Multi-start heuristics for the Two-Echelon Vehicle Routing Problem

In this paper we address the Two-Echelon Vehicle Routing Problem (2E-VRP), an extension of the classical Capacitated VRP, where the delivery from a single depot to the customers is managed by routing and consolidating the freight through intermediate depots called satellites. We present a family of Multi-Start heuristics based on separating the depot-to-satellite transfer and the satellite-to-customer delivery by iteratively solving the two resulting routing subproblems, while adjusting the satellite workloads that link them. The common scheme on which all the heuristics are based consists in, after having found an initial solution, applying a local search phase, followed by a diversification; if the new obtained solutions are feasible, then local search is applied again, otherwise a feasibility search procedure is applied, and if it successful, the local search is applied on the newfound solution. Different diversification strategies and feasibility search rules are proposed. We present computational results on a wide set of instances up to 50 customers and 5 satellites and compare them with results from the literature, showing how the new methods outperform previous existent methods, both in efficiency and accurac

A Reactive GRASP with Path Relinking for the Two-Echelon Vehicle Routing Problem

We propose a meta-heuristic based on GRASP combined with Path Relinking to address the Two-Echelon Vehicle Routing Problem, an extension of the Capacitated Vehicle Routing Problem in which the delivery from a single depot to customers is achieved by routing and consolidating the freight through intermediate depots called satellites. The problem is treated by separating the depot-to-satellite transfer and the satellite-to-customer delivery, and iteratively solving the two resulting routing subproblems, while adjusting the satellite workloads that link them. The meta-heuristic scheme consists of applying a GRASP and a local search procedures in sequence. Then, the resulting solution is linked to an elite solution by means of a Path Relinking procedure. To escape from infeasible solutions, which are quite common in this kind of problem, a feasibility search procedure is applied within Path Relinking. Extensive computational results on instances with up to 50 customers and 5 satellites show that the meta-heuristic is able to improve literature results, both in efficiency and accurac

L'intégration des joueurs de football africains en Suisse

A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path-relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path-relinking) and the GRASP with path-relinking illustrates the effectiveness of path-relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem

An annotated bibliography of GRASP - Part I: Algorithms

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the first of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. This paper covers algorithmic aspects of GRASP

A Parallel GRASP for MAX-SAT Problems

The weighted maximum satisfiability (MAX-SAT) problem is central in mathematical logic, computing theory, and many industrial applications. In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for solving MAX-SAT problems. Experimental results indicate that almost linear speedup is achieved

Speeding up continuous GRASP

Continuous GRASP (C-GRASP) is a stochastic local search metaheuristic for finding cost-efficient solutions to continuous global optimization problems subject to box constraints (Hirsch et al., 2007). Like a greedy randomized adaptive search procedure (GRASP), a C-GRASP is a multi-start procedure where a starting solution for local improvement is constructed in a greedy randomized fashion. In this paper, we describe several improvements that speed up the original C-GRASP and make it more robust. We compare the new C-GRASP with the original version as well as with other algorithms from the recent literature on a set of benchmark multimodal test functions whose global minima are known. Hart's sequential stopping rule (1998) is implemented and C-GRASP is shown to converge on all test problems.GRASP Continuous GRASP Global optimization Multimodal functions Continuous optimization Heuristic Stochastic algorithm Stochastic local search Nonlinear programming