An exact -constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits

Bérubé, Jean-François; Gendreau, Michel; Potvin, Jean-Yves

doi:10.1016/j.ejor.2007.12.014

Cited by 316 publications

(121 citation statements)

References 27 publications

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“…This method is one of the most well-known approaches for dealing with the multi-objective optimization problems, which solves such problems by transferring all the objective functions, except one, to the constraints at each stage. In fact, in this method, one of the objectives of the given problem is optimized as the main objective relative to the other objectives as constraints, which is called epsilon constraint (Ehrgott, 2005;Bérubé et al, 2009). This method was first developed by Haimes et al (1971) and, then, its details were described in Changkong and Haimes (1983) study.…”

Section: Solution and Resultsmentioning

confidence: 99%

Redesigning fruit and vegetable distribution network in Tehran using a city logistics model

Saeedi¹,

Teimoury²,

Makui³

2019

10.5267/j.dsl

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Tehran, as one of the most populated capital cities worldwide, is categorized in the group of highly polluted cities in terms of the geographical location as well as increased number of industries, vehicles, domestic fuel consumption, intra-city trips, increased manufacturing units, and in general excessive increase in the consumption of fossil energies. City logistics models can be effectively helpful for solving the complicated problems of this city. In the present study, a queuing theory-based bi-objective mathematical model is presented, which aims to optimize the environmental and economic costs in city logistics operations. It also tries to reduce the response time in the network. The first objective is associated with all beneficiaries and the second one is applicable for perishable and necessary goods. The proposed model makes decisions on urban distribution centers location problem. Subsequently, as a case study, the fruit and vegetable distribution network of Tehran city is investigated and redesigned via the proposed modelling. The results of the implementation of the model through traditional and augmented ε-constraint methods indicate the efficiency of the proposed model in redesigning the given network.

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Section: Solution and Resultsmentioning

confidence: 99%

Redesigning fruit and vegetable distribution network in Tehran using a city logistics model

Saeedi¹,

Teimoury²,

Makui³

2019

10.5267/j.dsl

View full text Add to dashboard Cite

show abstract

“…Paquete and Stützle (2003) develop a two-phase local search method and Jaszkiewicz and Zielniewicz (2009) consider a Pareto memetic algorithm using path relinking and Pareto local search. Jozefowiez et al (2008), Karademir (2008) and Bérubé et al (2009) consider a special traveling salesperson problem (TSP), TSP with profits. Jozefowiez et al approximate the nondominated frontier by an evolutionary algorithm (EA), Karademir proposes a genetic algorithm and Bérubé generates the nondominated frontier using the ε-constraint method (see Chankong and Haimes 1983).…”

Section: Generalized Biobjective Traveling Salesperson Problemmentioning

confidence: 99%

An interactive approach for biobjective integer programs under quasiconvex preference functions

Öztürk

Köksalan

2016

Ann Oper Res

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We develop an interactive algorithm for biobjective integer programs that finds the most preferred solution of a decision maker whose preferences are consistent with a quasiconvex preference function to be minimized. During the algorithm, preference information is elicited from the decision maker. Based on this preference information and the properties of the underlying quasiconvex preference function, the algorithm reduces the search region and converges to the most preferred solution progressively. Finding the most preferred solution requires searching both supported and unsupported nondominated points, where the latter is harder. We develop theory to further restrict the region where unsupported nondominated points may lie. We demonstrate the algorithm on the generalized biobjective traveling salesperson problem where there are multiple efficient edges between node pairs and show its performance on a number of randomly generated instances.

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“…Moreover, a Pareto-based approach could also support the identification of preferences by providing the decision-maker with a set of feasible, objectively equally-valued, highquality solutions as an excellent starting point for selecting the (subjectively) best solution. In the literature on Pareto-based approaches, there are few reports on exact algorithms for solving multi-objective problems (e.g., Dhaenens, Lemesre, and Talbi 2010, Bérubé, Gendreau, and Potvin 2009, Mezmaz, Melab, and Talbi 2007. However, the applicability of exact algorithms still is often limited to rather small instances.…”

Section: Multi-objective Optimization Approachesmentioning

confidence: 99%

GRASP with Hybrid Path Relinking for Bi-Objective Winner Determination in Combinatorial Transportation Auctions

Buer

Pankratz

2010

Bus Res

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An exact -constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits

Cited by 316 publications

References 27 publications

Redesigning fruit and vegetable distribution network in Tehran using a city logistics model

Redesigning fruit and vegetable distribution network in Tehran using a city logistics model

An interactive approach for biobjective integer programs under quasiconvex preference functions

GRASP with Hybrid Path Relinking for Bi-Objective Winner Determination in Combinatorial Transportation Auctions

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