Solution of a Min-Max Vehicle Routing Problem

Applegate, David; Cook, William J.; Dash, Sanjeeb; Rohe, André

doi:10.1287/ijoc.14.2.132.118

Cited by 98 publications

(58 citation statements)

References 17 publications

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“…Their paper presents lower bounds, an insertion heuristic and a local search procedure. Maximal arrival time minimization is also addressed by Applegate et al [3] via a branch-and-cut algorithm, while Hemel et al [38] solve a practical problem aiming at minimizing the maximal tour length, using the average arrival time to break ties. Dell et al add a multi-period horizon and equity constraints [27].…”

Section: Context and Problems Related To The Mt-ccvrpmentioning

confidence: 99%

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

2014

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The multitrip cumulative capacitated vehicle routing problem (mt-CCVRP) is a non-trivial extension of the classical CVRP: the goal is to minimize the sum of arrival times at demand nodes and each vehicle may perform several trips. Applications of this NP-hard problem can be found in disaster logistics and maintenance operations. Contrary to the CVRP, the cost of a solution varies if a trip is reversed or if its rank in a multitrip is changed. Moreover, evaluating local search moves in constant time is not obvious. This article presents a mixed integer linear program (MILP), a dominance rule, and a hybrid metaheuristic: a multi-start iterated local search (MS-ILS) calling a variable neighborhood descent with O(1) move evaluations. On three sets of instances, MS-ILS obtains good solutions, not only on the mt-CCVRP, but also on the cumulative CVRP where it competes with four existing algorithms. Moreover, the metaheuristic retrieves the optimal solutions of the MILP, which can be computed for small instances using a commercial solver.

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Section: Context and Problems Related To The Mt-ccvrpmentioning

confidence: 99%

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

2014

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“…However, within the instance generation for 2-opt in [6] it is accounted for randomness by using several different ini- tial tours. OP T (I) is obtained by using the exact TSP solver Concorde [1]. In order to evolve easy and hard instances for approximation algorithms, we use the evolutionary algorithm introduced by Mersmann et al [6].…”

Section: Hard and Easy Instance Generationmentioning

confidence: 99%

“…Cities are generated in [0, 1] 2 and placed on a discretised grid enabling cross comparison of features. Instances with varying difficulty levels in between easy and hard are generated by a sophisticated morphing strategy which includes a heuristic point matching strategy between easy and hard instances and computes convex combinations of the respective points of both instance classes.…”

Section: Convex Hull Featuresmentioning

confidence: 99%

A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem

Nallaperuma

Wagner

Neumann

et al. 2013

Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII

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Understanding the behaviour of well-known algorithms for classical NP-hard optimisation problems is still a difficult task. With this paper, we contribute to this research direction and carry out a feature based comparison of local search and the well-known Christofides approximation algorithm for the Traveling Salesperson Problem. We use an evolutionary algorithm approach to construct easy and hard instances for the Christofides algorithm, where we measure hardness in terms of approximation ratio. Our results point out important features and lead to hard and easy instances for this famous algorithm. Furthermore, our cross-comparison gives new insights on the complementary benefits of the different approaches.

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“…An evolutionary programming method has been proposed by Kota and Jarmai (2015) to solve mTSP. The swarm intelligence techniquebased ACO (Applegate et al 2002;Dorigo and Gambardella 1997a, b) has been first applied to TSP which is based on the foraging strategies of ants. The basic idea underlying this ant-based algorithm is to use a positive feedback mechanism, based on an analogy with the pheromone-laying, pheromone-following behaviour of some species of ants and some other social insects.…”

Section: Introductionmentioning

confidence: 99%

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

Changdar

Pal

Mahapatra³

2016

Soft Comput

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In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely 'refinement'. In this paper, we have utilized cyclic crossover and two-point's mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate Communicated by V. Loia. B Chiranjit Changdar chiranjit_changdar@yahoo.co.in Rajat Kumar Pal crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made.

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Solution of a Min-Max Vehicle Routing Problem

Cited by 98 publications

References 17 publications

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem

A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

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