Solving high objective problems in fixed interactions with the decision maker

In recent advancements towards handling high objective optimization problems, it is proposed to progressively integrate the decision maker with the execution of an evolutionary multi-objective optimization algorithm. Preferences from the decision maker are accepted at the intermediate steps of the algorithm and a progress towards the most preferred point is made. In this paper, we extend the work on `progressively interactive evolutionary multi-objective optimization using value function' (PI-EMO-VF) by allowing the optimization to be performed in a fixed number of interactions with the decision maker. In the PI-EMO-VF procedure, information is accepted from the decision maker, which is utilized by the evolutionary algorithm to perform a focused search in the region of interest. However, it is not possible to restrict the number of interactions required to handle an optimization problem. This paper contributes towards, solving the optimization problem in a pre-decided number of decision maker calls. Once the available budget of decision maker calls are known, it is optimally utilized to get close to the most preferred point on the Pareto-frontier. The paper evaluates the performance of the modified PI-EMOVF algorithm on two, three and five objective test problems. A comparative study is performed against the previous proposal for the PI-EMO-VF procedure.

[1]  Jürgen Branke,et al.  Interactive Evolutionary Multiobjective Optimization Using Robust Ordinal Regression , 2009, EMO.

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

[4]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[5]  A. Jaszkiewicz,et al.  Interactive multiobjective optimization with the Pareto memetic algorithm , 2007 .

[6]  Jyrki Wallenius,et al.  Interactive evolutionary multi-objective optimization for quasi-concave preference functions , 2010, Eur. J. Oper. Res..

[7]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[8]  W. Marsden.  I and J , 2012 .

[9]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions , 2010, IEEE Transactions on Evolutionary Computation.

[10]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[11]  Kalyanmoy Deb,et al.  Progressively interactive evolutionary multi-objective optimization method using generalized polynomial value functions , 2010, IEEE Congress on Evolutionary Computation.

[12]  Murat Köksalan,et al.  An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization , 2003, Manag. Sci..

[13]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[14]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[15]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[16]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multi-objective Optimization Method Based on Polyhedral Cones , 2010, LION.