Reference direction based immune clone algorithm for many-objective optimization

Abstract

In this paper, a new preference multi-objective optimization algorithm called immune clone algorithm based on reference direction method (RD-ICA) is proposed for solving many-objective optimization problems. First, an intelligent recombination operator, which performs well on the functions comprising many parameters, is introduced into an immune clone algorithm so as to explore the potentially excellent gene segments of all individuals in the antibody population. Second, a reference direction method, a very strict ranking based on the desire of decision makers (DMs), is used to guide selection and clone of the active population. Then a light beam search (LBS) is borrowed to pick out a small set of individuals filling the external population. The proposed method has been extensively compared with other recently proposed evolutionary multi-objective optimization (EMO) approaches over DTLZ problems with from 4 to 100 objectives. Experimental results indicate RD-ICA can achieve competitive results.

Keywords

many-objective optimization / preference multiobjective optimization / artificial immune system / reference direction method / light beam search / intelligent recombination operator

References

[1] Farina M, Amato P. On the optimal solution definition for many-criteria optimization problems. In: Proceedings of International Conference of the NAFIPS-FLINT. 2002, 233-238

[2] Freschi F, Repetto M. Multiobjective optimization by a modified artificial immune system algorithm. In: Proceedings of the 4th International Conference on Artificial Immune Systems. 2005, 3627: 248-261

[3] Rachmawati L, Srinivasan D. Preference incorporation in multiobjective evolutionary algorithms: a survey. In: Proceedings of 2006 IEEE Congress on Evolutionary Computation. 2006, 3385-3391

[4] Yang D D, Jiao L C, Gong M G, Feng J. Adaptive ranks clone and k-nearest neighbor list-based immune multi-objective optimization. Computational Intelligence, 2010, 26(4): 359-385

[5] Deb K, Kummar A. Light beam search based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 2007 IEEE Congress on Evolutionary Computation. 2007, 2125-2132

[6] Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 2000, 8(2): 173-195

[7] Deb K, Thiele L, Laumanns M, Zitzler E. Scalable test problems for evolutionary multi-objective optimization. In: Abraham A, Jain L and Goldberg R, eds. Evolutionary multiobjective optimization, Springer London, 2005, 105-145

[8] Gong M G, Jiao L C, Du H F, Bo L F. Multiobjective immune algorithm with nondominated neighbor-based selection. Evolutionary Computation, 2008, 16(2): 225-255

[9] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197

[10] Zitzler E, Laumanns M, Thiele L. SPEA2: improving the performance of the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich, 2001

[11] Corne D W, Knowles J D, Oates M J. The Pareto-envelope based selection algorithm for multi-objective optimization. In: Proceedings of the Parallel Problem Solving from Nature VI Conference. 2000, 839-848

[12] Coello Coello C A, Cortes N C. Solving multiobjective optimization problems using an artificial immune system. Genetic Programming and Evolvable Machines, 2005, 6(2): 163-190

[13] Jiao L C, Gong M G, Shang R H, Du H F, Lu B. Clonal selection with immune dominance and energy based multi-objective optimization. In: Proceeding of the 3rd International Conference on Evolutionary Multicriterion Optimization, EMO. 2005, 474-489

[14] Freschi F, Repetto M. VIS: an artificial immune network for multiobjective optimization. Engineering Optimization, 2006, 38(8): 975-996

[15] Garza-Fabre M, Pulido G T, Coello Coello C A. Ranking methods for many-objective optimization. Lecture Notes in Computer Science, 2009, 5845: 633-645

[16] di Pierro F. Many-objective evolutionary algorithms and applications to water resources engineering. PhD thesis, University of Exeter, UK, <month>August</month>2006

[17] di Pierro F, Djordjevic S, Khu S, Savic D, Walters G A. Automatic calibration of urban drainage model using a novel multi-objective GA. Water Science and Technology, 2005, 52(5): 43-52

[18] Garcia S, Molina D, Lozano M, Herrera F. A study on the use of nonparametric tests for analyzing the evolutionary algorithms’ behavior: a case study on the CEC’2005 special session on real parameter optimization. Journal of Heuristics, 2005, 15: 617-644

[19] Praditwong K, Yao X. A new multi-objective evolutionary optimization algorithm: the two-archive algorithm. In: Proceeding of International Conference on Computational Intelligence and Security. 2006, 1: 286-291

[20] Fonseca C M, Fleming P J. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proceedings of the 5th International Conference on Genetic Algorithms. 1993, 416-423

[21] Deb K, Sundar J, Uday Bhaskara Rao N, Chandhuri S. Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research, 2006, 2(3): 273-286

[22] Jaszkiewicz A, Slowinski R. The light beam search approach–an overview of methodology and applications. European Journal of Operation Research, 1999, 113(2): 300-314

[23] Thiele L, Miettinen K, Korhonen P J, Molina J. A preference-based evolutionary algorithm for multi-objective optimization. Evolutionary Computation, 2009, 17(3): 411-436

[24] Molina J, Santana L V, Hernandez-Diaz A G, Coello Coello C A, Caballero R. g-dominance: reference point based dominance for multiobjective metaheuristics. European Journal of Operational Research, 2009, 197(2): 685-692

[25] Lamjed B S, Slim B, Khaled G. The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Transactions on Evolutionary Computation, 2010, 14(5): 801-818

[26] Laumanns M, Thiele L, Deb K. Combining convergence and diversity in evolutionary multiobjective optimization. Evolutionary Computation, 2002, 10(3): 263-282

[27] Deb K, Mohan M, Mishra S. Toward a quick computation of wellspread Pareto-optimal solutions. In: Proceedings of the 2nd International Conference of Evolutionary Multi-criterion Optimization. 2003, 2632: 222-236

[28] Farina M, Amato P. On the optimal solution definition for many-criteria optimization problems. In: Proceedings of International Conference of the NAFIPS-FLINT. 2002, 233-238

[29] Park S H. Robust design and analysis for quality engineering. Taylor & Francis, 1998, 40(4): 348-349

[30] Leung Y W, Wang Y. An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Transactions on Evolutionary Computation, 2001, 5(1): 41-53

[31] Ho S, Shu L, Chen J. Intelligent evolutionary algorithms for large parameter. IEEE Transactions on Evolutionary Computation, 2004, 8(6): 522-541

[32] de Castro L N, Von Zuben F J. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, Special Issue on Artificial Immune Systems, 2002, 6(3): 239-251

[33] Cutello V, Nicosia G, Pavone M. Exploring the capability of immune algorithms: a characterization of hypermutation operators. In: Proceedings of 3rd International Conference on Artificial Immune Systems. 2004, 3239: 263-276

[34] Deb K, Kumar A. Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Proceeding of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO’07). 2007, 781-788

[35] Van Veldhuizen D A. Multi-objective evolutionary algorithms: classification, analyzes, and new innovations. PhD thesis, Wright-Patterson AFB: Air Force Institute of Technology, <month>June</month>1999

[36] Schott J R. Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s thesis, Massachusetts Institute of Technology, <month>May</month><?Pub Caret?>1995

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg