A memetic algorithm for a vehicle routing problem with backhauls

https://doi.org/10.1016/j.amc.2006.01.059Get rights and content

Abstract

This paper considers an extension of a vehicle routing problem with backhauls (VRPB). In this problem, a set of costumers are divided in two subsets consisting of linehaul and backhaul costumers. Each linehaul costumer requires delivering its demands from the depot. In addition, a specified quantity of products should be picked up from the backhaul nodes to the depot. The VRPB is a well-known NP-hard problem in strong sense and a number of algorithms are proposed for approximate solutions of such a hard problem. In this paper, a memetic algorithm (MA) is proposed which uses different local search algorithms to solve the VRPB. Exploiting power of memetic algorithm, inter and intra-route node exchanges are used as a part of this evolutionary algorithm. Extensive computational tests on some instances taken from the literature reveal the effectiveness of the proposed algorithm.

Introduction

This paper considers an extension of a vehicle routing problem with backhauls (VRPB). In this problem, a set of costumers are divided in two subsets consisting of linehaul and backhaul costumers. Each linehaul costumer requires delivering its demands from the depot. In addition, a specified quantity of products should be picked up from the backhaul nodes to the depot. A good example of this costumer set can be the grocery industry. An instance of this costumer partitioning is represented by the grocery industries. In this case, supermarkets and shops are the linehaul nodes and grocery suppliers are the backhaul nodes. In recent years, it is discovered that a great amount of savings have been achieved with combining the pickup/delivery context and exactly by visiting backhaul costumer along the distribution route. For example, the Interstate Commerce Commission estimated to save $160 million each year in USA grocery industries due to the introduction of backhauling [1].

More precisely, the VRPB can be defined as a problem of determining a set of vehicle routes visiting all costumers subject to the constraints as follows: (i) each vehicle performs just one route; (ii) for each route, the total load assigns to linehaul and backhaul node, in which should not separately exceed the vehicle capacity; (iii) one each route, backhaul nodes should be visited after all linehaul routes; and (iv) the total transportation cost should be minimized. The third condition (i.e., precedence constraint) generally puts here by the fact that in many applications, linehaul costumers have higher service priority than backhauls.

The model and algorithm presented here consider the heterogeneous fleet and associated networks can be symmetric or asymmetric. In the heterogeneous fleet, different type of vehicle with dissimilar capacities may be introduced. More over in symmetric networks, the distance between two nodes is same in two directions, whereas in asymmetric network this assumption does not hold. The VRPB is NP-hard in strong sense, since it generalizes the capacitated VRP arising when there is no backhaul node available.

Section snippets

Relevant literature

All previous researches from the literature have been considered only the homogeneous fleet version of the VRP. Toth and Vigo [2] developed a branch-and-bound algorithm in which a lower bound on the optimal solution is derived from a Lagrangean relaxation of some constraints of their linear programming (LP) formulation. Iteratively, the Lagrangean relaxation bound is further strengthened by adding valid inequalities in a cutting plane fashion. Yano et al. [3] developed a set covering based on

Mathematical model

In contrast to the previous researches, in this paper a heterogeneous VRPB model is presented. The proposed model considers different types of vehicles in the fleet in terms of the capacity and transportation cost. A mixed-integer programming (MIP) formulation of the problem is presented below.

Memetic algorithm for the VRPB

Memetic Algorithms (MAs) belong to the class of evolutionary algorithms (EAs) that apply a separate local search process to refine individuals (i.e. improve their fitness by hillclimbing). These methods are inspired by models of adaptation in natural systems that combine evolutionary adaptation of populations of individuals with individual learning within a lifetime. Additionally, MAs are inspired by Dawkin’s concept of a meme [15], which represents a unit of cultural evolution that can exhibit

Experiments and computational results

This section presents experimental results. Three experiments are carried out to test the performance of the proposed memetic algorithm (MA). The first experiment evaluates the effectiveness of using the nearest neighbor algorithm in order to generate the initial population. The second experiment examines the performance of MA in comparison with the mathematical programming method. Following tests investigate in functioning MA related to different heuristic algorithms that propose to solve the

Conclusion

In this paper, we have presented a memetic algorithm (MA) to solve the vehicle routing problem with backhaul (VRPB) and heterogeneous VRPB. The proposed algorithm used a greedy heuristic method to generate initial solutions in order to improve its performance in terms of the solution quality and computational time. The proposed MA employs different types of evolutionary operators such as PMX, OX, PBX, OBX, and several mutations which have already been applied for the traveling salesman problem

Acknowledgements

The authors would like to acknowledge the Iran National Science Foundation (INSF) for the financial support of this work. We would also thank the scholars who recommended and helped through the preparation of this paper.

References (20)

  • P. Toth et al.

    A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls

    European Journal of Operation Research

    (1999)
  • B.L. Golden, E. Baker, J. Alfaro, J. Schaffer, The vehicle routing problem with backhauling: two approaches. in: R....
  • P. Toth et al.

    An exact algorithm for the vehicle routing problem with backhauls

    Transportation Science

    (1997)
  • C.A. Yano et al.

    Vehicle routing at quality stores

    Interfaces

    (1987)
  • A. Mingozzi et al.

    An exact method for the vehicle routing problem with backhauls

    Transportation Science

    (1996)
  • I. Deif, L. Bodin, Extension of the Clarke and Wright algorithm for solving the vehicle routing problem with...
  • G. Clarke et al.

    Scheduling of vehicles from a central depot to a number of delivery points

    Operations Research

    (1964)
  • O. Casco, L. Golden, A. Wasil, Vehicle routing with back hauls: Models, algorithms, and case studies, in: L. Golden,...
  • M. Goeschalckx et al.

    The vehicle routing problem with backhauls

    European Journal of Operational Research

    (1989)
  • M. Goestschalckz, B. Jachobs, The vehicle routing problem with backhauls: properties and solution algorithms,...
There are more references available in the full text version of this article.

Cited by (51)

  • Vehicle routing with backhauls: Review and research perspectives

    2018, Computers and Operations Research
    Citation Excerpt :

    Experiments were conducted on the Gélinas et al. (1995) instances. The heterogeneous fleet variant of the VRPB was first studied by Tavakkoli-Moghaddam et al. (2006) who described a memetic algorithm and presented a mathematical formulation. This problem is an extension of the VRPB in which one must additionally decide on the fleet composition.

  • Memetic Extreme Learning Machine

    2016, Pattern Recognition
    Citation Excerpt :

    The local search strategy (e.g., Simulated Annealing [29] or Tabu Search [30]), is good at exploiting the neighborhood areas of an individual and obtains sufficient precision to find the local optimal value. In recent years, the potential of MA has been explored and exploited in various real-world applications, including clustering [31], optimization [32], vehicle routing problem [33] and extending wireless sensor network lifetime [34]. However, the advantage of MA for Extreme Learning Machine classification has received very little attention.

  • Fuzzy multi-objective programming algorithm for vehicle routing problems with backhauls

    2015, Expert Systems with Applications
    Citation Excerpt :

    In details of these metaheuristics, Osman and Wassan (2002) propose a reactive tabu search. Tavakkoli-Moghaddam et al. (2006) developed a memetic algorithm that uses different local search algorithms, and a mixed integer programming formulation is proposed. Ghaziri and ve Osman (2006) developed a self-organizing feature algorithm.

View all citing articles on Scopus
View full text