Abstract
Since the 60s, several approaches (genetic algorithms, evolution strategies etc.) have been developed which apply evolutionary concepts for simulation and optimization purposes. Also in the area of multiobjective programming, such approaches (mainly genetic algorithms) have already been used (Evolutionary Computation 3(1), 1–16).
In our presentation, we consider a generalization of common approaches like evolution strategies: a multiobjective evolutionary algorithm (MOEA) for analyzing decision problems with alternatives taken from a real-valued vector space and evaluated according to several objective functions. The algorithm is implemented within the Learning Object-Oriented Problem Solver (LOOPS) framework developed by the author. Various test problems are analyzed using the MOEA: (multiobjective) linear programming, convex programming, and global programming. Especially for ‘hard’ problems with disconnected or local efficient regions, the algorithms seems to be a useful tool.
Similar content being viewed by others
References
Bäck, T., F. Hoffmeister, and H.-P. Schwefel. (1991). “A Survey of Evolution Strategies. ” In R.K. Belew and L.B. Booker (eds.), Genetic Algorithms, Proceedings of the Fourth International Conference. San Mateo: Morgan Kaufmann, pp. 2–9.
Bäck, T. and H.-P. Schwefel. (1992). “Evolutionary Algorithms: Some Very Old Strategies for Optimization and Adaptation. ” In D. Perret-Gallix (ed.), New Computing Techniques in Physics Research II. Singapore: World Scientific, pp. 247–254.
Bäck, T. and H.-P. Schwefel. (1993). “An Overview of Evolutionary Algorithms for Parameter Optimization. ” Evolutionary Computation 1(1), 1–23.
Fonseca, C.M. and P.J. Fleming. (1993). “Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. ” In S. Forrest (ed.), Genetic Algorithms: Proceedings of the Fifth International Conference. San Mateo: Morgan Kaufmann, pp. 416–423.
Fonseca, C.M. and P.J. Fleming. (1995). “An Overview of Evolutionary Algorithms in Multiobjective Optimization. ” Evolutionary Computation 3(1), 1–16.
Gal, T. (1977). “A General Method for Determining the Set of All Efficient Solutions to a Linear Vectormaximum Problem. ” European Journal of Operations Research 1, 307–322.
Gal, T. (1986). “On Efficient Sets inVectorMaximumProblems-A Brief Survey. ” European Journal of Operations Research 24, 253–264.
Gal, T. (1995). Postoptimal Analyses, Parametric Programming, and Related Topics. Degeneracy, Multicriteria Decision Making, Redundancy. 2nd edn. Berlin: De Gruyter.
Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Reading: Addison-Wesley.
Hanne, T. (1993). “An Object-Oriented Decision Support System for MCDM. ” In Operations Research Proceedings DGOR/NSOR 22nd Annual Meeting. Berlin: Springer, pp. 449–455.
Hanne, T. (1997a). “Decision Support for MCDM that is Neural Network-Based and can Learn. ” In J. Climaco (ed.), Multicriteria Analysis, Proceedings of the XIth International Conference on MCDM, Coimbra, Aug. 1–6, 1994. Berlin: Springer, pp. 401–410.
Hanne, T. (1997b). “Concepts of a Learning Object-Oriented Problem Solver (LOOPS). ” In G. Fandel and T. Gal, in collaboration with T. Hanne (eds.), Multiple Criteria Decision Making, Proceedings of the Twelfth International Conference, Hagen 1995. Berlin: Springer, pp. 330–339.
Hanne, T. (1999). “On the Convergence of Multiobjective Evolutionary Algorithms. ” European Journal of Operational Research 117(3), 553–564.
Hoffmeister, F. and T. Bäck. (1992). “Genetic Algorithms and Evolution Strategies: Similarities and Differences. ” Technical Report No. SYS-1/92, University of Dortmund, Department of Computer Science.
Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press.
Horn, J. (1997). “Multicriterion Decision Making. ” In T. Bäck, D.B. Fogel, and Z. Michalewicz (eds.), Handbook of Evolutionary Computation. New York and Bristol: IOP Publishing and Oxford University Press, pp. F1.9:1–F1.9:15.
Jahn, J. (1984). “Scalarization in Vector Optimization. ” Mathematical Programming 29, 203–218.
Koza, J.R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, Massachussetts: MIT Press.
Kursawe, F. (1991). “A Variant of Evolution Strategies for Vector Optimization. ” In H.-P. Schwefel and R. Männer (eds.), Parallel Problem Solving from Nature, 1st Workshop, PPSN 1, Oct. 1–3, 1990. Berlin: Springer, pp. 193–197.
Kursawe, F. (1992). “Evolution Strategies for Vector Optimization. ” In Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei, Vol. III, pp. 187–193.
Michalewicz, Z. (1994). Genetic Algorithms + Data Structures = Evolution Programs, 2nd edn. Berlin: Springer.
Nakayama, H. (1997). “Some Remarks on Trade-Off Analysis in Multi-Objective Programming. ” In J. Climaco (ed.), Multicriteria Analysis; Proceedings of the XIth International Conference on MCDM, Aug. 1–6, 1994, Coimbra, Portugal. Berlin: Springer, pp. 179–190.
Rechenberg, I. (1973). Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart: Frommann-Holzboog.
Sawaragi, Y., H. Nakayama, and T. Tanino. (1985). Theory of Multiobjective Optimization. Orlando: Academic Press.
Schwefel, H.-P. (1977). Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie. Basel: Birkhäuser.
Schwefel, H.-P. (1981). Numerical Optimization of Computer Models. Chichester: Wiley.
Steuer, R.E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons.
Steuer, R.E. and F.W. Harris. (1980). “Intra-Set Point Generation and Filtering in Decision and Criterion Space. ” Computers and Operations Research 7, 41–53.
Tamaki, H., H. Kita, and S. Kobayashi. (1996). “Multi-Objective Optimization by Genetic Algorithms: A review. ” In Proceedings of the 3rd IEEE International Conference on Evolutionary Computation. Piscataway (NJ): IEEE Press, pp. 517–522.
Vincke, P. (1992). Multicriteria Decision-Aid. Chichester: Wiley.
White, D.J. (1982). Optimality and Efficiency. Chichester: Wiley.
Zeleny, M. (1982). Multiple Criteria Decision Making. New York: McGraw-Hill.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hanne, T. Global Multiobjective Optimization Using Evolutionary Algorithms. Journal of Heuristics 6, 347–360 (2000). https://doi.org/10.1023/A:1009630531634
Issue Date:
DOI: https://doi.org/10.1023/A:1009630531634