A Metaheuristic to Solve a Location-Routing Problem with Non-Linear Costs

Abstract

The paper deals with a location-routing problem with non-linear cost functions. To the best of our knowledge, a mixed integer linear programming formulation for the addressed problem is proposed here for the first time.Since the problem is NP-hard exact algorithms are able to solve only particular cases, thus to solve more general versions heuristics are needed. The algorithm proposed in this paper is a combination of a p-median approach to find an initial feasible solution and a metaheuristic to improve the solution. It is a hybrid metaheuristic merging Variable Neighborhood Search (VNS) and Tabu Search (TS) principles and exploiting the synergies between the two. Computational results and conclusions close the paper.

A solution method for a two-layer sustainable supply chain distribution model

“…A presentation of these different solution approaches to distribution system models is provided in Table 1. Marinakis and Marinaki (2008b) Hybrid particle swarm optimisation; multiple phase neighbourhood search -greedy randomized adaptive search procedure Yang and Zi-Xia (2009) Sequential and iterative procedure using particle swarm optimisation Liu et al (2012) Multi-objective particle swarm optimisation combined with grey relational analysis and entropy weight Gendreau et al (1994) Tabu search heuristic with a generalised insertion procedure Tuzun and Burke (1999) Two-phase Tabu search algorithm coded in C Chiang and Russell (2004) Set partitioning approach and tabu search algorithm Melechovský et al (2005) p-median approach to find an initial feasible solution and a meta-heuristic integrating variable neighbourhood search and Tabu search to improve the solution Albareda-Sambola et al (2005) Tabu search metaheuristic solution with CPLEX 6.5 solver Lin and Kwok (2006) A combined Tabu search and simulated annealing metaheuristics Caballero et al (2007) Multi-objective combinatorial optimisation based on tabu search Russell et al (2008) Reactive Tabu search method based metaheuristics approach Schwardt and Fischer (2009) A neural network approach based on a self-organising map Lin et al (2002) Metaheuristics approach based on threshold accepting and simulated annealing Wu et al (2002) Simulated annealing Yu et al (2010) Simulated annealing Stenger et al (2012) Simulated annealing Prins et al (2006a) Greedy randomised adaptive search procedure Duhamel et al (2010) Greedy randomised adaptive search procedure Nguyen et al (2012) Greedy randomised adaptive search procedure Ghodsi and Amiri (2010) Variable neighbourhood search algorithm Derbel et al (2011) Variable neighbourhood search algorithm Bell and McMullen (2004) Ant colony optimisation Bin et al (2009) Ant colony optimisation Ting and Chen (2012) Ant colony optimisation Hwang (2002) Genetic algorithm Prins et al (2006b) Genetic algorithm Zhou and Liu (2007) Genetic algorithm Marinak...…”

A case analysis of a sustainable food supply chain distribution system—A multi-objective approach

“…Lin et al (2002), Yu et al (2010), Stenger et al (2012). Greedy randomised adaptive search optimisation Prins et al (2006), Duhamel et al (2010), Nguyen et al (2012) Variable neighbourhood search optimisation Melechovský et al (2005), Ghodsi and Amiri (2010), Derbel et al (2011) Genetic algorithms Zhou and Liu (2007), , Jin et al (2010), Karaoglan and Altiparmak (2010) Branch and cut optimisation Belenguer et al (2011), Karaoglan et al (2011) Mixed-integer programming; Integer linear programming Alumur and Kara (2007), Diabat and Simchi-Levi (2009);Laporte et al (1989); Ambrosino and Scutella (2005) …”

A Heuristic Based Approach to Solve a Capacitated Location-routing Problem

“…Wu et al, (2002) decompose the standard LRP with capacitated depots into a facility location-allocation Problem and a vehicle routing problem, and try then to solve both subproblems using simulated annealing. Melechovsky et al (2005) address an LRP with nonlinear depot costs that grow with the total demand satisfied by the depots. They present a hybrid metaheuristic method consisting of tabu search and variable neighborhood search heuristics.…”