Abstract
Evolutionary multi-objective optimization algorithms have been developed to find a representative set of Pareto-optimal solutions in the past decades. However, researchers have pointed out that finding a representative set of Pareto-optimal solutions is not sufficient; the task of choosing a single preferred Pareto-optimal solution is also another important task which has received a widespread attention so far. In this paper, we propose an algorithm to help the decision maker (DM) choose the final preferred solution based on his/her preferred objectives. Our algorithm is called an adaptive angle based pruning algorithm with independent bias intensity tuning parameter (ADA-τ). The method begins by calculating the angle between a pair of solutions by using a simple arctangent function. The bias intensity parameter of each objective is introduced independently in order to approximate the portions of desirable solutions based on the DM’s preferred objectives. We consider several benchmark problems including two and three-objective problems. The experimental results have shown that our pruning algorithm provides a robust sub-set of Pareto-optimal solutions for the benchmark problems.
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References
Branke, J., Kauber, T., Schech, H.: Guidance in Evolutionary Multi-objective Optimization. J. on Adv. Eng. Software 32, 449–507 (2001)
Kim, J.H., Han, J.H., Choi, S.H., Kim, E.S.: Preference-Based Solution Selection Algorithm for Evolutionary Multiobjective Optimization. IEEE Tran. on Evolutionary Computation 16, 20–34 (2012)
Konak, S.K., Coit, D., Baheranwala, F.: Pruned Pareto-optimal Sets for the System Redundancy Allocation Problem Based on Multiple Prioritized Objectives. J. of Heuristics 14, 335–357 (2008)
Soylu, B., Ulusoy, S.K.: A preference ordered classification for a multi-objective max-min redundancy allocation problem. Computer and Operation Research 13, 1855–1866 (2011)
Karahan, I., Koksalan, M.: A Territory Defining Multiobjective Evolutionary Algorithms and Preference Incorporation. IEEE Trans. on Evolutionary Computation 14, 636–664 (2010)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. on Evolutionary Computation 11, 712–731 (2007)
Coit, D., Konak, A.: Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem. IEEE Trans. on Reliability 55, 4471–4479 (2006)
Jaszkiewicz, A., Branke, J.: Interactive Multiobjective Evolutionary Algorithms. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 179–193. Springer, Heidelberg (2008)
Branke, J.: Consideration of Partial User Preferences in Evolutionary Multioobjective Optimization. LNCS, pp. 157–178. Springer, Berlin (2008)
Goldberg, D.E.: Genetic algorithms in search, optimization & machine learning. Addison-Wesley, Reading (1989)
Leesutthipornchai, P.: Multi-Objective Optimization for Grooming, Routing and Wavelength Assignment in Optical Network Design. PhD dissertation. Department of computer engineering. King Mongkut’s University of Technology Thonburi, Thailand (2010)
Wang, R., Purshouse, R.C., Fleming, P.J.: Local Preference-inspired Co-evolutionary Algorithms. In: Genetic and Evolutionary Computation Conference (GECCO 2012), Philadelphia, Pensylvania, USA, pp. 513–520 (2012)
Bechikh, S., Said, L.B., Ghedira, K.: Negotiating decision makers’ reference points for group preference-based Evolutionary Multi-objective Optimization. In: The 11th International Conference on Hybrid Intelligent Systems (HIS), pp. 377–382. IEEE Press, Melacca (2011)
Branke, J., Deb, K.: Integrating User Preferences into Evolutionary Multi-objective Optimization. KangGAL Technical report, Report Number 20004004 (2004)
Mohammadi, A., Omidvar, M.N., Li, X.: Reference Point Based Multi-objective Optimization Through Decomposition. In: World Congress on Computational Intelligence, WCCI 2011, Brisbane, Australia, pp. 1150–1157 (2012)
Friedrich, T., Kroeger, T., Neumann, F.: Weighted Preferences in Evolutionary Multi-objective Optimization. In: 24th Australian Joint Conference on Advances in Artificial Intelligence, Perth, Australia, pp. 291–300 (2011)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Computer Engineering and Network Laboratory (TIK), Department of Electrical Engineering, Swiss Federal Institute of Technology (ETH) Zurich, Swithzerland, pp. 1–21 (2001)
Deb, K., Pratab, A., Agarwal, S., Meyarivan, T.: Fast and Elitist Multi-objective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 182–197 (2002)
Branke, J., Deb, K., Dierof, H., Osswald, M.: Finding knees in multi-objective optimization. In: The Eight Conference of Parallel Problem Solving from Nature (PPSSN VIII) (2004)
Deb, K.: Multi-objective Evolutionary Algorithms: Introducing Bias Among Pareto-optimal Solutions. Adv. in Evolutionary Computing, 263–292 (2003)
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Sudeng, S., Wattanapongsakorn, N. (2014). Finding Robust Pareto-optimal Solutions Using Geometric Angle-Based Pruning Algorithm. In: Chen, L., Kapoor, S., Bhatia, R. (eds) Intelligent Systems for Science and Information. Studies in Computational Intelligence, vol 542. Springer, Cham. https://doi.org/10.1007/978-3-319-04702-7_16
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DOI: https://doi.org/10.1007/978-3-319-04702-7_16
Publisher Name: Springer, Cham
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