An integration of Lagrangian split and VNS: The case of the capacitated vehicle routing problem

Abstract

In this paper, we propose an efficient and novel Lagrangian relaxation method which incorporates a new integer linear programming (ILP) formulation to optimally partition a giant tour in the context of a capacitated vehicle routing problem (CVRP). This approach, which we call Lagrangian split (Ls), is more versatile than the ILP which, in most cases, can be intractable using a conventional solver. An effective repair mechanism followed by a local search are also embedded into the process. The mathematical validity of the repair mechanism and its time complexity are also provided. An integration of Ls into a powerful variable neighbourhood search (VNS) is also presented. Computational experiments are conducted to demonstrate that Ls provides encouraging results when applied on benchmark instances and that the integration of Ls into a metaheuristic scheme produces good results when compared to those found by state-of-the-art methods.

Heurística de Busca de Vizinhança Variável para Otimização do Problema de Roteamento de Veículos

“…No trabalho apresentado em [7] é introduzido um algoritmo de otimização baseado em reatores químicos, combinado com um algoritmo de busca tabu unificada adaptável. Em [8] foi desenvolvido uma nova estratégia de divisão de rotas e a integrou com busca de vizinhança variável.…”

Depot Location Analysis for Capacitated Vehicle Routing Problem: A Case Study of Solid Waste Management

“…1, 2,..., kK = is available at the depot to either collect or deliver demand as the case maybe Z is the number of depot, q is the quantity of demand at a customer point. A route is established by the summation of multiple links [1,[13][14][15][16]. A link is formed with the notation k ij P which moves from customer i through to customer j , by a vehicle k, where the decision variables are dependent of the vehicle capacity and the customer demand which are modelled as follows [1]:…”

An efficient meta-heuristic algorithm for solving capacitated vehicle routing problem

“…[11] propose a two-stage, shape-based clustering approach to decompose the problem into smaller subproblem and employ Concorde TSP solver to generate routes for each individual cluster separately. Bouzid & Hacene [12] integrate Lagrangian Split with powerful variable neighborhood search and yield competitive result. The Lagrangian Split used to generate good quality initial solution and improve the local search performance for the VNS.…”