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Article

Optimization of scalarizing functions through evolutionary multiobjective optimization

Authors:

Hisao Ishibuchi,

Yusuke NojimaAuthors Info & Claims

EMO'07: Proceedings of the 4th international conference on Evolutionary multi-criterion optimization

Pages 51 - 65

Published: 05 March 2007 Publication History

Abstract

This paper proposes an idea of using evolutionary multiobjective optimization (EMO) to optimize scalarizing functions. We assume that a scalarizing function to be optimized has already been generated from an original multiobjective problem. Our task is to optimize the given scalarizing function. In order to efficiently search for its optimal solution without getting stuck in local optima, we generate a new multiobjective problem to which an EMO algorithm is applied. The point is to specify multiple objectives, which are similar to but different from the scalarizing function, so that the location of the optimal solution is near the center of the Pareto front of the generated multiobjective problem. The use of EMO algorithms helps escape from local optima. It also helps find a number of alternative solutions around the optimal solution. Difficulties of Pareto ranking-based EMO algorithms in the handling of many objectives are avoided by the use of similar objectives. In this paper, we first demonstrate that the performance of EMO algorithms as single-objective optimizers of scalarizing functions highly depends on the choice of multiple objectives. Based on this observation, we propose a specification method of multiple objectives for the optimization of a weighted sum fitness function. Experimental results show that our approach works very well in the search for not only a single optimal solution but also a number of good alternative solutions around the optimal solution. Next we evaluate the performance of our approach in comparison with a hybrid EMO algorithm where a single-objective fitness evaluation scheme is probabilistically used in an EMO algorithm. Then we show that our approach can be also used to optimize other scalarizing functions (e.g., those based on constraint conditions and reference solutions). Finally we show that our approach is applicable not only to scalarizing functions but also other single-objective optimization problems.

References

[1]

Colombo, G., Mumford, C. L.: Comparing Algorithms, Representations and Operators for the Multi-Objective Knapsack Problem. Proc. of 2005 Congress on Evolutionary Computation (2005) 2241-2247

[2]

Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)

Digital Library

[3]

Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6 (2002) 182-197

Digital Library

[4]

Deb, K., Sundar, J.: Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms. Proc. of Genetic and Evolutionary Computation Conference (2006) 635-642

Digital Library

[5]

Fonseca, C. M., Fleming, P. J.: On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers. Lecture Notes in Computer Science, Vol. 114: PPSN IV. Springer, Berlin (1996) 584-593

Digital Library

[6]

Hughes, E. J.: Multiple Single Objective Sampling. Proc. of 2003 Congress on Evolutionary Computation (2003) 2678-2684

[7]

Hughes, E. J.: Evolutionary Many-Objective Optimization: Many Once or One Many? Proc. of 2005 Congress on Evolutionary Computation (2005) 222-227

[8]

Ishibuchi, H., Doi, T., Nojima, Y.: Incorporation of Scalarizing Fitness Functions into Evolutionary Multiobjective Optimization Algorithms. Lecture Notes in Computer Science, Vol. 4193: PPSN IX. Springer, Berlin (2006) 493-502

Digital Library

[9]

Ishibuchi, H., Murata, T.: A Multi-Objective Genetic Local Search Algorithm and Its Application to Flowshop Scheduling. IEEE Trans. on Systems, Man, and Cybernetics - Part C: Applications and Reviews 28 (1998) 392-403

Digital Library

[10]

Ishibuchi, H., Nojima, Y., Doi, T.: Application of Multiobjective Evolutionary Algorithms to Single-Objective Optimization Problems. Abstract Booklet of 7th International Conference on Multi-Objective Programming and Goal Programming (2006) 4 pages

[11]

Ishibuchi, H., Yoshida, T., Murata, T.: Balance between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling. IEEE Trans. on Evolutionary Computation 7 (2003) 204-223

Digital Library

[12]

Jaszkiewicz, A.: Genetic Local Search for Multi-Objective Combinatorial Optimization. European Journal of Operational Research 137 (2002) 50-71

[13]

Jaszkiewicz, A.: On the Performance of Multiple-Objective Genetic Local Search on the 0/1 Knapsack Problem - A Comparative Experiment. IEEE Trans. on Evolutionary Computation 6 (2002) 402-412

Digital Library

[14]

Jaszkiewicz, A.: On the Computational Efficiency of Multiple Objective Metaheuristics: The Knapsack Problem Case Study. European Journal of Operational Research 158 (2004) 418-433

[15]

Knowles, J. D., Watson, R. A., Corne, D. W.: Reducing Local Optima in Single-Objective Problems by Multi-Objectivization. Lecture Notes in Computer Science, Vol. 1993: EMO 2001. Springer, Berlin (2001) 269-283

Digital Library

[16]

Mumford, C. L.: A Hierarchical Solve-and-Merge Framework for Multi-Objective Optimization. Proc. of 2005 Congress on Evolutionary Computation (2005) 2241-2247

[17]

Purshouse, R. C., Fleming, P. J.: Evolutionary Many-Objective Optimization: An Exploratory Analysis. Proc. of 2003 Congress on Evolutionary Computation (2003) 2066-2073

[18]

