On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

Vérel, Sebástien; Liefooghe, Arnaud; Jourdan, Laëtitia; Dhaenens, Clarisse

doi:10.1016/j.ejor.2012.12.019

Cited by 92 publications

(120 citation statements)

References 20 publications

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“…Intuitively, if this is true for each objective of a multi-objective problem, it will be true for the multi-objective problem itself. This assumption in the multi-objective case is supported empirically by some studies [6,15,21,37,44], and to some extent by the results of this paper.…”

Section: Alternative Algorithmic Components For Anytime Optimizationsupporting

confidence: 70%

Anytime Pareto local search

Dubois-Lacoste

López-Ibáñez

Stützle

2015

European Journal of Operational Research

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Pareto Local Search (PLS) is a simple and effective local search method for tackling multi-objective combinatorial optimization problems. It is also a crucial component of many state-of-the-art algorithms for such problems. However, PLS may be not very effective when terminated before completion. In other words, PLS has poor anytime behavior. In this paper, we study the effect that various PLS algorithmic components have on its anytime behavior. We show that the anytime behavior of PLS can be greatly improved by using alternative algorithmic components. We also propose Dynagrid, a dynamic discretization of the objective space that helps PLS to converge faster to a good approximation of the Pareto front and continue to improve it if more time is available. We perform a detailed empirical evaluation of the new proposals on the bi-objective traveling salesman problem and the bi-objective quadratic assignment problem. Our results demonstrate that the new PLS variants not only have significantly better anytime behavior than the original PLS, but also may obtain better results for longer computation time or upon completion.

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Section: Alternative Algorithmic Components For Anytime Optimizationsupporting

confidence: 70%

Anytime Pareto local search

Dubois-Lacoste

López-Ibáñez

Stützle

2015

European Journal of Operational Research

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“…To this end, we plan to study the correlation between the main problem features and the algorithm performance through fitness landscapes analysis in multiobjective combinatorial optimization [35,51]. Last, we hope that the challenge proposed by multiobjective UBQP will gain the attention of other researchers.…”

Section: Discussionmentioning

confidence: 99%

“…The generation of correlated data follows a multivariate uniform law of dimension m [35]. In order to validate the behavior of the objective correlation coefficient experimentally, we conduct an empirical study for n = 18 in order to enumerate the decision space exhaustively.…”

Section: Problem Instancesmentioning

confidence: 99%

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Liefooghe

Vérel

Hao

2014

Applied Soft Computing

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The conventional Unconstrained Binary Quadratic Programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.

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“…Later, Verel et al [15] conducted a study on the landscape of local optima in such problems. Verel et al [16] proposed to carry out a priori analysis of a problem by evaluating the problem size, its epistasis, the number of objectives and the correlation values between objectives, to suggest the best way to tackle it. They concluded that, depending on the problem features, different types of algorithms (scalar or Pareto approach) and sizes of the solution archive should be employed.…”

Section: Related Workmentioning

confidence: 99%

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Pinheiro

Landa-Silva

Atkin

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Understanding the relationships between objectives in manyobjective optimisation problems is desirable in order to develop more effective algorithms. We propose a technique for the analysis and visualisation of complex relationships between many (three or more) objectives. This technique looks at conflicting, harmonious and independent objectives relationships from different perspectives. To do that, it uses correlation, trade-off regions maps and scatter-plots in a four step approach. We apply the proposed technique to a set of instances of the well-known multiobjective multidimensional knapsack problem. The experimental results show that with the proposed technique we can identify local and complex relationships between objectives, trade-offs not derived from pairwise relationships, gaps in the fitness landscape, and regions of interest. Such information can be used to tailor the development of algorithms.

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On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

Cited by 92 publications

References 20 publications

Anytime Pareto local search

Anytime Pareto local search

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

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