A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows

Abstract

The purpose of this paper is to present a new deterministic metaheuristic based on a modification of Variable Neighborhood Search of Mladenovic and Hansen (1997) for solving the vehicle routing problem with time windows. Results are reported for the standard 100, 200 and 400 customer data sets by Solomon (1987) and Gehring and Homberger (1999) and two real-life problems by Russell (1995). The findings indicate that the proposed procedure outperforms other recent local searches and metaheuristics. In addition four new best-known solutions were obtained. The proposed procedure is based on a new four-phase approach. In this approach an initial solution is first created using new route construction heuristics followed by route elimination procedure to improve the solutions regarding the number of vehicles. In the third phase the solutions are improved in terms of total traveled distance using four new local search procedures proposed in this paper. Finally in phase four the best solution obtained is improved by modifying the objective function to escape from a local minimum.

A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows

“…It is also important to mention that concurrent and independent work (e.g., Berger et al 2001;Bräysy 2001a, b;2003) have confirmed the main theses of this paper: the benefits of optimizing the number of vehicles and travel time independently, the value of hybrid approach, and the potential of large neighborhood search. This new generation of algorithms has, we believe, significantly enhanced our understanding of the local search approaches to the VRPTW.…”

“…Its travel times are, in general, much higher than ours, but the overall algorithm is a very interesting approach to finding high-quality solutions quickly (e.g., under two minutes). Bräysy (2003) proposes a sophisticated fourstage algorithm that extends the previous approach with variable and large neighborhood search. The algorithm focuses on producing high-quality solutions, but its results seem to be weaker than ours on the Solomon benchmarks.…”

A Variable Neighbourhood Search Algorithm with Compound Neighbourhoods for VRPTW

“…Constraint (11) defines the domain of the decision variable X k i j . Most researchers consider minimizing the number of vehicles as the primary objective (Bräysy, 2003), while others study it as a multi-objective problem (Ghoseiri and Ghannadpour, 2010). In the former case, a two-phase approach is often used, to minimize the vehicle number firstly and then minimize the distance with a fixed route number in the second phase.…”

Integrating packing and distribution problems and optimization through mathematical programming

“…With the additional requirement that the total demand on a route cannot exceed the capacity of the corresponding vehicle we get the Capacitated Vehicle Routing Problem (CVRP) (Frutos & Tohmé, 2012;Kao et al, 2013;Sitek, 2014). In turn, CVRP with Time Windows (CVRPTW) is the CVRP with the added constraint that each customer has a time window for delivery (Bräysy, 2003). In the case of single depot, the CVRPTW requires to find m routes (one for each vehicle) such that: (i) each route starts and ends at the depot, (ii) each customer is visited by just one vehicle, (iii) the total demand on a route does not exceed the capacity of the vehicle serving it, (iv) the departure and arrival times at the depot fall inside a given time window, and (v) the total cost (distance plus the penalties for violating the time windows of the customers) are minimal.…”

“…If capacity is measured only on a single dimension, the problem of loading and distributing cargo in a fleet of vehicles would be represented by CVRPTW (Bräysy, 2003). But real world goods have several features each of which corresponds to a dimension of capacity, e.g.…”