been developed since 1956. The standard solution to the one-to-one shortest path problem, which is the target of our study, is Dijkstra’s algorithm [1]. Its running time depends on the selected data structure. For the average case, one can get an O (|E|+|V|*log|V|) (|V| #Vertices, |E| #Edges). To deal with negative edge weight, we have the Bellman-Ford algorithm. SPP was also solved using MILP technique but its running time is usually higher than standard algorithms. MILP is widely used for solving many variants of SPP when standard algorithms fail for a lack of flexibility to cope with additional constraints but this usually leads to a significant execution time. In practice, several speed-up techniques have been proposed to reduce the search space such as bidirectional search, A* algorithm, preprocessing techniques, etc. Although, those techniques are efficient and fast enough, they become less performant when the size of the network becomes very large or when additional constraints are added such as dynamic arcs weight, multi-criteria paths optimization. To overcome such shortcomings, we believe that meta-heuristics such as GA, local search may be efficient candidates to give near optimal solutions within acceptable time.
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Omar Dib, Alexandre Caminada, Marie-Ange Manier. Memetic algorithm for solving one-to-one shortest path problem. 16ème conférence de la Société Française de Recherche Opérationnelle et Aide à la Décision (ROADEF 2015), Aix-Marseille Université, Feb 2015, Marseille, France. ⟨hal-01586879⟩

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