DOI QR코드

DOI QR Code

균일분포의 파레토 최적해 생성을 위한 다목적 최적화 진화 알고리즘

Evolutionary Multi-Objective Optimization Algorithms for Uniform Distributed Pareto Optimal Solutions

  • 장수현 (명지대학교 대학원 컴퓨터공학과) ;
  • 윤병주 (명지대학교 컴퓨터공학과)
  • 발행 : 2004.12.01

초록

진화 알고리즘은 여러 개의 상충하는 목적을 갖는 다목적 최적화 문제를 해결하기에 적합한 방법이다. 특히, 파레토 지배관계에 기초하여 개체의 적합도를 평가하는 파레토 기반 진화알고리즘들은 그 성능에 있어서 비교적 우수한 평가를 받고 있다. 그러나 일반화된 다목적 최적화 진화알고리즘은 복잡한 문제들에서 찾아진 해들의 분포가 전체 파레토 경계면에 대하여 균일하지 못하고 특정 지역에서 집중적으로 해를 생성하는 문제점을 가지고 있다. 본 논문에서 우리는 이러한 문제점을 보완하기 위한 다목적 최적화 진화알고리즘을 제안한다. 제안한 알고리즘은 현재까지 찾아진 최적해들 중 특정 지역에 관중되지 않은 해를 우수 종자로 복제 연산에 참여시킨다. 따라서 특별한 지역탐색 기법을 사용하지 않아도 종자가 되는 개체 주위에 새로운 개체를 생성할 확률이 높기 때문에 지역탐색의 효과를 가질 수 있고, 비교적 고른 분포의 파레토 최적 해를 생성한 수 있다. 5개의 테스트 함수에 대한 실험 결과, 제안한 알고리즘은 모든 문제에서 전체 파레토 경계면에 균일한 분포의 해들을 생성할 수 있었으며, 많은 지역해를 가지는 문제를 제외한 모든 문제에서 NSGA-II보다 우수한 수렴 결과를 보였다.

Evolutionary a1gorithms are well-suited for multi-objective optimization problems involving several, often conflicting objectives. Pareto-based evolutionary algorithms, in particular, have shown better performance than other multi-objective evolutionary algorithms in comparison. However, generalized evolutionary multi-objective optimization algorithms have a weak point, in which the distribution of solutions are not uni-formly distributed onto Pareto optimal front. In this paper, we propose an evolutionary a1gorithm for multi-objective optimization which uses seed individuals in order to overcome weakness of algorithms Published. Seed individual means a solution which is not located in the crowded region on Pareto front. And the idea of our algorithm uses seed individuals for reproducing individuals for next generation. Thus, proposed a1go-rithm takes advantage of local searching effect because new individuals are produced near the seed individual with high probability, and is able to produce comparatively uniform distributed pareto optimal solutions. Simulation results on five testbed problems show that the proposed algo-rithm could produce uniform distributed solutions onto pareto optimal front, and is able to show better convergence compared to NSGA-II on all testbed problems except multi-modal problem.

키워드

참고문헌

  1. Carlos A. Coello Coello, 'An Updated Survey of GA-Based Multiobjective Optimization Techniques,' ACM Computing Surveys, Vol.32, No.2, pp.109-143, June, 2000 https://doi.org/10.1145/358923.358929
  2. Frank Kursawe, 'A Variant of evolution strategies for vector optimization,' In Parallel Problem Solving from Nature. 1st Workshop, PPSN I, Vol.496 of Lecture Notes in Computer Science, pp.193-197, 1991
  3. Carlos M. Fonseca and Peter J. Fleming, 'Genetic Algorithms for Multiobjective Optimization : Formulation, Discussion and Generalization,' In Proceedings of the Fifth International Conference on Genetic Algorithms, pp.416-423, 1993
  4. Jeffrey Horn and Nicholas Nafpliotis, 'Multiobjective Optimization using the Niched Pareto Ganetic Algorithm,' Technical Report IlliGAl Report 93005, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA, 1993
  5. N. Srinivas and Kalyanrnoy Deb, 'Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,' Evolutionary Computation, Vol.2, No.3 pp.221-248, 1994 https://doi.org/10.1162/evco.1994.2.3.221
  6. Kalyanmoy Deb, Samir Agrawal, Amrit Pratab, and T. Meyarivan, 'A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization : NSGA- II,' Proceedings of the Parallel Problem Solving from Nature VI Conference, pp.849-858, Springer, 2000
  7. Eckart Zitzler, Marco Laumanns and Lothar Thiele, 'SPEA 2 : Improving the Strength Pareto Evolutionary Algorithm,' EUROGEN 2001, Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pp.12-21, 2001
  8. Carlos A. Coello Coello and Nareli Cruz Cortes, 'Solving Multiobjective Optimization Problems using an Artificial Immune System,' Technical Report EVOCINV-05-2002, Evolutionary Computation Group at CINVESTAV, Kluwer Academic, 2002
  9. J. D. Schaffer, 'Multiple objective optimization with vector evaluated genetic algorithms,' In Genetic Algorithms and their Applications : Proceedings of the First International Conference on Genetic Algorithms, pp.93-100, 1985
  10. Eckart Zitzler and Lothar Thiele, 'Multiobjective optimization using evolutionary algorithms - a Comparative study,' In Parallel Problem Solving from Nature V, pp.292-301, 1998
  11. Jason R. Schott, Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. Master's thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1995
  12. Kalyanmoy Deb, 'Multi-Objective Genetic Algorithms : Problem Difficulties and Construction of Test Problems,' Evolutionary Computation, Vol.7, No.3, pp.205-230, 1999 https://doi.org/10.1162/evco.1999.7.3.205
  13. Eckart Zitzler, Kalyanmoy Deb, and Lothar Thiele, 'Comparison of Multiobjective Evolutionary Algorithms : Empirical Results,' Evolutionary Computation, Vol.8, No.2, pp.173- 195, 2000 https://doi.org/10.1162/106365600568202
  14. 장수현, 윤병주, '유전자알고리즘에서의 실수처리 방법 비교', 정보처리학회논문지, Vol.5, No.2, pp.361-371, 1998