Abstract：Two evolutionary models, individual based evolutionary model (IND) and population based evolutionary model (POP) are proposed. Based on these two models, two kinds of multi-objective evolutionary algorithms (LHS) are designed based on Latin hypercube sampling, namely LHS-MOEAs. In LHS-MOEAs, the LHS local search is designed for exploiting promising areas and the evolutionary operator is designed for exploring new searching areas in feasible space. The combination of LHS local search and evolutionary operator in LHS-MOEA can prevent degeneration effectively. Experimental results demonstrate that the proposed LHS-MOEAs performs better and it is more preponderant than the classical NSGA-II in solving CPS_MOPs.
[1] Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms // Proc of the 1st International Conference on Genetic Algorithm. Hillsdale, USA, 1985: 93-100 [2] Coello C C A. Evolutionary Multiobjective Optimization: A Historical View of the Field. IEEE Computational Intelligence Magazine, 2006, 1(1): 28-36 [3] Coello C C A. 20 Years of Evolutionary Multi-Objective Optimization: What Has Been Done and What Remains to Be Done // Yen G Y, Fogel D B, eds. Computational Intelligence: Principles and Practice, Chapter 4. New York, USA: IEEE Computational Intelligence Society, 2006: 73-88 [4] Fonseca C M, Fleming J. Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization // Proc of the 5th International Conference on Genetic Algorithms. San Mateo, USA, 1993: 416-423 [5] Srinivas N, Deb K. Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation. 1994, 2(3): 221-248 [6] Horn J, Nafpliotis N, Goldberg D E. A Niched Pareto Genetic Algorithm for Multiobjective Optimization // Proc of the 1st IEEE World Congress on Evolutionary Computational Intelligence. Piscataway, USA, 1994: 82-87 [7] Zitzler E, Thiele L. Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Study // Proc of the 5th International Conference on Parallel Problem Solving from Nature. Amsterdam, Netherlands, 1998: 292-304 [8] Zitzler E, Thiele L. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans on Evolutionary Computation, 1999, 3(4): 257-271 [9] Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report, 103, Zurich, Switzerland: ETH Zurich. Computer Engineering and Networks Laboratory (TIK), 2001 [10] Knowles J, Corne D. Properties of an Adaptive Archiving Algorithm for Storing Nondominated Vectors. IEEE Trans on Evolutionary Computation, 2003, 7(2): 100-116 [11] Deb K, Goldberg D E. An Investigation of Niche and Species Formation in Genetic Function Optimization // Proc of the 3rd International Conference on Genetic Algorithms. San Mateo, USA, 1989: 42-50 [12] Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans on Evolutionary Computation, 2002, 6(2): 182-197 [13] Corne D, Knowles J D, Oates M J. The Pareto Envelope-Based Selection Algorithm for Multiobjecitve Optimization // Proc of the 6th International Conference on Parallel Problem Solving from Nature. Paris, France, 2000: 839-848 [14] Corne D W, Jerram N R, Knowles J D, et al. PESA-II: Region-Based Selection in Evolutionary Multiobjective Optimization // Proc of the Genetic and Evolutionary Computation Conference. San Francisco, USA, 2001: 283-290 [15] Cui Xunxue. Multiobjective Evolutionary Algorithms and Their Applications. Beijing, China: National Defense Industry Press, 2006 (in Chinese) (崔逊学.多目标进化算法及其应用.北京:国防工业出版社, 2006) [16] Zheng Jinhua. Multiobjective Evolutionary Algorithms and Applications. Beijing, China: Science Press, 2007 (in Chinese) (郑金华.多目标进化算法及其应用.北京:科学出版社, 2007) [17] Zhang Qingfu, Zhou Aimin, Jin Yaochu. RM-MEDA: A Regularity Model Based Multiobjective Estimation of Distribution Algorithm. IEEE Trans on Evolutionary Computation, 2008, 12(1): 41-63 [18] Edgeworth F Y. Mathematical Psychics. London, UK: Kegan Paul & Co., 1881 [19] Pareto V. Cours D'Economie Politique. Lausanne, Switzerland: Rouge Press, 1896 [20] Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation, 1999, 7(3): 205-230 [21] Deb K. Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Technical Report, CI-49/98, Dortmund: Germany: University of Dortmund. Department of Computer Science/LS11, 1999 [22] Deb K, Sinha A, Kukkonen S. Multi-Objective Test Problems, Linkages, and Evolutionary Methodologies // Proc of the 8th Annual Conference on Genetic and Evolutionary Computation. Seattle, USA, 2006, Ⅱ: 1141-1148 [23] Li Hui, Zhang Qingfu. A Multiobjective Differential Evolution Based on Decomposition for Multiobjective Optimization with Variable Linkages // Proc of the International Conference on Parallel Problem Solving from Nature. Reykjavik, Iceland, 2006: 583-592 [24] Mckay M D, Beckman R J, Conover W J. A Comparison of Three Methods for the Selecting Values of Input Variables in the Analysis of Out Put from a Computer Code. Technometrics, 1979, 21(2): 239-245 [25] Deb K, Agrawal R B. Simulated Binary Crossover for Continuous Search Space. Complex Systems, 1995, 9(6): 115-148 [26] Deb K, Beyer H. Self-Adaptive Genetic Algorithms with Simulated Binary Crossover. Evolutionary Computation, 2001, 9(2): 197-221 [27] Deb K, Goyal M. A Combined Genetic Adaptive Search (GeneAS) for Engineering Design. Computer Science and Informatics, 1996, 26(4): 30-45 [28] Wolpert D H, Macready W G. No Free Lunch Theorems for Optimization. IEEE Trans on Evolutionary Computation, 1997, 1(1): 67-82
2009, Vol. 22 
