Solving multi‐objective dynamic optimization problems with fuzzy satisfying method

This article proposes a novel algorithm integrating iterative dynamic programming and fuzzy aggregation to solve multi-objective optimal control problems. First, the optimal control policies involving these objectives are sequentially determined. A payoff table is then established by applying each optimal policy in series to evaluate these multiple objectives. Considering the imprecise nature of decision-maker's judgment, these multiple objectives are viewed as fuzzy variables. Simple monotonic increasing or decreasing membership functions are then defined for degrees of satisfaction for these linguistic objective functions. The optimal control policy is finally searched by maximizing the aggregated fuzzy decision values. The proposed method is rather easy to implement. Two chemical processes, Nylon 6 batch polymerization and Penicillin G fed-batch fermentation, are used to demonstrate that the method has a significant potential to solve real industrial problems. Copyright © 2003 John Wiley & Sons, Ltd.

[1]  Ajay K. Ray,et al.  Optimization of nonvaporizing nylon 6 reactors with stopping conditions and end‐point constraints , 1986 .

[2]  Miguel Delgado,et al.  A Possibilistic Approach for Multiobjective Programming Problems. Efficiency of Solutions , 1990 .

[3]  J. E. Cuthrell,et al.  Simultaneous optimization and solution methods for batch reactor control profiles , 1989 .

[4]  Feng-Sheng Wang,et al.  Extension of iterative dynamic programming to multiobjective optimal control problems , 1997 .

[5]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[6]  Hideo Tanaka,et al.  Fuzzy Mathematical Programming , 1973 .

[7]  J. Banga,et al.  Dynamic Optimization of Batch Reactors Using Adaptive Stochastic Algorithms , 1997 .

[8]  George J. Klir,et al.  Fuzzy sets and fuzzy logic , 1995 .

[9]  H. Zimmermann.  DESCRIPTION AND OPTIMIZATION OF FUZZY SYSTEMS , 1975 .

[10]  Masatoshi Sakawa,et al.  Fuzzy Sets and Interactive Multiobjective Optimization , 1993 .

[11]  Christodoulos A. Floudas,et al.  Deterministic Global Optimization in Nonlinear Optimal Control Problems , 2000, J. Glob. Optim..

[12]  Jared L. Cohon,et al.  Multiobjective programming and planning , 2004 .

[13]  Hideo Tanaka,et al.  On Fuzzy-Mathematical Programming , 1973 .

[14]  Frerich J. Keil,et al.  PARALLELIZATION OF ITERATIVE DYNAMIC PROGRAMMING (IDP) , 1999 .

[15]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[16]  田中 英夫.  Masatoshi Sakawa著, Fuzzy Sets and Interactive Multiobjective Optimization, ・出版社 Plenum Press (New York and London), ・発行 1993年, ・B5判, 308頁, $78.00 , 1993 .

[17]  Anil Kumar,et al.  Optimal temperature profiles for nylon 6 polymerization in plug‐flow reactors , 1983 .

[18]  Rein Luus,et al.  Optimal control of batch reactors by iterative dynamic programming , 1994 .

[19]  R. Sargent,et al.  Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints , 1994 .

[20]  G. T. Tsao,et al.  Fuzzy-Decision-Making Problems of Fuel Ethanol Production Using a Genetically Engineered Yeast , 1998 .

[21]  Joos Vandewalle,et al.  Optimal control of the penicillin G fed-batch fermentation: an analysis of the model of Bajpai and Reuss , 1991 .

[22]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[23]  Cheng-Liang Chen,et al.  Solution of Fuzzy Dynamic Optimization Problems by Adaptive Stochastic Algorithm , 2000, Int. J. Artif. Intell. Tools.

[24]  Kok Lay Teo,et al.  Control parametrization: A unified approach to optimal control problems with general constraints , 1988, Autom..

[25]  D. N. Butala,et al.  An experimental study of multiobjective dynamic optimization of a semibatch copolymerization process , 1991 .

[26]  Masahiro Inuiguchi,et al.  A fuzzy satisficing method for multiobjective linear optimal control problems , 1996, Fuzzy Sets Syst..

[27]  Santosh K. Gupta,et al.  Multiobjective dynamic optimization of a nonvaporizing nylon 6 batch reactor , 1994 .

[28]  J. J.A,et al.  Nonlinear multi-objective optimization of metal forming process , 2003 .