Preference-based Pareto optimization in certain and noisy environments

In this article a method for including a priori preferences of decision makers into multicriteria optimization problems is presented. A set of Pareto-optimal solutions is determined via desirability functions of the objectives which reveal experts’ preferences regarding different objective regions. An application to noisy objective functions is not straightforward but very relevant for practical applications. Two approaches are introduced in order to handle the respective uncertainties by means of the proposed preference-based Pareto optimization. By applying the methods to the original and uncertain Binh problem and a noisy single cut turning cost optimization problem, these approaches prove to be very effective in focusing on different parts of the Pareto front of the ori-ginal problem in both certain and noisy environments.

[1]  Hirotaka Nakayama,et al.  Theory of Multiobjective Optimization , 1985 .

[2]  Mohammad Ahsanullah,et al.  Further results on a distribution of Meinhold and Singpurwalla , 1989 .

[3]  Achille Messac,et al.  Physical programming - Effective optimization for computational design , 1996 .

[4]  Claus Weihs,et al.  Statistische Methoden zur Qualitätssicherung und -optimierung , 1998 .

[5]  Jiří Tlustý,et al.  Manufacturing processes and equipment , 1999 .

[6]  Jürgen Teich,et al.  Pareto-Front Exploration with Uncertain Objectives , 2001, EMO.

[7]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[8]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

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

[10]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[11]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[12]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[13]  Kalyanmoy Deb,et al.  Integrating User Preferences into Evolutionary Multi-Objective Optimization , 2005 .

[14]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[15]  Heike Trautmann,et al.  Integration of Expert's Preferences in Pareto Optimization by Desirability Function Techniques , 2006 .

[16]  Kay Chen Tan,et al.  Noise Handling in Evolutionary Multi-Objective Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[17]  Eckart Zitzler,et al.  A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006, EvoWorkshops.

[18]  Heike Trautmann,et al.  On the distribution of the desirability index using Harrington’s desirability function , 2006 .