Abstract
One common characterization of how simple hill-climbing optimization methods can fail is that they become trapped in local optima - a state where no small modification of the current best solution will produce a solution that is better. This measure of ‘better’ depends on the performance of the solution with respect to the single objective being optimized. In contrast, multi-objective optimization (MOO) involves the simultaneous optimization of a number of objectives. Accordingly, the multi-objective notion of ‘better’ permits consideration of solutions that may be superior in one objective but not in another. Intuitively, we may say that this gives a hill-climber in multi-objective space more freedom to explore and less likelihood of becoming trapped. In this paper, we investigate this intuition by comparing the performance of simple hill-climber-style algorithms on single-objective problems and multi- objective versions of those same problems. Using an abstract building- block problem we illustrate how ‘multi-objectivizing’ a single-objective optimization (SOO) problem can remove local optima. Then we investigate small instances of the travelling salesman problem where additional objectives are defined using arbitrary sub-tours. Results indicate that multi-objectivization can reduce local optima and facilitate improved optimization in some cases. These results enlighten our intuitions about the nature of search in multi-objective optimization and sources of difficulty in single-objective optimization.
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References
R. Bellman. Dynamic programming and multi-stage decision processes of stochastic type. In Proceedings of the second symposium in linear programming, volume 2, pages 229–250, Washington D.C., 1955. NBS and USAF.
D. W. Corne and J. D. Knowles. The Pareto-envelope based selection algorithm for multiobjective optimization. In Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature (PPSN VI), pages 839–848, Berlin, 2000. Springer-Verlag.
M. M. Flood. The travelling-salesman problem. Operations Research, 4:61–75, 1956.
J. Horn, D. Goldberg, and K. Deb. Long path problems for mutation-based algorithms. Technical Report 92011, Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana-Champaign, Urbana IL, 1992.
M. Huynen, P. Stadler, and W. Fontana. Smoothness within ruggedness: The role of neutrality in adaptation. Proceedings of the National Academy of Sciences (USA), 93:397–401, 1996.
D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215–310. John Wiley and Sons, 1997.
T. Jones. Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico, Albuquerque, 1995.
J. D. Knowles and D. W. Corne. The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimisation. In 1999 Congress on Evolutionary Computation, pages 98–105, Washington,D.C., July 1999. IEEE Service Center.
J. D. Knowles and D. W. Corne. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation, 8(2):149–172, 2000.
S. J. Louis and G. J. E. Rawlins. Pareto optimality, GA-easiness and deception. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA-5), pages 118–123, San Mateo, CA, 1993. Morgan Kaufmann.
S. W. Mahfoud. Niching methods for genetic algorithms. PhD thesis, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1995. IlliGAL Report 95001.
W. Mendenhall and R. J. Beaver. Introduction to Probability and Statistics-9th edition. Duxbury Press, International Thomson Publishing, Pacific Grove, CA, 1994.
M. G. Norman and P. Moscato. The euclidean traveling salesman problem and a space-filling curve. Chaos, Solitons and Fractals, 6:389–397, 1995.
C. R. Reeves. Modern heuristic techniques. In V. Rayward-Smith, I. Osman, C. Reeves, and G. Smith, editors, Modern Heuristic Search Methods, chapter 1, pages 1–26. John Wiley and Sons Ltd., 1996.
D. A. Van Veldhuizen and G. B. Lamont. Multiobjective Optimization with Messy Genetic Algorithms. In Proceedings of the 2000 ACM Symposium on Applied Computing, pages 470–476, Villa Olmo, Como, Italy, 2000. ACM.
R. A. Watson, G. S. Hornby, and J. B. Pollack. Modeling building-block interdependency. In Parallel Problem Solving from Nature-PPSN V, pages 97–106. Springer-Verlag, 1998.
R. A. Watson and J. B. Pollack. Analysis of recombinative algorithms on a hierarchical building-block problem. In Foundations of Genetic Algorithms (FOGA), 2000.
R. A. Watson and J. B. Pollack. Symbiotic combination as an alternative to sexual recombination in genetic algorithms. In Proceedings of the Sixth International Conference of Parallel Problem Solving From Nature (PPSN VI), pages 425–436. Springer-Verlag, 2000.
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Knowles, J.D., Watson, R.A., Corne, D.W. (2001). Reducing Local Optima in Single-Objective Problems by Multi-objectivization. In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., Corne, D. (eds) Evolutionary Multi-Criterion Optimization. EMO 2001. Lecture Notes in Computer Science, vol 1993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44719-9_19
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DOI: https://doi.org/10.1007/3-540-44719-9_19
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