Abstract
Optimization of problems spanning more than three objectives, called many-objective optimization, is often hard to achieve using modern algorithm design and currently available computational resources. In this paper a multiobjective evolutionary algorithm, called the Surface Evolutionary Algorithm, is extended into many-objective optimization by utilizing, for the first time, the taxi-cab metric in the optimizer. The Surface Evolutionary Algorithm offers an alternative to multi-objective optimizers that rely on the principles of domination, hypervolume and so forth. The taxi-cab metric, or Manhattan distance, is introduced as the selection criterion and the basis for calculating attraction points in the Surface Evolutionary Algorithm. This allows for fast and efficient many-objective optimization previously not attainable using this method. The Taxi-Cab Surface Evolutionary Algorithm is evaluated on a set of well-known many-objective benchmark test problems. In problems of up to 20 dimensions, this new algorithm of low complexity is tested against several modern multi-objective evolutionary algorithms. The results reveal the Taxi- Cab Surface Evolutionary Algorithm as a conceptually simple, yet highly efficient many-objective optimizer.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons Ltd., West Sussex (2001)
Knowles, J., Corne, D., Deb, K. (eds.): Multiobjective Problem Solving from Nature. From Concepts to Applications, Natural Computing Series. Springer, Berlin (2008)
Rahmat-Samii, Y., Christodoulou, C.: Special Issue, IEEE Trans. Antennas Propag. 55(3) (2007)
Hughes, E.J.: Radar Waveform Optimisation as a Many-Objective Application Benchmark. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 700–714. Springer, Heidelberg (2007)
Holland, J.H.: Adaption in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Longman Inc. (1989)
Koza, J.R.: Genetic Programming. On the Programming of Computers by Means of Natural Selection. The MIT Press (1992)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proc. IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)
Purshouse, R.C., Fleming, P.J.: Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 16–30. Springer, Heidelberg (2003)
Purshouse, R.C., Fleming, P.J.: Evolutionary many-objective optimization: An exploratory analysis. In: Proc. of IEEE CEC 2003, vol. 3, pp. 2066–2073 (2003)
Hughes, E.J.: Evolutionary many-objective optimization: Many once or one many? In: Proc. of IEEE CEC 2005, vol. 1, pp. 222–227 (2005)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. TIK-Report 103, ETH, Zurich, Switzerland (2001)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Beume, N., Naujoks, B., Emmerich, M.: SMS- EMOA: Multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181, 1653–1669 (2007)
Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-objective Optimization. Evol. Comput. 15(1), 1–28 (2007)
Beume, N., Fonseca, C.M., Lopez-Ibanez, M., Paquete, L., Vahrenhold, J.: On the Complexity of Computing the Hypervolume Indicator. IEEE Trans. Evol. Comput. 13(5), 1075–1082 (2009)
Hughes, E.J.: Many-Objective Directed Evolutionary Line Search. In: Proc. of GECCO 2011, pp. 761–768. ACM (2011)
Hughes, E.J.: Multiple Single Objective Pareto Sampling. In: Proc. of IEEE CEC 2003, vol. 4, pp. 2678–2684 (2003)
Hughes, E.J.: MSOPS-II: A general-purpose Many-Objective optimizer. In: Proc. of IEEE CEC 2007, pp. 3944–3951 (2007)
Moen, H.J.F., Kristoffersen, S.: Spanning the Pareto Front of a Counter Radar Detection Problem. In: Proc. of GECCO 2011, pp. 1835–1842. ACM (2011)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Proc. of IEEE CEC 2002, pp. 825–830 (2002)
Deb, K.: A Robust Evolutionary Framework for Multi-Objective Optimization. In: Proc. of GECCO 2008, pp. 633–640. ACM (2008)
Bandyopadhyay, S., Saha, S., Maulik, U., Deb, K.: A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA. IEEE Trans. Evol. Comput. 12(3), 269–283 (2008)
Adra, S.F., Fleming, P.J.: Diversity Management in Evolutionary Many-Objective Optimization. IEEE Trans. Evol. Comput. 15(2), 183–195 (2011)
Hughes, E.J.: http://code.evanhughes.org
Deb, K., Goyal, M.: A Combined Genetic Adaptive Search (GeneAS) for Engineering Design. Computer Science and Informatics 26(4), 30–45 (1996)
Deb, K., Agrawal, R.B.: Simulated Binary Crossover for Continuous Search Space. Complex Systems 9, 115–148 (1995)
Matlab Distributed Computing Server. The MathWorks Inc. (1994-2011)
Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithm: Classifications, Analyses, and New Innovations. Ph.D. thesis, Air Force Institute of Technology (1999)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Ph.D. thesis, ETH, Zurich, Switzerland (November 1999)
Farhang-Mehr, A., Azarm, S.: Diversity Assessment of Pareto Optimal Solutions: An Entropy Approach. In: Proc. of CEC 2002, pp. 723–728 (2002)
Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN V. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. M.Sc. thesis, Cambridge, Massachusetts (1995)
Bandyopadhyay, S., Pal, S.K., Aruna, B.: Multiobjective GAs, Quantitative Indices, and Pattern Classification. IEEE Trans. Syst. Man Cybern. Syst.:B 34(5), 2088–2099 (2004)
Shannon, C.E.: A Mathematical Theory of Communication. Bell Systems Technical Journal 27, 379–423, 623–656 (1948)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moen, H.J.F., Hansen, N.B., Hovland, H., Tørresen, J. (2013). Many-Objective Optimization Using Taxi-Cab Surface Evolutionary Algorithm. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-37140-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37139-4
Online ISBN: 978-3-642-37140-0
eBook Packages: Computer ScienceComputer Science (R0)