Running time analysis of evolutionary algorithmson a simplified multiobjective knapsack problem

  • Authors:
  • Marco Laumanns;Lothar Thiele;Eckart Zitzler

  • Affiliations:
  • Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology Zurich, ETH-Zentrum, CH-8092 Zürich, Switzerland (E-mail: laumanns@tik.ee.ethz.ch);Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology Zurich, ETH-Zentrum, CH-8092 Zürich, Switzerland (E-mail: thiele@tik.ee.ethz.ch);Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology Zurich, ETH-Zentrum, CH-8092 Zürich, Switzerland (E-mail: zitzler@tik.ee.ethz.ch)

  • Venue:
  • Natural Computing: an international journal
  • Year:
  • 2004

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Abstract

In this paper, the expected running time of two multiobjectiveevolutionary algorithms, SEMO and FEMO, is analyzed for a simpleinstance of the multiobjective 0/1 knapsack problem. The considered problem instance has two profit values per item andcannot be solved by one-bit mutations. In the analysis, we make use of two general upper bound techniques, thedecision space partition method and the graph search method. The paperdemonstrates how these methods, which have previously only beenapplied to algorithms with one-bit mutations, are equally applicablefor mutation operators where each bit is flipped independently with acertain probability.