A set-covering based heuristic algorithm for the periodic vehicle routing problem

We present a hybrid optimization algorithm for mixed-integer linear programming, embedding both heuristic and exact components. In order to validate it we use the periodic vehicle routing problem (PVRP) as a case study. This problem consists of determining a set of minimum cost routes for each day of a given planning horizon, with the constraints that each customer must be visited a required number of times (chosen among a set of valid day combinations), must receive every time the required quantity of product, and that the number of routes per day (each respecting the capacity of the vehicle) does not exceed the total number of available vehicles. This is a generalization of the well-known vehicle routing problem (VRP). Our algorithm is based on the linear programming (LP) relaxation of a set-covering-like integer linear programming formulation of the problem, with additional constraints. The LP-relaxation is solved by column generation, where columns are generated heuristically by an iterated local search algorithm. The whole solution method takes advantage of the LP-solution and applies techniques of fixing and releasing of the columns as a local search, making use of a tabu list to avoid cycling. We show the results of the proposed algorithm on benchmark instances from the literature and compare them to the state-of-the-art algorithms, showing the effectiveness of our approach in producing good quality solutions. In addition, we report the results on realistic instances of the PVRP introduced in Pacheco et al. (2011) [24] and on benchmark instances of the periodic traveling salesman problem (PTSP), showing the efficacy of the proposed algorithm on these as well. Finally, we report the new best known solutions found for all the tested problems

Variable Neighborhood Search for Robust Optimization and Applications to Aerodynamics

Abstract. Many real-life applications lead to the definition of robust optimization problems where the objective function is a black box. This may be due, for example, to the fact that the objective function is evaluated through computer simulations, and that some parameters are uncertain. When this is the case, existing algorithms for optimization are not able to provide good-quality solutions in general. We propose a heuristic algorithm for solving black box robust optimization problems based on the minimax formulation of the problem. We also apply this algorithm for the solution of a wing shape optimization where the objective function is a computationally expensive black box. Preliminary computational experiments are reported.

Multiple Variable Neighborhood Search Enriched with ILP Techniques for the Periodic Vehicle Routing Problem with Time Windows

In this work we extend a VNS for the periodic vehicle routing problem with time windows (PVRPTW) to a multiple VNS (mVNS) where several VNS instances are applied cooperatively in an intertwined way. The mVNS adaptively allocates VNS instances to promising areas of the search space. Further, an intertwined collaborative cooperation with a generic ILP solver applied on a suitable set covering ILP formulation with this mVNS is proposed, where the mVNS provides the exact method with feasible routes of the actual best solutions, and the ILP solver takes a global view and seeks to determine better feasible route combinations. Experimental results were conducted on newly derived instances and show the advantage of the mVNS as well as of the hybrid approach. The latter yields for almost all instances a statistically significant improvement over solely applying the VNS in a standard way, often requiring less runtime, too

An ELSxPath Relinking Hybrid for the Periodic Location-Routing Problem

International audienceThe well-known Vehicle Routing Problem (VRP) has been deeply studied over the last decades. Nowadays, generalizations of VRP are developed toward tactical or strategic decision levels of companies. The tactical extension plans a set of trips over a multiperiod horizon, subject to frequency constraints. The related problem is called the Periodic VRP (PVRP). On the other hand, the strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems. Low-quality solutions are obtained if depots are located first, regardless the future routes. In the Location-Routing Problem (LRP), location and routing decisions are simultaneously tackled. The goal here is to combine the PVRP and LRP into an even more realistic problem covering all decision levels: the Periodic LRP or PLRP. A hybrid evolutionary algorithm is proposed to solve large size instances of the PLRP. First, an individual representing an assignment of customers to combinations of visit days is randomly generated. Then, a heuristic based on the Randomized Extended Clarke and Wright Algorithm (RECWA) creates feasible solutions. The evolution operates through an Evolutionary Local Search (ELS) on visit days assignments. The algorithm is hybridized with a Path Relinking between individuals from an elite list. The method is evaluated on three sets of instances and solutions are compared to the literature on particular cases such as one-day horizon (LRP) or one depot (PVRP). This metaheuristic outperforms the previous methods for the PLRP