Abstract
The term ‘multiobjectivization’ refers to the casting of a single-objec-tive optimization problem as a multiobjective one, a transformation that can be achieved by the addition of supplementary objectives or by the decomposition of the original objective function. In this paper, we analyze how multiobjectivization by decomposition changes the fitness landscape of a given problem and affects search. We find that decomposition has only one possible effect: to introduce plateaus of incomparable solutions. Consequently, multiobjective hillclimbers using no archive ‘see’ a smaller (or at most equal) number of local optima on a transformed problem compared to hillclimbers on the original problem. When archived multiobjective hillclimbers are considered this effect may partly be reversed. Running time analyses conducted on four example functions demonstrate the (positive and negative) influence that both the multiobjectivization itself, and the use vs. non-use of an archive, can have on the performance of simple hillclimbers. In each case an exponential/polynomial divide is revealed.
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Brockhoff, D., Friedrich, T., Hebbinghaus, N., Klein, C., Neumann, F., Zitzler, E.: Do additional objectives make a problem harder. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 765–772. ACM Press, New York (2007)
Forrest, S., Mitchell, M., Whitley, L.: Relative Building-Block Fitness and the Building-Block Hypothesis. In: Foundations of Genetic Algorithms 2, pp. 109–126. Morgan Kaufmann, San Mateo (1993)
Garnier, J., Kallel, L., Schoenauer, M.: Rigorous hitting times for binary mutations. Evolutionary Computation 7(2), 173–203 (1999)
Hagerub, T., Rüb, C.: A guided tour of Chernoff bounds. Information Processing Letters 33, 305–308 (1989)
Hanne, T.: On the convergence of multiobjective evolutionary algorithms. European Journal of Operational Research 117(3), 553–564 (1999)
Jansen, T., Wegener, I.: Evolutionary algorithms — how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Transactions on Evolutionary Computation 5(6), 589–599 (2001)
Jensen, M.T.: Helper-objectives: Using multi-objective evolutionary algorithms for single-objective optimisation. Journal of Mathematical Modelling and Algorithms 3(4), 323–347 (2004)
Juels, A., Wattenberg, M.: Stochastic Hillclimbing as a Baseline Method for Evaluating Genetic Algorithms. In: Touretzky, D.S. (ed.) Advances in Neural Information Processing Systems 8, pp. 430–436. MIT Press, Cambridge (1995)
Knowles, J.: Local-search and hybrid evolutionary algorithms for Pareto optimization. PhD thesis, University of Reading, UK (2002)
Knowles, J., Watson, R., Corne, D.: Reducing local optima in single-objective problems by multi-objectivization. In: Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, pp. 269–283. Springer, Berlin (2001)
Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)
Neumann, F., Wegener, I.: Minimum spanning trees made easier via multi-objective optimization. Natural Computing 5(3), 305–319 (2006)
Oliveto, P.S., Witt, C.: Simplified drift analysis for proving lower bounds in evolutionary computation. In: Rudolph, G., et al. (eds.) PPSN X 2008. LNCS, vol. 5199, pp. 82–91. Springer, Berlin (2008)
Scharnow, J., Tinnefeld, K., Wegener, I.: The analysis of evolutionary algorithms on sorting and shortest paths problems. Journal of Mathematical Modelling and Algorithms 3(4), 346–366 (2004)
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Handl, J., Lovell, S.C., Knowles, J. (2008). Multiobjectivization by Decomposition of Scalar Cost Functions. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_4
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DOI: https://doi.org/10.1007/978-3-540-87700-4_4
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