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Running Time Analysis of a Multiobjective Evolutionary Algorithm on Simple and Hard Problems

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Foundations of Genetic Algorithms (FOGA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3469))

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Abstract

In this paper, we suggest a multiobjective evolutionary algorithm based on a restricted mating pool (REMO) with a separate archive for storing the remaining population. Such archive based algorithms have been used for solving real-world applications, however, no theoretical results are available. In this paper, we present a rigorous running time complexity analysis for the algorithm on two simple discrete pseudo boolean functions and on the multiobjective knapsack problem which is known to be NP-complete. We use two well known simple functions LOTZ (Leading Zeros: Trailing Ones) and a quadratic function. For the knapsack problem we formalize a ( 1+ ε)-approximation set under a constraint on the weights of the items. We then generalize the idea by eliminating the constraints based on a principle of partitioning the items into blocks and analyze REMO on it. We use a simple strategy based on partitioning of the decision space into fitness layers for the analysis.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, WB, 721 302, India

    Rajeev Kumar & Nilanjan Banerjee

Authors
  1. Rajeev Kumar
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  2. Nilanjan Banerjee
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Montana, 59812, Missoula, Montana, USA

    Alden H. Wright

  2. Computer Science Department, University of Tennessee, 37996, Knoxville, TN, USA

    Michael D. Vose

  3. Computer Science Department, George Mason University, 4400 University Drive, 22030, Fairfax, VA, USA

    Kenneth A. De Jong

  4. School of Computer Science and Engineering, The University of Aizu, 965-8580, Aizu-Wakamatsu City, Fukushima Prefecture, Japan

    Lothar M. Schmitt

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© 2005 Springer-Verlag Berlin Heidelberg

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Kumar, R., Banerjee, N. (2005). Running Time Analysis of a Multiobjective Evolutionary Algorithm on Simple and Hard Problems. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds) Foundations of Genetic Algorithms. FOGA 2005. Lecture Notes in Computer Science, vol 3469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11513575_7

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  • DOI: https://doi.org/10.1007/11513575_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27237-3

  • Online ISBN: 978-3-540-32035-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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