Abstract
Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of optimums, which constitute the so called Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, most problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. The objective of this work is to compare the performance of a new hybrid method here proposed, with several well-known multi-objective evolutionary algorithms (MOEA). The main attraction of these methods is the integration of selection and diversity maintenance. Since it is very difficult to describe exactly what a good approximation is in terms of a number of criteria, the performance is quantified with adequate metrics that evaluate the proximity to the global Pareto-front. In addition, this work is also one of the few empirical studies that solves three-objective optimization problems using the concept of global Pareto-optimality.
Similar content being viewed by others
References
(1995). Handbook of global optimization. Kluwer Academic Publishers, Dordrecht
Benson H.P. (1998). An Outer Approximation Algorithm for Generating all Efficient Extreme Points in the Outcome set of a Multiple-objective Linear Programming Problem. J. Global Optim. 13: 1–24
Horst R. and Thoai N.V. (1999). Maximizing a Concave Function Over the Efficient or Weakly-efficient Set. Eur. J. Oper. Res. 117: 239–252
Hajela P. and Y-Lin C. (1992). Genetic Search Strategies in Multi-criterion Optimal Design. Struct. Optim. 4: 99–107
Goldberg D.E. (1989). Genetic algorithms in search, optimization and machine learning. Addison Wesley, New York
Deb K.: Multi-objective optimization using evolutionary algorithms. John Wiley & Sons (2002)
Coello, C. A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers (2002)
Fonseca, C. M., Flemming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discusion and generalization. Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, California, 416–423 (1993)
Horn, J., Nafpliotis N., Goldberg D.: A niched pareto genetic algorithm for multiobjective optimization. Proceedings of the First IEEE Conference on Evolutionary Computation, Piscataway, New Jersey, USA, 82–87 (1994)
Srinivas N. and Deb K. (1994). Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evol. Comput. 2(3): 221–248
Deb K., Agrawal S., Pratap A. and Meyarivan T. (2000). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multiobjective Optimization: NUSA-II. Springer Lecture Notes in Computer Science. 1917: 849–858
Zitzler E. and Thiele L. (1999). Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans. Evol. Comput. 3(4): 257–271
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Switzerland (2001)
Knowles, J.D., Corne D.W.: The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. Proceedings of the Congress on Evolutionary Computation, Piscataway, NJ, 98–105 (1999)
Corne D.W., Knowles J.D. and Oates H.J. (2000). The Pareto-Envelope based Selection Algorithm for Multiobjective Optimisation. Springer Lecture Notes in Computer Science. 1917: 869–878
Baños, R., Gil, C., Paechter, B., Ortega, J.: A hybrid meta-heuristic for multi-objective optimization: MOSATS. J. Math. Model. Algorithm, DOI: 10.1007/s10852-006-9041-6: (2006)
Talbi E. (2002). A Taxonomy of Hybrid Metaheuristics. J. Heuristics. 8(5): 541–564
Deb, K., Thiele, L., Laumanns, M., Zitzler, E. Scalable test problems for evolutionary multi-objective optimization. Evolutionary computation based multi-criteria optimization: theoretical advances and applications. Springer-Verlag, USA 105–145: (2005)
Zitler E., Deb K. and Thiele L. (2000). Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolu. Comput. 8(2): 173–195
Veldhuizen, D.V.: Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. PhD thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)
Deb, K., Thiele, L., Laumanns, M., Zitler, E.: Constrained test problems for multi-objective evolutionary optimization. Proceedings of First International Conference on Evolutionary Multi-Criterion Optimization, 284–298 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gil, C., Márquez, A., Baños, R. et al. A hybrid method for solving multi-objective global optimization problems. J Glob Optim 38, 265–281 (2007). https://doi.org/10.1007/s10898-006-9105-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9105-1