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

Authors:
Kalyanmoy Deb;Kaisa Miettinen;Deepak Sharma
Affiliations:
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India PIN 208016;Department of Mathematical Information Technology, University of Jyväskylä, Finland FI-40014;Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India PIN 208016
Venue:
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Year:
2009

Citing 3
Cited 1

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Abstract

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.