Abstract
This paper proposes an idea of probabilistically using a scalarizing fitness function in evolutionary multiobjective optimization (EMO) algorithms. We introduce two probabilities to specify how often the scalarizing fitness function is used for parent selection and generation update in EMO algorithms. Through computational experiments on multiobjective 0/1 knapsack problems with two, three and four objectives, we show that the probabilistic use of the scalarizing fitness function improves the performance of EMO algorithms. In a special case, our idea can be viewed as the probabilistic use of an EMO scheme in single-objective evolutionary algorithms (SOEAs). From this point of view, we examine the effectiveness of our idea. Experimental results show that our idea improves not only the performance of EMO algorithms for multiobjective problems but also that of SOEAs for single-objective problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Colombo, G., Mumford, C.L.: Comparing Algorithms, Representations and Operators for the Multi-objective Knapsack Problem. In: Proc. of 2005 Congress on Evolutionary Computation, pp. 2241–2247 (2005)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 182–197 (2002)
Fonseca, C.M., Fleming, P.J.: On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers. In: Parallel Problem Solving from Nature - PPSN IV. LNCS, vol. 114, pp. 584–593. Springer, Heidelberg (1996)
Hughes, E.J.: Multiple Single Objective Sampling. In: Proc. of 2003 Congress on Evolutionary Computation, pp. 2678–2684 (2003)
Hughes, E.J.: Evolutionary Many-objective Optimization: Many Once or One Many? In: Proc. of 2005 Congress on Evolutionary Computation, pp. 222–227 (2005)
Ishibuchi, H., Murata, T.: A Multi-Objective Genetic Local Search Algorithm and Its Application to Flowshop Scheduling. IEEE Trans. on Systems, Man, and Cybernetics - Part C: Applications and Reviews 28, 392–403 (1998)
Ishibuchi, H., Nojima, Y., Doi, T.: Comparison between Single-objective and Multi-objective Genetic Algorithms: Performance Comparison and Performance Measures. In: Proc. of 2006 Congress on Evolutionary Computation (in press, 2006)
Ishibuchi, H., Yoshida, T., Murata, T.: Balance between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling. IEEE Trans. on Evolutionary Computation 7, 204–223 (2003)
Jaszkiewicz, A.: Genetic Local Search for Multi-Objective Combinatorial Optimization. European Journal of Operational Research 137, 50–71 (2002)
Jaszkiewicz, A.: On the Performance of Multiple-Objective Genetic Local Search on the 0/1 Knapsack Problem - A Comparative Experiment. IEEE Trans. on Evolutionary Computation 6, 402–412 (2002)
Jaszkiewicz, A.: On the Computational Efficiency of Multiple Objective Metaheuristics: The Knapsack Problem Case Study. European Journal of Operational Research 158, 418–433 (2004)
Knowles, J.D., Watson, R.A., Corne, D.W.: Reducing Local Optima in Single-Objective Problems by Multi-Objectivization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 269–283. Springer, Heidelberg (2001)
Mumford, C.L.: A Hierarchical Solve-and-Merge Framework for Multi-Objective Optimization. In: Proc. of 2005 Congress on Evolutionary Computation, pp. 2241–2247 (2005)
Murata, T., Ishibuchi, H., Gen, M.: Specification of Genetic Search Directions in Cellular Multi-Objective Genetic Algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 82–95. Springer, Heidelberg (2001)
Purshouse, R.C., Fleming, P.J.: Evolutionary Many-Objective Optimization: An Exploratory Analysis. In: Proc. of 2003 Congress on Evolutionary Computation, pp. 2066–2073 (2003)
Schaffer, J.D.: Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Proc. of 1st International Conference on Genetic Algorithms and Their Applications, pp. 93–100 (1985)
Watanabe, S., Sakakibara, K.: Multi-Objective Approaches in a Single-Objective Optimization Environment. In: Proc. of 2005 Congress on Evolutionary Computation, pp. 1714–1721 (2005)
Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans. on Evolutionary Computation 3, 257–271 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ishibuchi, H., Doi, T., Nojima, Y. (2006). Incorporation of Scalarizing Fitness Functions into Evolutionary Multiobjective Optimization Algorithms. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_50
Download citation
DOI: https://doi.org/10.1007/11844297_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
eBook Packages: Computer ScienceComputer Science (R0)