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Merging Variables: One Technique of Search in Pseudo-Boolean Optimization

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

In the present paper we describe new heuristic technique, which can be applied to the optimization of pseudo-Boolean functions including Black-Box functions. This technique is based on a simple procedure which consists in transition from the optimization problem over Boolean hypercube to the optimization problem of auxiliary function in a specially constructed metric space. It is shown that there is a natural connection between the points of the original Boolean hypercube and points from new metric space. For a Boolean hypercube with fixed dimension it is possible to construct a number of such metric spaces. The proposed technique can be considered as a special case of Variable Neighborhood Search, which is focused on pseudo-Boolean optimization. Preliminary computational results show high efficiency of the proposed technique on some reasonably hard problems. Also it is shown that the described technique in combination with the well-known (1+1)-Evolutionary Algorithm allows to decrease the upper bound on the runtime of this algorithm for arbitrary pseudo-Boolean functions.

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Authors and Affiliations

  1. ISDCT SB RAS, Irkutsk, Russia

    Alexander A. Semenov

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  1. Alexander A. Semenov
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Correspondence to Alexander A. Semenov .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Semenov, A.A. (2019). Merging Variables: One Technique of Search in Pseudo-Boolean Optimization. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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