An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows

Abstract

This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality initial solutions are generated by means of a savings-based heuristic that combines diversification strategies with learning mechanisms. In Phase 2, an attempt is made to reduce the number of routes in the initial solution with a new local search procedure. In Phase 3, the solution from Phase 2 is further improved by a set of four local search operators that are embedded in a deterministic annealing framework to guide the improvement process. Some new implementation strategies are also suggested for efficient time window feasibility checks. Extensive computational experiments on the 168 benchmark instances have shown that the suggested method outperforms the previously published results and found 167 best-known solutions. Experimental results are also given for the new problem variant.

A deterministic annealing algorithm for the pre- and end-haulage of intermodal container terminals

“…Applications of DA to vehicle routing problems can be found amongst others in Tarantilis et al (2004) and Bräysy et al (2008). DA is applied to the problem formulation described in this paper based on the implementation strategy of Bräysy et al (2008).…”

“…DA is applied to the problem formulation described in this paper based on the implementation strategy of Bräysy et al (2008). The final solution of the multistart local search heuristic serves as initial solution for the DA algorithm, presented in Algorithm 1.…”

A Solution for the Bi-Objective Vehicle Routing Problem With Time Windows Using Local Search and Genetic Algorithms

“…The fleet size and mix vehicle routing problem with time windows (FSMVR PTW) is a specific problem of the classic vehicle routing problem. Solutions are proposed by Belfiore and Fávero (2007), Bräysy et al (2008), Dell'Amico et al (2007), Dullaert et al (2002) and Repoussis and Tarantilis (2010). In Solomon's paper, the time-oriented nearest neighbor insertion heuristic has shown to be very successful.…”

Simulation and optimisation of intermodal barge transport networks

“…However, when a solution is required in a shorter time span, the number of moves evaluated by the local search operators could be reduced. Bräysy et al (2008) propose to focus only on moves that involve customers that are close to each other. In order to define closeness, a distance limit is initialized in the first solution and updated during the search.…”

“…The authors allow to reset the threshold to its maximum value. A further extension of this DA approach is applied to the fleet size and mix vehicle routing problem with time windows by Bräysy et al (2008). Cho and Wang (2005) …”