The bi-objective mixed capacitated general routing problem with different route balance criteria

Halvorsen-Weare, Elin Espeland

doi:10.1016/j.ejor.2015.11.024

Cited by 33 publications

(14 citation statements)

References 46 publications

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“…In the cases when the approximation of the Pareto front are discontinuous, the nondominated solutions are polarized in the extreme of the regions; that is, the solutions are very good for one objective function but very bad for the other objective function (this can be seen from Figures 2-11). In addition, the obtained approximation of the Pareto front is nonconvex for almost all the tested instances and, as remarked by [71], the number of nondominated solutions obtained depends on the manner that the workload balance objective is modeled. In this paper, we modeled it aiming to have a workload with less deviation from a target value (the one associated with the equally balanced case).…”

Section: Discussionmentioning

confidence: 94%

“…Some regions without nondominated solutions are observed. As reported by [71], depending on the modeling approach for balancing workload, it is possible to find less number of solutions for the approximated Pareto front. They tested four different schemes to model the workload balance objective function for a capacitated vehicle routing problem and results show that the number of Pareto optimal solutions varies substantially.…”

Section: Computational Experimentation and Resultsmentioning

confidence: 99%

“…If no significant increase in the number of nondominated solutions is obtained, we may experimentally conclude the discontinuity. Moreover, different modeling approaches to balance the workload can be used (as in [71]). By doing the latter, we may theoretically evaluate their appropriateness and applicability to the production-distribution problem considered in this paper.…”

Section: Discussionmentioning

confidence: 99%

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Optimizing a Biobjective Production‐Distribution Planning Problem Using a GRASP

et al. 2018

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This paper addresses a biobjective production-distribution planning problem. The problem is formulated as a mixed integer programming problem with two objectives. The objectives are to minimize the total costs and to balance the total workload of the supply chain, which consist of plants and depots, considering that it represents a company vertically integrated. In order to solve the model, we propose an adapted biobjective GRASP to obtain an approximation of the Pareto front. To evaluate the performance of the proposed algorithm, numerical experimentations are conducted over a set of instances used for similar problems. Results indicate that the proposed GRASP obtains a relatively small number of nondominated solutions for each tested instance in very short computational time. The approximated Pareto fronts are discontinuous and nonconvex. Moreover, the solutions clearly show the compromise between both objective functions.

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Section: Discussionmentioning

confidence: 94%

Section: Computational Experimentation and Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Optimizing a Biobjective Production‐Distribution Planning Problem Using a GRASP

et al. 2018

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“…To define the objective function whose purpose is balancing the routes in Halvorsen and Savelsbergh (2016) and Schwarze and Voß (2013), different approaches available in the literature are describe that include load-balance VRP modifications. In all the cases, lr, lt and lu are the lengths of the routes r, t and u, that belong to the set of routes T, being |T| the number of routes in the solution and l the average route length.…”

Section: Objective Function For Route Balancingmentioning

confidence: 99%

“…The objective function (9) is formulated considering (Halvorsen, Savelsbergh, 2016) and the minimization of the standard deviation of the distance traveled by every route in the solution, where µ is the average distance of every route in the solution and lr is the length of every route. A greater computational effort is required to calculate the mean due to the need of knowing the length of all the routes in the solution; however, better results are obtained.…”

Section: Variablesmentioning

confidence: 99%

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

Galindres-Guancha¹,

Toro-Ocampo²,

Rendón³

2018

10.5267/j.ijiec

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The multi-objective problem of multi-depot vehicle routing (MOMDVRP) is proposed by considering the minimization of the traveled arc costs and the balance of routes. Seven mathematical models were reviewed to determine the route balance equation and the bestperforming model is selected for this purpose. The solution methodology consists of three stages; in the first one, beginning solutions are built up by means of a constructive heuristic. In the second stage, fronts are constructed from each starting solution using the iterated local search multi-objective metaheuristics (ILSMO). In the third stage, we obtain a single front by using concepts of dominance, taking as a base the fronts of the previous stage. Thus, the first two fronts are taken and a single front is formed that corresponds to the current solution of the problem; next the third front is added to the current Pareto front of the problem, the procedure is repeated until exhaustion of the list of the fronts initially obtained. The resulting front is the solution to the problem. To validate the methodology we use instances from the specialized literature, which have been used for the multi-depot routing problem (MDVRP). The results obtained provide very good quality. Finally, decision criteria are used to select the most appropriate solution for the front, both from the point of view of the balance and the route cost.

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An updated annotated bibliography on arc routing problems

Mourão

Pinto

2017

Networks

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The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post‐disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 144–194 2017

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The bi-objective mixed capacitated general routing problem with different route balance criteria

Cited by 33 publications

References 46 publications

Optimizing a Biobjective Production‐Distribution Planning Problem Using a GRASP

Optimizing a Biobjective Production‐Distribution Planning Problem Using a GRASP

Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic

An updated annotated bibliography on arc routing problems

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