A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

Kirlik, Gokhan; Sayın, Serpil

doi:10.1016/j.ejor.2013.08.001

Cited by 132 publications

(129 citation statements)

References 18 publications

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“…Our key performance metric is the time to enumerate the complete set of nondominated solutions. We compare our approach with another general-purpose MODO solver developed by Kirlik and Sayın [23], an -constraint scalarization method which is currently regarded as one of the state of the art approaches for MODOs. We note in passing that we have also investigated other MODO solvers, such as the one proposed byÖzlen et al [29], but the method by Kirlik and Sayın was the best performing and numerically stable method across all solvers tested in our empirical setting.…”

Section: Numerical Studymentioning

confidence: 99%

“…We generated 10 instances per pair (n, p). Table 1 presents the average cardinalities of the nondominated sets (|Y N |) and average solution times (within solved instances) for p = 3, 4, 5, where Kirlik and BDD denotes the method by Kirlik and Sayın [23] and the BDD technique, respectively. Figure 2(a) depicts a scatter plot comparing solution times for all instances, where the size of a point is proportional to n. The BDD method is substantially faster and more robust than Kirlik, in particular when p is large.…”

Section: Numerical Studymentioning

confidence: 99%

“…We generated random MKP instances following the procedure by Kirlik and Sayın [23]. The values v j i and w i were drawn uniformly at random from the set {1, .…”

Section: Numerical Studymentioning

confidence: 99%

“…The -constraint method was first used by Laumanns et al [24], where an adaptive search over weighted objectives was proposed.Özlen et al [27,29] and Kirlik and Sayın [23] provide algorithmic improvements and are the basis for the comparison in the computational results presented in this paper. Other utilized scalarization techniques include Benson's method [3] (a combination of the weight-sum technique and theconstraint method) and the augmented weighted Chebychev method [32].…”

Section: Introductionmentioning

confidence: 99%

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Multiobjective Optimization by Decision Diagrams

Bergman

Ciré

2016

Lecture Notes in Computer Science

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Always cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the author manuscript from TSpace because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page.This article was made openly accessible by U of T Faculty. Please tell us how this access benefits you. Your story matters. Abstract. In this paper we present a technique for solving multiobjective discrete optimization problems using decision diagrams. The proposed methodology is related to an algorithm designed for multiobjective optimization for dynamic programming, except utilizing decision diagram theory to reduce the state space, which can lead to orders of magnitude performance gains over existing algorithms. The decision diagrambased technique is applied to knapsack, set covering, and set partitioning problems, exhibiting improvements over state-of-the-art general-purpose multiobjective optimization algorithms. Multiobjective Optimization by Decision Diagrams

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Section: Numerical Studymentioning

confidence: 99%

Section: Numerical Studymentioning

confidence: 99%

“…We generated random MKP instances following the procedure by Kirlik and Sayın [23]. The values v j i and w i were drawn uniformly at random from the set {1, .…”

Section: Numerical Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiobjective Optimization by Decision Diagrams

Bergman

Ciré

2016

Lecture Notes in Computer Science

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“…Laumanns et al (2006) as well as the follow-up work of Dhaenens et al (2010), Kirlik and Sayın (2014) and Boland et al (2014a) do not compute a representation of the nondominated set but aim at finding the exact nondominated set. Their method fixes one coordinate, projects the p-dimensional outcome space onto the remaining (p − 1)-dimensional space and partitions the projection by means of boxes into a grid.…”

Section: Definitionmentioning

confidence: 99%

A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

Kühn

Ruzika

2016

J Glob Optim

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Abstract. A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondominated points only, ideas to calculate bounds for the representation error are given. Moreover, the incorporation of domination during the algorithm and other quality measures are discussed.

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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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A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

Cited by 132 publications

References 18 publications

Multiobjective Optimization by Decision Diagrams

Multiobjective Optimization by Decision Diagrams

A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

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

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