Evolutionary Multi-Objective Optimization

Many practical problems require the simultaneous optimization of several non-commensurable and often competing objectives. The 

There have been many surveys on evolutionary techniques for MOO (Fonseca and Fleming, 1995 Coello Coello, 1998 Van Veldhuizen and Lamont, 2000 Tan et al, 2002 Chapter 3 in this book). While conventional methods combined multiple criteria to form a composite scalar objective function, modern approach incorporates the concept of Pareto optimality or modified selection schemes to evolve a family of solutions at multiple points along the tradeoffs simultaneously (Tan et al, 2002). 

The /th objective component that corresponds to a hard constraint is assigned to the value of G(i) whenever the hard constraint has been satisfied. The underlying reason is that there is no ranking preference for any particular objective component that has the same value in an evolutionary optimization process, and thus the evolution will only be directed toward optimizing soft constraints and any unattained hard constraints. 

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Keywords Evolutionary Multi-objective Optimization, Chemical Engineering, Metaheuristics, Evolutionary Algorithms. 

Laumanns, M., Thiele, L., Deh, K. and Zitzler, E. (2002). Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation, 10(3), pp. 263-282. 

Liefooghe, A., Basseur, M., Jourdan, L. and Talbi, E.-G. (2007). ParadisEO-MOEO A framework for evolutionary multi-objective optimization, in S. Obayashi et al. (eds.). Evolutionary Multi-Criterion Optimization, 4th International Conference, EMO 2007 (Springer. LNCS Vol. 4403, Matshushima, Japan), pp. 386-400. 

Santana-Quinter, L. V., Serrano-Hernandez, V. A., Coello Coello, C. A., Hemandez-Diaz, A. G. and Mohna, J. (2007). Use of radial basis functions and rough sets for evolutionary multi-objective optimization, in Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Multicriteria Decision Making (MCDM 2007) (IEEE Press, Honolulu, Hawaii, USA), pp. 107-114. 

Vol. 186. Chi-Keong Goh and Kay Chen Tan Evolutionary Multi-objective Optimization in Uncertain Environments, 2009 ISBN 978-3-540-95975-5... 

Tan KC, Goh CK, Yang YJ, Lee TH (2006) Evolving better population distribution and exploration in evolutionary multi-objective optimization. Eur J Oper Res 171(2) 463-495... 

Deb, K. (2001). Multi-objective Optimization Using Evolutionary Algorithms, Wiley, Chichester, UK. 

Babu, B. and Jeban, M. M. L. (2003). Differential evolution for multi-objective optimization, in Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Vol.4 (IEEE Press, Canberra, Australia), pp. 2696-2703. 

Surrogate Assisted Evolutionary Algorithm for Multi-Objective Optimization... 

Keywords multi-objective optimization, surrogate models, radial basis function network, evolutionary algorithm... 

Jaimes, A.L. and CoeUo Coello, C.A. (2008). Multiobjective Evolutionary Algorithms A Review of the State-of-the-Art and some of their AppUcations in Chemical Engineering. Chapter 2 in G.P. Rangaiah (Ed.) Multi-Objective Optimization Techniques and Applications in Chemical Engineering, World Scientific. 

Shim, M., Suh, M., Eurukawa, T., Yagawa, G., and Yoshimura, S. (2002). Pareto-based continuous evolutionary algorithms for multi-objective optimization. Engineering Computations, 19, 1, 22-48. 

Fonseca, C. M. and Fleming, P. J. (1995). An Overview of Evolutionary Algorithms in Multi-objective Optimization, Journal of Evolutionary Computation 3(1), pp. 1-16. 

Tan, K. C., Lee, T. H. and Khor, E. F. (1999). Evolutionary Algorithms with Goal and Priority Information for Multi-Objective Optimization, IEEE Conf. Evolutionary Computation, 1, pp. 106-113. 

Keywords Emergency Planning, Decision Making, Major Accident, Evacuation, Multi-objective Optimization, Evolutionary Algorithm. 

Deb, K., Rao N, U., and Karthik, S. Dynamic multi-objective optimization and decisionmaking using modified nsga-ii a case study on hydro-thermal power scheduling. In Evolutionary Multi-Criterion Optimization, pages 803-817. Springer, New York, 2007. 

Muschalla D (2006) Evolutionare und multikriterielle Optimierung komplexer wasserwirtschaftlicher Systeme [Evolutionary and multi-objective optimization of complex water management systems]. Dissertation. Fachbereich fur Bauingenieurwesen und Geodasie, TU Darmstadt... 

To solve the above optimization problem, a Multiple-Objective Evolutionary Algorithms (MOEA) is embraced here. MOEA is a term employed in the Evolutionary Multi-criteria Optimization field to refer to a family of evolutionary algorithms formulated to deal with MO. MOEA are able to deal with non-continuos, non-convex and/or non-linear objectives/constraints, and objective functions possibly not explicitly known (e.g. the output of Monte Carlo simulation tuns). 

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