Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems


This work investigates one immune optimization approach for dynamic constrained multi-objective multimodal optimization in terms of biological immune inspirations and the concept of constraint dominance. Such approach includes mainly three functional modules, environmental detection, population initialization and immune evolution. The first, inspired by the function of immune surveillance, is designed to detect the change of such kind of problem and to decide the type of a new environment; the second generates an initial population for the current environment, relying upon the result of detection; the last evolves two sub-populations along multiple directions and searches those excellent and diverse candidates. Experimental results show that the proposed approach can adaptively track the environmental change and effectively find the global Pareto-optimal front in each environment.

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Z. Zhang, M. Liao and L. Wang, "Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems," American Journal of Operations Research, Vol. 2 No. 2, 2012, pp. 193-202. doi: 10.4236/ajor.2012.22022.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Farina, K. Deb and P. Amato, “Dynamic Multi-Objective Optimization Problems: Test Case, Approximations, and Applications,” Evolutionary Computation, Vol. 8, No. 5, 2004, pp. 425-442. doi:10.1109/TEVC.2004.831456
[2] K. Deb, B. R. N. Udaya and S. Karthik, “Dynamic Multi-Objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-Thermal Power Scheduling Bi-Objective Optimization Problems,” Lecture Notes in Computer Science, Vol. 4403, 2007, pp. 803-817. doi:10.1007/978-3-540-70928-2_60
[3] J. Mehnen, T. Wagner and G. Rudolph, “Evolutionary Optimization of Dynamic Multi-Objective Test Functions,” Proceedings of the Second Italian Workshop on Evolutionary Computation, Siena, September 2006.
[4] A. Zhou, Y. C. Jin, Q. Zhang, B. Sendhoff and E. Tsang, “Prediction-Based Population Re-Initialization for Evolutionary Dynamic Multi-Objective Optimization,” The Fourth International Conference on Evolutionary Multi- Criterion Optimization, Matsushima, 5-8 March 2007, pp. 832-846.
[5] I. Hatzakis and D. Wallace, “Dynamic Multi-Objective Optimization with Evolutionary Algorithms: A Forward-Looking Approach,” Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Seattle, Washington, 2006, pp. 1201-1208.
[6] C. A. Liu and Y. P. Wang, “Multi-Objective Evolutionary Algorithm for Dynamic Nonlinear Constrained Optimization Problems,” Systems Engineering and Electronics, Vol. 20, No. 1, 2009, pp. 204-210.
[7] K. C. Tan, “A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multi-Objective Optimization,” IEEE Transactions on Evolutionary Computation, Vol. 13, No. 1, 2009, pp. 103-127. doi:10.1109/TEVC.2008.920671
[8] R. H. Shang, L. C. Jiao, M. G. Gong and B. Lu, “Clonal Selection Algorithm for Dynamic Multi-Objective Optimization,” In: Y. Hao, et al., Eds., Computational Intelligence and Security, Springer, Berlin, Heidelberg, Vol. 3801, 2005, pp. 846-851. doi:10.1007/11596448_125
[9] Z. H. Zhang, “Multi-Objective Optimization Immune Algorithm in Dynamic Environments and Its Application to Greenhouse Control,” Applied Soft Computing, Vol. 8, No. 2, 2008, pp. 959-971. doi:10.1016/j.asoc.2007.07.005
[10] Z. H. Zhang and S. Q. Qian, “Artificial Immune System in Dynamic Environments Solving Time-Varying Non- Linear Constrained Multi-Objective Problems,” Soft Computing, Vol. 15, No. 7, 2011, pp. 1333-1349. doi:10.1007/s00500-010-0674-z
[11] E. Hart and J. Timmis, “Application Areas of AIS: The Past, Present and the Future,” Applied Soft Computing, Vol. 8, No. 1, 2008, pp. 191-201. doi:10.1016/j.asoc.2006.12.004
[12] J. Timmis, P. Andrews and E. Hart, “On Artificial Immune Systems and Swarm Intelligence,” Swarm Intelligence, Vol. 4, No. 4, 2010, pp. 247-273. doi:10.1007/s11721-010-0045-5
[13] C. A. Coello Coello and N. Cruz Cortés, “An Approach to Solve Multi-Objective Optimization Problems Based on an Artificial Immune System,” In: J. Timmis and P. J. Bentley, Eds., First International Conference on Artificial Immune Systems, Canterbury, 2002, pp. 212-221.
[14] N. Cruz Cortés and C. A. Coello Coello, “Using Artificial Immune Systems to Solve Optimization Problems,” Workshop Program of Genetic and Evolutionary Computation Conference, 2003, pp. 312-315.
[15] I. Aydin, M. Karakose and E. Akin, “A Multi-Objective Artificial Immune Algorithm for Parameter Optimization in Support Vector Machine,” Applied Soft Computing, Vol. 11, No. 1, 2011, pp. 120-129. doi:10.1016/j.asoc.2009.11.003
[16] Z. H. Hu, “A Multiobjective Immune Algorithm Based on a Multiple-Affinity Model,” European Journal of Operational Research, Vol. 202, No. 1, 2010, pp. 60-72. doi:10.1016/j.ejor.2009.05.016
[17] J. Q. Gao and J. Wang, “WBMOAIS: A Novel Artificial Immune System for Multi-objective Optimization,” Computers & Operations Research, Vol. 37, No. 1, 2010, pp. 50-61. doi:10.1016/j.cor.2009.03.009
[18] K. Deb, A. Pratap, and T. Meyarivan, “Constrained Test Problems for Multi-Objective Evolutionary Optimization,” Evolutionary Multi-Criterion Optimization Lecture Notes in Computer Science, Vol. 1993, 2001, pp. 284- 298.
[19] A. Kurpati, S. Azarm and J. Wu, “Constraint Handling Improvements for Multiobjective Genetic Algorithms,” Structural Multidisciplinary Optimization, Vol. 23, No. 3, 2002, pp. 204-213. doi:10.1007/s00158-002-0178-2
[20] K. Deb and A. Srinivasan, “Monotonicity Analysis, Evolutionary Multi-Objective Optimization, and Discovery of Design Principles,” Indian Institute of Technology, Kanpur Genetic Algorithm Laboratory (KanGAL), Report No. 2006004, 2006.

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