Abstract
A bio-inspired artificial immune system is developed to track dynamically the Pareto fronts of time-varying constrained multi-objective problems with changing variable dimensions. It executes in order T-module, B-module, and M-module within a run period. The first module is designed to examine dynamically whether the environment changes or whether a change takes place in the optimization problem, while creating an initial population by means of the history information. Thereafter, the second one is a loop of optimization that searches for the desired non-dominated front of a given environment, in which the evolving population is sorted into several subpopulations. Each of such subpopulations, relying upon the population diversity, suppresses its redundant individuals and evolves the winners. The last one stores temporarily the resultant non-dominated solutions of the environment that assist T-module to create some initial candidates helpful for the coming environment. These dynamic characteristics, along with the comparative experiments guarantee that the artificial immune system can track adaptively the time-varying environment and maintain the diversity of population while being of potential use for complex dynamic constrained multi-objective problems.
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References
Aragón VS, Esquivel SC, Coello Coello CA (2008) Optimizing constrained problems through a T-cell artificial immune system. J Comput Sci Technol 8(3):158–165
Aydin I, Karakose M, Akin E (2011) A multi-objective artificial immune algorithm for parameter optimization in support vector machine. Appl Soft Comput 11(1):120–129
Basu M (2005) A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems. Electric Power Energy Syst 27(2):147–153
Brownlee J (2006) IIDLE: an immunological inspired distributed learning environment for multiple objective and hybrid optimisation. In: 2006 IEEE congress on evolutionary computation, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16–21
Bui LT, Nguyen MH, Branke J et al (2008) Tackling dynamic problems with multiobjective evolutionary algorithms. In: Knowles J, Corne D, Deb K (eds) Multi-objective problem solving from nature: from concepts to applications. Springer, Berlin, pp 77–91
Campelo F, Guimaraes FG, Igarashi H (2007) Overview of artificial immune systems for multi-objective optimization. In: Obayashi S, et al (eds) EMO 2007, LNCS 4403, pp 937–951
Chen JY, Lin QZ, Ji Z (2010) A hybrid immune multiobjective optimization algorithm. Eur J Oper Res 204(2):294–302
Coello Coello CA (2005) Solving multiobjective optimization problems using an artificial immune system. Genet Program Evolvable Mach 6(2):163–190
Coello Coello CA, Efrén MM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inf 16:193–203
Coello Coello CA, Nareli CC (2001) Use of emulations of the immune system to handle constraints in evolutionary algorithms. In: Dagli CH, Buczak AL, Ghosh J et al (eds) Intelligent engineering systems through artificial neural networks (ANNIE’ 2001), vol 11. ASME Press, St. Louis Missouri, pp 141–146
Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Evol Comput 6:182–197
Deb K, Pratap A, Meyarivan T (2002) Constrained test problems for multi-objective evolutionary optimization. KanGAL report, 200002. Indian Institute Technology
Deb K, Udaya BRN, Karthik S (2007) Dynamic multi-objective optimization and decision-making using modified NSGA-II: a case study on hydro-thermal power scheduling bi-objective optimization problems. In: Obayashi S, Deb K, Poloni C et al (eds) Evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 4403, pp 803–817
de Castro LN, Timmis J (2002) Artificial immune systems: a new computational intelligence approach. Springer
Farina M, Deb K, Amato P (2004) Dynamic multiobjective optimization problems: test case, approximations, and applications. Evol Comput 8(5):425–442
Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3:1–16
Fonseca CM, Fleming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms-Part I: a unified formulation. IEEE Trans SMC-Part B: Cybernetics 28:26–37
Freschi F, Coello Coello CA, Repetto M (2010) Multiobjective optimization and artificial immune system: a review. http://www.igi-global.com/downloads/excerpts/33155.pdf
Gao JQ, Wang J (2010) WBMOAIS: a novel artificial immune system for multiobjective optimization. Comput Oper Res 37(1):50–61
Gong FL (2003) Immunology in medicine. Chinese Science Press
Gong MG, Jiao LC, Du HF et al (2008) Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput 16(2):225–255
Hajela P, Lee J (1996) Constrained genetic search via schema adaptation, an immune network solution. Struct Optim 12:11–15
Hatzakis I, Wallace D (2006) Dynamic multiobjective optimization with evolutionary algorithms: a forward-looking approach. In: Proceedings of the 8th annual conference on genetic and evolutionary computation, Seattle, Washington, USA, pp 1201–1208
Hong L (2009) An adaptive multi-objective immune optimization algorithm. In: 2009 IITA international conference on control, automation and systems engineering, pp 140–143
Hu ZH (2010) A multiobjective immune algorithm based on a multiple-affinity model. Eur J Oper Res 202(1):60–72
