An Objective-Based Gradient Method for Locating the Pareto Domain

In this paper, an objective-based gradient multi-objective optimization (MOO) technique, the Objective-Based Gradient Algorithm (OBGA), is proposed with the goal of defining the Pareto domain more precisely and efficiently than current MOO techniques. The performance of the OBGA in locating the Pareto domain was evaluated in terms of precision, computation time and number of objective function calls, and compared to two current MOO algorithms: Dual Population Evolutionary Algorithm (DPEA) and Non-Dominated Sorting Genetic Algorithm II (NSGA-II), using four test problems. For all test problems, the OBGA systematically produced a more precise Pareto domain than DPEA and NSGA-II. With the adequate selection of the OBGA parameters, computation time required for the OBGA can be lower than that required for DPEA and NSGA-II. Results clearly show that the OBGA is a very effective and efficient algorithm for locating the Pareto domain.

[1]  J. Impe,et al.  Efficient deterministic multiple objective optimal control of (bio)chemical processes , 2009 .

[2]  Peter A. N. Bosman,et al.  Exploiting gradient information in numerical multi--objective evolutionary optimization , 2005, GECCO '05.

[3]  C. Poloni,et al.  Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics , 2000 .

[4]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[5]  Ralf Salomon,et al.  Evolutionary algorithms and gradient search: similarities and differences , 1998, IEEE Trans. Evol. Comput..

[6]  Christian Fonteix,et al.  Multicriteria optimization using a genetic algorithm for determining a Pareto set , 1996, Int. J. Syst. Sci..

[7]  Ajay K. Ray,et al.  Multiobjective optimization of an industrial styrene monomer manufacturing process , 2005 .

[8]  Christian Fonteix,et al.  Multicriteria optimization of an emulsion polymerization process , 2004, Eur. J. Oper. Res..

[9]  Santosh K. Gupta,et al.  Jumping gene adaptations of NSGA-II and their use in the multi-objective optimal design of shell and tube heat exchangers , 2008 .

[10]  Abdelhafid Khellaf,et al.  Optimal Solutions of Multiproduct Batch Chemical Process Using Multiobjective Genetic Algorithm with Expert Decision System , 2009, Journal of Automated Methods and Management in Chemistry.

[11]  Jules Thibault,et al.  Multi-objective optimization for chemical processes and controller design: Approximating and classifying the Pareto domain , 2006, Comput. Chem. Eng..

[12]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[13]  Nicolas Lalonde,et al.  Multiobjective Optimization Algorithm Benchmarking and Design Under Parameter Uncertainty , 2009 .

[14]  Chunshan Li,et al.  Environmentally conscious design of chemical processes and products: Multi-optimization method , 2009 .

[15]  Dirk V. Arnold,et al.  Evolutionary Gradient Search Revisited , 2007, IEEE Transactions on Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.