A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point

A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure.

[1]  R. Benayoun,et al.  Linear programming with multiple objective functions: Step method (stem) , 1971, Math. Program..

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

[3]  Simon French,et al.  Multiple Criteria Decision Making: Theory and Application , 1981 .

[4]  Ralph E. Steuer,et al.  Computational experience concerning payoff tables and minimum criterion values over the efficient set , 1988 .

[5]  Jian L. Zhou,et al.  User's Guide for CFSQP Version 2.0: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints , 1994 .

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

[7]  Ralph E. Steuer,et al.  A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming , 1997, Oper. Res..

[8]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

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

[10]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

[11]  Yun Li,et al.  Optimization and robustness for crashworthiness of side impact , 2001 .

[12]  Matthias Ehrgott,et al.  Computation of ideal and Nadir values and implications for their use in MCDM methods , 2003, Eur. J. Oper. Res..

[13]  A. P. Wierzbicki,et al.  Application of multiple criteria evolutionary algorithms to vector optimisation, decision support and reference point approaches , 2003 .

[14]  Peter A. N. Bosman,et al.  Proceedings of the Genetic and Evolutionary Computation Conference - GECCO - 2006 , 2006 .

[15]  Kalyanmoy Deb,et al.  Towards estimating nadir objective vector using evolutionary approaches , 2006, GECCO.

[16]  Kathrin Klamroth,et al.  Integrating Approximation and Interactive Decision Making in Multicriteria Optimization , 2008, Oper. Res..

[17]  K. Deb,et al.  Estimating Nadir Objective Vector : Hybrid of Evolutionary and Local Search , 2008 .

[18]  K. Deb,et al.  A Review of Nadir Point Estimation Procedures Using Evolutionary Approaches: A Tale of Dimensionality Reduction , 2008 .

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

[20]  Kathrin Klamroth,et al.  Pareto navigator for interactive nonlinear multiobjective optimization , 2010, OR Spectr..