Huang XY, Zhang ZH, He CJ et al (2005) Modern intelligent algorithms: theory and applications. Chinese Science Press
Jiao LC, Du HF, Liu F et al (2006) Immunological computation for optimization, learning and recognition. Science Press, China
Jin Y, Branke J (2005) Evolutionary optimization in uncertain environments—a survey. Evol Comput 9(3):303–317
Kirley KA, Buyya M (2009) The Pareto-following variation operator as an alternative approximation model. In: 2009 congress on evolutionary computation (CEC’ 2009), pp 8–15
Kurpati A, Azarm S, Wu J (2002) Constraint handling improvements for multiobjective genetic algorithms. Struct Multidisc Optim 23:204–213
Liu CA, Wang YP (2009) Multiobjective evolutionary algorithm for dynamic nonlinear constrained optimization problems. J Syst Eng Electr 20(1):204–210
Luh GC, Chueh HC, Liu WW (2003) MOIA: multi-objective immune algorithm. Eng Optim 35(2):143–164
Maravall D, de Lope J (2006) Multi-objective dynamic optimization with genetic algorithms for automatic parking. Soft Comput 11(3):249–257
Mehnen J, Wagner T, Rudolph G (2006) Evolutionary optimization of dynamic multi-objective test functions. In: Proceedings of the second Italian workshop on evolutionary computation (GSICE2), Siena, Italy, September 2006
Michalewicz Z (1995) A survey of constraint handling techniques in evolutionary computation methods. In: John RM, Robert GR, David BF (eds) Proceedings of the 4th annual conference on evolutionary programming, Cambridge, MA, pp 135–155
Mitra K, Majumdar S, Raha S (2004) Multiobjective dynamic optimization of a semi-batch epoxy polymerization process. Comput Chem Eng 28(12):2583–2594
Nareli CC, Daniel TP, Coello Coello CA (2005) Handling constraints in global optimization using an artificial immune system. In: Jacob et al (eds) 4th international conference on artificial immune systems ICARIS 2005, vol 3627. LNCS, Canada, Agosto, pp 234–247
Omkar SN, Khandelwal R, Yathindra S et al (2008) Artificial immune system for multi-objective design optimization of composite structures. Eng Appl Artif Intell 21(8):1416–1429
Osman MS, Abo-Sinna MA, Mousa AA (2006) IT-CEMOP: an iterative co-evolutionary algorithm for multiobjective optimization problem with nonlinear constraints. Appl Math Comput 183:373–389
Oyama A, Shimoyama K, Fujii K (2005) New constraint-handling method for multiobjective multiconstraint evolutionary optimization and its application to space plane design. In: Schilling R, Haase W, Periaux J, et al (eds) Evolutionary and deterministic methods for design, optimization and control with applications to industrial and societal problems (Eurogen 2005). Munich, Germany, pp 1–13
Shang RH, Jiao LC, Gong MG, et al (2005) Clonal selection algorithm for dynamic multiobjective optimization. In: Hao Y, et al (eds) CIS 2005, Part, LNAI 3801. Springer, Berlin, Heidelberg, pp 846–851
Shimoyama K, Oyama A, Fujii K et al (2005) A new efficient and useful robust optimization approach-design for multi-objective six sigma. Evol Comput 1:950–957
Tan KC (2009) A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans Evol Comput 13(1):103–127
Tan KC, Goh CK, Mamun AA et al (2008) An evolutionary artificial immune system for multi-objective optimization. Eur J Oper Res 187(2):371–392
Trojanowski K, Wierzchoń ST (2009) Immune-based algorithms for dynamic optimization. Inf Sci 179(10):1495–1515
Xiao HS, Zu JA (2007) A new constrained multiobjective optimization algorithm based on artificial immune systems. In: 2007 international conference on mechatronics and automation, Harbin, China, pp 3122–3127
Zhang ZH (2006) Constrained multiobjective optimization immune algorithm: convergence and application. Comput Math Appl 52(5):791–808
Zhang ZH (2007) Immune optimization algorithm for constrained nonlinear multiobjective optimization problems. Appl Soft Comput 7:840–857
Zhang ZH (2008) Multiobjective optimization immune algorithm in dynamic environments and its application to greenhouse control. Appl Soft Comput 8:959–971
Zhang ZH, Qian SQ (2009) Multi-objective immune optimization in dynamic environments and its application to signal simulation. In: 2009 International conference on measuring technology and mechatronics automation, vol 3. Hunan, China, pp 246–250
Zhou A, Zhang Q, Jin Y et al (2007) Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization. In: The fourth international conference on evolutionary multi-criterion optimization, Matsushima, Japan, LNCS 4403, pp 832–846, March 5–8
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. Evol Comput 3:257–271
Acknowledgments
The authors are grateful to the anonymous reviewers for their helpful comments. They also thank the editors of this work for their support. The work is supported in part by National Natural Science Foundation NSFC (61065010, 60565002), Key Natural Science Research of National Education Department (208125) and Provincial Education Department of Guizhou (2007004), China.
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Zhang, Z., Qian, S. Artificial immune system in dynamic environments solving time-varying non-linear constrained multi-objective problems. Soft Comput 15, 1333–1349 (2011). https://doi.org/10.1007/s00500-010-0674-z
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DOI: https://doi.org/10.1007/s00500-010-0674-z