Watanabe, S., Sakakibara K.: Multi-Objective Approaches in a Single-Objective Optimization Environment. Proc. of 2005 Congress on Evolutionary Computation (2005) 1714-1721

Digital Library

[19]

Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans. on Evolutionary Computation 3 (1999) 257-271

Digital Library

Cited By

Chen PChen TLi M(2024)MMO: Meta Multi-Objectivization for Software Configuration TuningIEEE Transactions on Software Engineering10.1109/TSE.2024.338891050:6(1478-1504)Online publication date: 15-Apr-2024
https://dl.acm.org/doi/10.1109/TSE.2024.3388910
Chen TLi M(2023)The Weights Can Be Harmful: Pareto Search versus Weighted Search in Multi-objective Search-based Software EngineeringACM Transactions on Software Engineering and Methodology10.1145/351423332:1(1-40)Online publication date: 13-Feb-2023
https://dl.acm.org/doi/10.1145/3514233
Pescador-Rojas MHernández Gómez RMontero ERojas-Morales NRiff MCoello Coello C(2017)An Overview of Weighted and Unconstrained Scalarizing Functions9th International Conference on Evolutionary Multi-Criterion Optimization - Volume 1017310.1007/978-3-319-54157-0_34(499-513)Online publication date: 19-Mar-2017
https://dl.acm.org/doi/10.1007/978-3-319-54157-0_34
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Optimization of scalarizing functions through evolutionary multiobjective optimization
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Information & Contributors

Information

Published In

cover image Guide Proceedings

EMO'07: Proceedings of the 4th international conference on Evolutionary multi-criterion optimization

March 2007

953 pages

ISBN:9783540709275

Editors:
Shigeru Obayashi
Tohoku University, Sendai, Japan
,
Kalyanmoy Deb
Indian Institute of Technology, Kanpur, India
,
Carlo Poloni
University of Trieste, Trieste, Italy
,
Tomoyuki Hiroyasu
Doshisha University, Kyoto, Japan
,
Tadahiko Murata
Kansai University, Osaka, Japan

Sponsors

Kansai University
JAXA: Japan Aerospace Exploration Agency
Institute of Fluid Science
Graduate School of Information Sciences

In-Cooperation

Cd-Adapco Japan Co., Ltd.
Cray Japan Inc.
BESTSYSTEMS Co., Ltd.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 05 March 2007

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Cited By

Chen PChen TLi M(2024)MMO: Meta Multi-Objectivization for Software Configuration TuningIEEE Transactions on Software Engineering10.1109/TSE.2024.338891050:6(1478-1504)Online publication date: 15-Apr-2024
https://dl.acm.org/doi/10.1109/TSE.2024.3388910
Chen TLi M(2023)The Weights Can Be Harmful: Pareto Search versus Weighted Search in Multi-objective Search-based Software EngineeringACM Transactions on Software Engineering and Methodology10.1145/351423332:1(1-40)Online publication date: 13-Feb-2023
https://dl.acm.org/doi/10.1145/3514233
Pescador-Rojas MHernández Gómez RMontero ERojas-Morales NRiff MCoello Coello C(2017)An Overview of Weighted and Unconstrained Scalarizing Functions9th International Conference on Evolutionary Multi-Criterion Optimization - Volume 1017310.1007/978-3-319-54157-0_34(499-513)Online publication date: 19-Mar-2017
https://dl.acm.org/doi/10.1007/978-3-319-54157-0_34
Cai DYuping W(2015)A new uniform evolutionary algorithm based on decomposition and CDAS for many-objective optimizationKnowledge-Based Systems10.1016/j.knosys.2015.04.02585:C(131-142)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.knosys.2015.04.025
Bandyopadhyay SChakraborty RMaulik U(2015)Priority based ε dominanceInformation Sciences: an International Journal10.1016/j.ins.2015.01.018305:C(97-109)Online publication date: 1-Jun-2015
https://dl.acm.org/doi/10.1016/j.ins.2015.01.018
Dai CWang Y(2015)A new decomposition based evolutionary algorithm with uniform designs for many-objective optimizationApplied Soft Computing10.1016/j.asoc.2015.01.06230:C(238-248)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1016/j.asoc.2015.01.062
Sato HAguirre HTanaka K(2013)Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problemsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-012-9293-y68:4(197-224)Online publication date: 1-Aug-2013
https://dl.acm.org/doi/10.1007/s10472-012-9293-y
Bong CRajeswari M(2011)Review ArticleApplied Soft Computing10.1016/j.asoc.2011.01.01411:4(3271-3282)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1016/j.asoc.2011.01.014
Peng FTang K(2011)Alleviate the hypervolume degeneration problem of NSGA-IIProceedings of the 18th international conference on Neural Information Processing - Volume Part II10.1007/978-3-642-24958-7_50(425-434)Online publication date: 13-Nov-2011
https://dl.acm.org/doi/10.1007/978-3-642-24958-7_50
Ishibuchi HSakane YTsukamoto NNojima YPelikan MBranke J(2010)Simultaneous use of different scalarizing functions in MOEA/DProceedings of the 12th annual conference on Genetic and evolutionary computation10.1145/1830483.1830577(519-526)Online publication date: 7-Jul-2010
https://dl.acm.org/doi/10.1145/1830483.1830577
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