The Journal of the Korea Contents Association (한국콘텐츠학회논문지)

The Korea Contents Association (한국콘텐츠학회)
권호 표지
DOI QR코드

DOI QR Code

A Two-tier Optimization Approach for Decision Making in Many-objective Problems

고도 다목적 문제에서의 의사 결정을 위한 이중 최적화 접근법

  • Received : 2015.05.27
  • Accepted : 2015.07.03
  • Published : 2015.07.28
Download PDF
⟨ Previous Next ⟩

Abstract

This paper proposes a novel two-tier optimization approach for decision making in many-objective problems. Because the Pareto-optimal solution ratio increases exponentially with an increasing number of objectives, simply finding the Pareto-optimal solutions is not sufficient for decision making in many-objective problems. In other words, it is necessary to discriminate the more preferable solutions from the other solutions. In the proposed approach, user preference-oriented as well as diverse Pareto-optimal solutions can be obtained as candidate solutions by introducing an additional tier of optimization. The second tier of optimization employs the corresponding secondary objectives, global evaluation and crowding distance, which were proposed in previous works, to represent the users preference to a solution and the crowdedness around a solution, respectively. To demonstrate the effectiveness of the proposed approach, decision making for some benchmark functions is conducted, and the outcomes with and without the proposed approach are compared. The experimental results demonstrate that the decisions are successfully made with consideration of the users preference through the proposed approach.

본 논문은 목적이 네 개 이상인 고도 다목적 문제(many-objective problem)에서의 의사 결정을 위한 새로운 이중(two-tier) 최적화 접근법을 제안한다. 목적의 개수가 증가할수록, 특히 네 개 이상부터는, 전체해(solution) 중에서 파레도 최적해(Parero-optimal solution)가 차지하는 비율이 기하급수적으로 증가한다. 그래서 일반 다목적 문제와는 달리, 의사 결정을 하는데 단순히 파레토 최적 해만을 찾는 것으로는 충분하지 않고, 찾은 파레토 최적 해들 중에서도 상대적으로 좀 더 선호하는 해들을 가려내는 것이 필요하다. 제안하는 접근법에서는 추가적인 최적화 단계를 추가함으로써 사용자의 선호도를 균형있게 반영하는 방향으로 파레토 최적해들을 찾는다. 이러한 2차 최적화는 관련된 2차 목적들을 수반하게 되는데, 2차 목적으로는 광역평가값과 혼잡 거리를 사용하였다. 광역평가값과 혼잡 거리는 각각 사용자의 선호도와 다양성을 대변하는 척도이다. 제안한 접근법의 우수성을 보이기 위해서는 잘 알려진 검증 함수들을 활용하는데, 같은 함수에 대해 제안한 접근법을 적용한 경우와 적용하지 않은 경우의 결과를 비교한다. 제안한 접근법을 적용함으로써 기존보다 사용자의 선호도를 잘 반영하면서 동시에 우수하고 다양한 의사 선택이 가능하다.

Keywords

References

  1. Z. Xu, Uncertain Multi-Attribute Decision Making: Methods and Application, Springer, 2015.
  2. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Trans. Evol. Comput., Vol.6, No.2, pp.182-197, 2002. https://doi.org/10.1109/4235.996017
  3. C. Coello and M. Lechuga, "MOPSO: A proposal for multiple objective particle swarm optimization," in Proc. IEEE Congress on Evolutionary Computation, pp.1051-1056, 2002.
  4. C. Coello, G. Pulido, and M. Lechuga, "Handling multiple objectives with particle swarm optimization," IEEE Trans. Evol. Comput., Vol.8, No.3, pp.256-279, 2004. https://doi.org/10.1109/TEVC.2004.826067
  5. J. Alvarez-Benitez, R. Everson, and J. Fieldsend, "A MOPSO algorithm based exclusively on Pareto dominance concepts," Evolutionary Multi-Criterion Optimization, pp.459-473, 2005.
  6. M. Reyes-Sierra and C. Coello, "Multi-objective particle swarm optimizers: A survey of the state-of-the-art," Int. J. Comput. Intelligence Research, Vol.2, No.3, pp.287-308, 2006.
  7. K. B. Lee and J. H. Kim, "Multiobjective particle swarm optimization with preference-based sort and its application to path following footstep optimization for humanoid robots," IEEE Trans. Evol. Comput., Vol.17, No.6, pp.755-766, 2013. https://doi.org/10.1109/TEVC.2013.2240688
  8. J. Kou, S. Xiong, Z. Fang, X. Zong, and Z. Chen, "Multiobjective optimization of evacuation routes in stadium using superposed potential field network based aco," Computational intelligence and neuroscience, Vol.2013, No.2, pp.14-25, 2013.
  9. R. Yager, "On ordered weighted averaging aggregation operators in multi-criteria decision making," IEEE Trans. Systems, Man and Cybernetics, Vol.18, No.1, pp.183-190, 1988. https://doi.org/10.1109/21.87068
  10. K. Miettinen, Nonlinear multiobjective optimization, Springer, 1999.
  11. 박종득, "공무원교육훈련정책의 상대적 중요도와 우선순위 분석: 계층의사결정방법(AHP)을 활용하여", 한국콘텐츠학회논문지, 제12권, 제4호, pp.263-272, 2012. https://doi.org/10.5392/JKCA.2012.12.04.263
  12. T. L. Saaty, "Decision making with the analytic hierarchy process," Int. J. Services Sciences, Vol.1, No.1, pp.83-98, 2008. https://doi.org/10.1504/IJSSCI.2008.017590
  13. H. Ishibuchi, N. Tsukamoto, and Y. Nojima, "Evolutionary manyobjective optimization: A short review," in Proc. IEEE Cong. Evol. Comput., pp.2419-2426, 2008.
  14. 이승관, 최진혁, "개미 집단 최적화에서 강화와 다양화의 조화", 한국콘텐츠학회논문지, 제11권, 제3호, pp.100-107, 2011. https://doi.org/10.5392/JKCA.2011.11.3.100
  15. E. Triantaphyllou, Multi-criteria decision making methods: a comparative study, Vol.44, Springer, 2013.
  16. T. Gal, T. Stewart, and T. Hanne, Multi criteria decision making: advances in MCDM models, algorithms, theory, and applications, Vol.21. Springer, 2013.
  17. K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, "Scalable multi-objective optimization test problems," in Proc. IEEE Cong. Evol. Comput., pp.825-830, 2002.
  18. E. Zitzler, Evolutionary algorithms for multiobjective optimization: Methods and applications, Doctoral dissertation, Swiss Federal Institute of Technology (ETH), 1999.
  19. H. Li, Q. Zhang, E. Tsang, and J. Ford, "Hybrid estimation of distribution algorithm for multiobjective knapsack problem," Evol. Comput. in Combinatorial Optimization, pp.145-154, 2004.
  20. E. Lehmann and J. Romano, Testing Statistical Hypotheses, Springer, 2006.
  21. B. L. Welch, "The generalization of 'student's' problem when several different population variances are involved," Biometrika, Vol.34, No.1, pp.28-35, 1947.
  22. G. G. Judge, R. C. Hill, W. Griffiths, H. Lutkepohl, T. C. Lee, J. Tuladhar, B. Banerjee, V. Kelly, R. Stevens, T. Stilwell, et al., "Introduction to the theory and practice of econometrics," Economic Development and Cultural Change, Vol.32, No.4, pp.767-768, 1984. https://doi.org/10.1086/451425