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Proceedings of GO 2005, pp. 213 – 218.A Multi-Objective Evolution Strategy for the Optimizationof Nonlinear Dynamic SystemsJosé-Oscar H. Sendín, Antonio A. Alonso, and Julio R. BangaProcess Engineering Group (IIM-CSIC), Vigo, Spain.osendin@iim.csic.es; antonio@iim.csic.es; julio@iim.csic.esAbstractKeywords:In this contribution, we consider the multicriteria optimization of nonlinear dynamic systems inthe field of biochemical process engineering. For these problems, computing the set of optimalsolutions can be a challenging task due to their highly constrained and non-linear nature. Thus,global optimization methods are needed to find suitable solutions.We present a new multi-objective evolution strategy for dealing with this class of problems.The proposed approach combines a well-known multicriteria optimization technique with a recentstochastic global optimization method. The usefulness and efficiency of this novel approach areillustrated by considering the integrated design and control of a wastewater treatment plant.Multiobjective optimization, evolution strategy, bioprocess engineering, nonlinear dynamic systems.1. IntroductionFor most real world applications, the optimization problem involves multiple performancecriteria (often conflicting) which must be optimized simultaneously. In general, there doesnot exist a single solution which is simultaneously optimal for all the objectives. Instead, thesolution of a multi-objective optimization problem is a set of optimal trade-offs between thedifferent criteria, the so-called Pareto-optimal set (or Pareto front). All points in this set areoptimal in the sense that an improvement in one objective can only be achieved by degradingone or more of the others. In the absence of any further information, no solution can beconsidered better than another and, ideally, the entire Pareto-optimal set should be found.In this work, we consider the multicriteria optimization of nonlinear dynamic systems inthe field of biochemical process engineering. Particularly, the integrated design and controlof bioprocesses is formulated as a nonlinear multi-objective optimization problem subject todynamic (differential-algebraic) constraints. As in the single-objective case, these problemscan be very challenging to solve due to the highly constrained, non-linear and sometimesnon-smooth nature of most bioprocess models [1]. Furthermore, the optimization problemsassociated with the integration of design and control are frequently multimodal (non-convex)as described by e.g. Schweiger and Floudas [7]. Thus, computing the Pareto-optimal set is farfrom trivial and global optimization methods are needed to find suitable solutions.Many methods have been suggested for finding Pareto-optimal solutions. Full reviews canbe found in the books by Deb [3] and Miettinen [4]. Traditionally, the most common strategyis to combine multiple criteria into one single objective function (e.g. a weighted sum of theobjectives), or to optimize one of the objectives while the others are converting to inequalityconstraints. In order to obtain different solutions, these approaches require solving repeatedlya set of single non-linear programming (NLP) problems (e.g. by changing the weights), andthe solution depends largely on the chosen parameters.