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Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem

  • Marco Laumanns
  • Lothar Thiele
  • Eckart Zitzler
  • Emo Welzl
  • Kalyanmoy Deb
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2439)

Abstract

For the first time, a running time analysis of populationbased multi-objective evolutionary algorithms for a discrete optimization problem is given. To this end, we define a simple pseudo-Boolean bi-objective problem (Lotz: leading ones– trailing zeroes) and investigate time required to find the entire set of Pareto-optimal solutions. It is shown that different multi-objective generalizations of a (1+1) evolutionary algorithm (EA) as well as a simple population-based evolutionary multi-objective optimizer (SEMO) need on average at least Θ(n 3) steps to optimize this function. We propose the fair evolutionary multi- objective optimizer (FEMO) and prove that this algorithm performs a black box optimization in Θ(n 2 log n) function evaluations where n is the number of binary decision variables.

Keywords

Evolutionary Algorithm Pareto Front Multiobjective Optimization Success Probability Multiobjective Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marco Laumanns
    • 1
  • Lothar Thiele
    • 1
  • Eckart Zitzler
    • 1
  • Emo Welzl
    • 2
  • Kalyanmoy Deb
    • 3
  1. 1.Computer Engineering and Networks LaboratoryETH ZürichZürich
  2. 2.Institute of Theoretical Computer ScienceETH ZürichZürich
  3. 3.Department of Mechanical EngineeringIndian Institute of Technology KanpurKanpurIndia

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