Approximating the Knee of an MOP with Stochastic Search Algorithms

In this paper we address the problem of approximating the 'knee' of a bi-objective optimization problem with stochastic search algorithms. Knees or entire knee-regions are of particular interest since such solutions are often preferred by the decision makers in many applications. Here we propose and investigate two update strategies which can be used in combination with stochastic multi-objective search algorithms (e.g., evolutionary algorithms) and aim for the computation of the knee and the knee-region, respectively. Finally, we demonstrate the applicability of the approach on two examples.

[1]  Lily Rachmawati,et al.  A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions , 2006, GECCO '06.

[2]  Kalyanmoy Deb,et al.  Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions , 2003 .

[3]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.

[4]  A. Messac,et al.  Smart Pareto filter: obtaining a minimal representation of multiobjective design space , 2004 .

[5]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

[6]  Hisao Ishibuchi,et al.  Incorporation of decision maker's preference into evolutionary multiobjective optimization algorithms , 2006, GECCO '06.

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

[8]  Lily Rachmawati,et al.  A Multi-Objective Genetic Algorithm with Controllable Convergence on Knee Regions , 2006, 2006 IEEE International Conference on Evolutionary Computation.

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

[10]  Kalyanmoy Deb,et al.  A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems , 2006, PPSN.

[11]  Joshua D. Knowles,et al.  Exploiting the Trade-off - The Benefits of Multiple Objectives in Data Clustering , 2005, EMO.

[12]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[13]  Indraneel Das On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection , 1999 .

[14]  J. Branke,et al.  Guidance in evolutionary multi-objective optimization , 2001 .