A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems

Zhang, Weihua; Reimann, Marc

doi:10.1016/j.ejor.2013.09.001

Cited by 86 publications

(40 citation statements)

References 18 publications

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“…Recently several prodedures have been described in literature to generate efficient solutions of integer programming problems for a larger number of objectives where all coefficients have integer values (or can be transformed to them), see Lokman and Köksalan [2013], Mavrotas and Florios [2013], Ozlen et al [2014], Zhang and Reimann [2014]. In the problem we consider this is not necessarily the case.…”

Section: Problem Descriptionmentioning

confidence: 97%

“…Needless to say that this target requires far less steps from an optimization problem that does not increase in size. Mavrotas and Florios [2013] and [Zhang and Reimann, 2014] elaborate further on the augmented -contraint method that is designed to deal with many objectives in an integer programming environment. Essential is the idea that the problem is converted in a problem with integer coefficients, such that the step sizes can be taken as one.…”

Section: Comparison With Other Algorithmsmentioning

confidence: 99%

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Bi-criterion procedures to support logistics decision making: cost and uncertainty

Rijpkema

Hendrix

Rossi

2015

Journal of the Operational Research Society

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In practical decision making, one often is interested in solutions that balance multiple objectives. In this study we focus on generating efficient solutions for optimization problems with two objectives and a large but finite number of feasible solutions. Two classical approaches exist, being the constraint method and the weighting method, for which a specific implementation is required for this problem class. This paper elaborates specific straightforward implementations and applies them to a practical allocation problem, in which transportation cost and risk of shortage in supplied livestock quality are balanced.The variability in delivered quality is modelled using a scenario-based model that exploits historical farmer quality delivery data. The behaviour of both implementations is illustrated on this specific case, providing insight in i.) the obtained solutions, ii.) their computational efficiency. Our results indicate how efficient trade-offs in bi-criterion problems can be found in practical problems.

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Section: Problem Descriptionmentioning

confidence: 97%

Section: Comparison With Other Algorithmsmentioning

confidence: 99%

Bi-criterion procedures to support logistics decision making: cost and uncertainty

Rijpkema

Hendrix

Rossi

2015

Journal of the Operational Research Society

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“…On the other hand, despite its advantages, the ε-constraint method has also some weaknesses that have been addressed in the literature (Mavrotas, 2009;Zhang & Reimann, 2014). Among them we can cite the generation of dominated solutions.…”

Section: Multi-objective Approachmentioning

confidence: 99%

“…This wastes time and computational effort. Because of this problem, some authors have proposed modifications in order to overcome it, like in Zhang and Reimann (2014) or in Mavrotas (2009). The former method, called the augmented ε-constraint method (AUGMECON), which was later improved in Mavrotas and Florios (2013), is the one that we will use in this paper.…”

Section: Multi-objective Approachmentioning

confidence: 99%

An application of the augmented ε-constraint method to design a municipal sorted waste collection system

Rossit¹,

Tohmé²,

Frutos³

et al. 2017

10.5267/j.dsl

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The separation at the source of Municipal Solid Waste (MSW) is an initiative that facilitates the subsequent recycling work and contributes to palliate the negative impacts of the traditional unsorted collection system. This paper presents a multi-objective integer linear programming model of the determination of the optimal location of assorted waste bins in an urban area. We consider, jointly, the objectives of minimizing the investment cost and the average distance from the dwellings to the bins. The model was applied in simulated instances of an Argentinian medium-size city, contributing to the transition from the current door-to-door based system to a community bins system. To solve this problem, we apply both the weighting method, which has been used to solve similar problems in the literature, and a novel version of the augmented ε-constraint method (AUGMECON2). The results over simulated scenarios show that, in general, AUGMECON2 has a better performance, yielding a larger number of efficient solutions at lower computation times.Growing Science Ltd. All rights reserved. 7

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“…Also, the cost of running multiple executions for the related single-objective problem treated is not elevated, since the algorithm proposed is significantly fast although a mutiobjective extension of the methodology will be investigated in the future introducing specific constructive and local searches for each of the objectives. Other improved -constraint methods especially suitable for Multiobjective Integer Programming (MOIP) problems have been proposed in [18][19][20].…”

Section: The Proposed Algorithmmentioning

confidence: 99%

An Interactive Biobjective Method for Solving a Waste Collection Problem

Delgado-Antequera

Pérez²,

Hernández-Díaz³

et al. 2016

Mathematical Problems in Engineering

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The aim of this paper is to propose a framework in order to solve the real-world waste collection problem in a city of southern Spain modeled as an Asymmetric Vehicle Routing Problem (AVRP) with side constraints and several variations. In this problem, not only are vehicle capacity and temporal constraints considered but multiple trips are also allowed. Furthermore, two objectives will be considered: the minimization of the total distance and the balance of the working day. Finally, in order to select a single solution among all efficient (or nondominated) solutions, an interactive method is designed using reference points.

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A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems

Cited by 86 publications

References 18 publications

Bi-criterion procedures to support logistics decision making: cost and uncertainty

Bi-criterion procedures to support logistics decision making: cost and uncertainty

An application of the augmented ε-constraint method to design a municipal sorted waste collection system

An Interactive Biobjective Method for Solving a Waste Collection Problem

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