An Optimality Theory Based Proximity Measure for Evolutionary Multi-Objective and Many-Objective Optimization

  • Kalyanmoy Deb
  • Mohamed Abouhawwash
  • Joydeep Dutta
Conference paper

DOI: 10.1007/978-3-319-15892-1_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9019)
Cite this paper as:
Deb K., Abouhawwash M., Dutta J. (2015) An Optimality Theory Based Proximity Measure for Evolutionary Multi-Objective and Many-Objective Optimization. In: Gaspar-Cunha A., Henggeler Antunes C., Coello C. (eds) Evolutionary Multi-Criterion Optimization. EMO 2015. Lecture Notes in Computer Science, vol 9019. Springer, Cham

Abstract

Evolutionary multi- and many-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performance metrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.

Keywords

Multi-objective optimization Evolutionary optimization Termination criterion KkT optimality conditions 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Kalyanmoy Deb
    • 1
  • Mohamed Abouhawwash
    • 1
  • Joydeep Dutta
    • 2
  1. 1.Computational Optimization and Innovation (COIN) LaboratoryMichigan State UniversityEast LansingUSA
  2. 2.Department of Humanities and Social SciencesIndian Institute of Technology KanpurKanpurIndia

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