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European Journal of Operational Research 000 (2014) 1–2
Contents lists available at ScienceDirect
European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor
Special issue on “Evolutionary multiobjective optimization”
Multiobjective optimization problems occur frequently in practice whenever more than one objective function have to be optimized simultaneously. Instead of reformulating a multiobjective optimization problem in terms of a scalarized (single-objective) function, the research ﬁeld of evolutionary multiobjective optimization (EMO) typically deals with randomized heuristic search algorithms that are able to ﬁnd multiple (near) Pareto-optimal solutions in a single algorithm run. Besides “classical” evolutionary algorithms, EMO also covers other types of meta-heuristics for multiobjective optimization, for both combinatorial and continuous search domains. The goal of this special issue on “Evolutionary multiobjective optimization” is to present salient current research and application studies using EMO methodologies to a general operational research audience. In total, 59 papers have been submitted to this special issue of which we carefully selected 12 papers after a thorough review process by two to three external reviewers per paper, following the high-quality standards of the European Journal on Operations Research (EJOR). At this point, we would like to use the opportunity to thank all the reviewers for their excellent reviews and their valuable opin´ ions. We would also like to thank Roman Słowinski, co-ordinating editor of the journal, for kindly accepting our proposal for this special issue as well as Rukmani Krishnan and Randy Van Grunsven from Elsevier for their continuous support with the issue. Thanks also go to the organizing committee of the MCDM’2013 conference and especially Francisco Ruiz who supported us by prominently advertising the special issue during and after the conference. Special thanks go, of course, to all authors who submitted a paper and who made the largest effort over all. Fortunately, a large variety of topics have been submitted such that we are able to present a wide spectrum over several current “hot topics” of EMO—covering both fundamental theoretical studies and application-oriented papers. The topics range from classical algorithm design for both discrete and continuous search spaces, over multiobjectivization, preference handling, many-objective optimization, and innovization to the opening of new research directions such as tackling problems where the evaluation costs differ between objective functions. In the ﬁrst paper of this issue, Miha Mlakar and his co-authors introduce an EMO algorithm based on a surrogate model, called Differential Evolution for Multiobjective Optimization based on Gaussian Process models (GP-DEMO). The algorithm is tailored toward problems with expensive objective functions and was tested extensively on well-known test functions and two real-world problems. Rafael Caballero and his co-authors present a new algorithm for combinatorial multiobjective optimization problems for which linear http://dx.doi.org/10.1016/j.ejor.2014.12.016 0377-2217/© 2015 Elsevier B.V. All rights reserved.
relaxations are available. Their method is an extension of the singleobjective cross-entropy method and it is experimentally compared with other known methods on multiobjective knapsack and linear assignment problem instances. The tuning and improvement of the Pareto Local Search (PLS) algorithm is the main topic of the paper by Jérémie Dubois-Lacoste et al., with the goal to obtain algorithms with a good “anytime” behavior for multiobjective combinatorial optimization problems. Besides tuning the algorithm’s internal parameters, a technique called “dynagrid” is proposed, and both introduced PLS variants are shown to improve its performance on the bi-objective traveling salesman and quadratic assignment problems. The next two papers deal with “multiobjectivization”, i.e., the idea of reformulating and solving a single-objective optimization problem as a multiobjective one. Darrell F. Lochtefeld and Frank W. Ciarallo, on the one hand, investigate the idea of decomposing a single objective function into separate objectives from a theoretical point-of-view, as well as experimentally, for the job-shop scheduling problem. Mario Garza-Fabre and his co-authors, on the other hand, investigate the multiobjectivization of a protein structure prediction problem, also both from the theoretical viewpoint of ﬁtness landscape analysis and via experimental validation. The following two papers by Rui Wang and colleagues cover the topic of preference articulation and how they can be used in EMO algorithms. The article “Preference-inspired co-evolutionary algorithms using weight vectors” tackles the problem of the diﬃcult a priori choice of weight vectors in decomposition-based EMO algorithms by proposing the algorithm PICEA-w, which co-evolves both solutions to a multiobjective problem and appropriate weight vectors. Experiments comparing PICEA-w with other decomposition-based methods with random, static, and adaptive weights illustrate the performance gain and the reduced sensibility to problem geometries. In “The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique”, a new “brushing” technique to specify preferences towards interesting solution sets graphically (i.e. by “drawing” in the objective space) is proposed and implemented in an interactive EMO algorithm. The next paper by Ruby L.V. Moritz et al. investigates two general ranking schemes to select solutions based on quality while the usual Pareto-dominance relation among the solutions is retained. Numerical experiments on the ﬂow-shop scheduling problem illustrate the usefulness of the rankings when implemented in an ant colony optimization algorithm.
JID: EOR 2
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Preface / European Journal of Operational Research 000 (2014) 1–2
Markus Wagner et al. then present the approximation-guided evolutionary (AGE) algorithm to approximate the Pareto front of manyobjective optimization problems (i.e. with more than three objective functions) in terms of the theoretical notion of ε -approximations. Innovization, i.e., the automated extraction of signiﬁcant mathematical relationships among Pareto-optimal solutions, is the topic of Sunith Bandaru and his co-authors’ paper. They particularly present new innovization techniques to extract mathematical relationships from various solutions sets that are generated by changing a higherlevel parameter of the problem at hand. Examples on a two-bar biobjective truss design problem and on the classic case of inventory management complete the paper. Last but not least, Richard Allmendinger and co-authors study a new type of multiobjective problem which has not gained interest in the research community so far although the problem is clearly relevant in practice: Three simple approaches are proposed and analyzed
experimentally to deal with multiobjective problems where the time to evaluate a solution varies from one objective function to another. The proposed strategies not only show considerable performance gains when compared to the case where the algorithm is waiting for the longest evaluation, but the paper also opens up a new interesting research direction in EMO with many practical applications. We hope you will enjoy reading the papers of this special issue.
Dimo Brockhoff∗ Bilel Derbel Arnaud Liefooghe Sébastien Verel ∗ Corresponding author. E-mail address: [email protected]