Multi-objective mixed integer programming: An objective space algorithm

Pettersson, William; Özlen, Melih

doi:10.1063/1.5090006

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…In another study, Pettersson and Ozlen [2019] developed an algorithm for identifying all supported and non-supported NDPs with an arbitrary number of objectives. The algorithm first identifies a super-set (which contains the EF) using Benson's method, then modifies the set of polytopes so that no two polytopes have a nonempty intersection, and finally, refines the super-set to exclude portions that are not part of the EF.…”

Section: General Casementioning

confidence: 99%

On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

Fallah¹,

Ralphs²,

Boland³

2023

Preprint

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In this paper, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. We demonstrate that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF so that any description of the EF suffices to describe the RVF and vice versa. In the first part of the paper, we describe the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. Because of the close relationship of the RVF to the EF, we observe that methods for constructing so-called value functions and methods for constructing the EF of a multiobjective optimization problem, each of which have been developed in separate communities, are effectively interchangeable. By exploiting this relationship, we propose a generalized cutting plane algorithm for constructing the EF of a multiobjective MILP based on a generalization of an existing algorithm for constructing the classical value function. We prove that the algorithm is finite under a standard boundedness assumption and comes with a performance guarantee if terminated early.

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Section: General Casementioning

confidence: 99%

On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

Fallah¹,

Ralphs²,

Boland³

2023

Preprint

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“…Pettersson and Özlen (2019a) provide the first algorithm for MOMILPs with an arbitrary number of objectives. Using a multiobjective pure integer algorithm (improved version of the algorithm provided by Özlen et al (2014), see Section 3.5, with no‐good constraints (Soylu & Yıldız, 2016, above) and slices), they find integer solutions and subsequently polytopes of feasible integer parts via Benson's method that contain the integer solutions and cover the nondominated set.…”

Section: Algorithms For Multiobjective Mixed‐integer Optimization Pro...mentioning

confidence: 99%

Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

Halffmann

Schäfer

Dächert

et al. 2022

Multi Criteria Decision Anal

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We provide a comprehensive overview of the literature of algorithmic approaches for multiobjective mixed-integer and integer linear optimization problems. More precisely, we categorize and display exact methods for multiobjective linear problems with integer variables for computing the entire set of nondominated images. Our review lists 108 articles and is intended to serve as a reference for all researchers who are familiar with basic concepts of multiobjective optimization and who have an interest in getting a thorough view on the state-of-the-art in multiobjective mixedinteger programming.

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“…The MOMILP model is conventionally used when there is a need to solve more than two objective functions which involves both the discrete and continuous variables in the equations (Pettersson and Ozlen, 2019). This paper aims at solving two objective functions relating to economic and carbon emissions which needs to be optimized in different directions, i.e.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Investigating the effect of carbon tax on sharing network participation

Vimal

Raja

Yendeti

et al. 2022

JM2

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Purpose The purpose of this paper is to investigate the effect of current carbon tax (CT) policy on organizations involved in a sharing network relation. Design/methodology/approach For finding the CT and economic value of the industries connected in a sharing network model a multi-objective multi-integer linear model has been formulated. The data set of the case organization is used for computation. The formulated mathematical model is computed with the aid of GAMS optimization program. Findings This research paper demonstrates the effectiveness of the sharing network strategy in increasing the economic value and decreasing the CT for industries involved in sharing network. The CT value INR 3,012.694 for the industries in Scenario II which incorporates the sharing network is less than the CT INR 3,580.167 for industries in Scenario I without sharing network. Research limitations/implications The data used for the computation is based on a particular sharing network under investigation. The formulated mathematical model can be checked with similar sharing networks by varying the parameters. Practical implications This work can aid in gaining complete knowledge on the sharing network strategy which can uplift the resources and the monetary value of the non-efficient industries moving them towards sustainable and greener supply chain practices. Social implications The presented work can impact various industries in developing countries providing them with a strategy to enhance their resources and economic value by maintaining an amicable relation. Originality/value This work uniquely was able to validate economic feasibility and CT in accordance with the carbon footprint involved in sharing network. This sharing network also incorporates the concepts of circular economy and reverse logistics for showcasing a better strategy.

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Multi-objective mixed integer programming: An objective space algorithm

Cited by 7 publications

References 9 publications

On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

Exact algorithms for multiobjective linear optimization problems with integer variables: A state of the art survey

Investigating the effect of carbon tax on sharing network participation

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