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Evolutionary Computation in Combinatorial Optimization

EvoCOP 2016: Evolutionary Computation in Combinatorial Optimization pp 121–137Cite as

Evolutionary Algorithms for Finding Short Addition Chains: Going the Distance

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9595))

Abstract

The problem of finding the shortest addition chain for a given exponent is of great relevance in cryptography, but is also very difficult to solve since it is an NP-hard problem. In this paper, we propose a genetic algorithm with a novel representation of solutions and new crossover and mutation operators to minimize the length of the addition chains corresponding to a given exponent. We also develop a repair strategy that significantly enhances the performance of our approach. The results are compared with respect to those generated by other metaheuristics for instances of moderate size, but we also investigate values up to \(2^{127} - 3\). For those instances, we were unable to find any results produced by other metaheuristics for comparison, and three additional strategies were adopted in this case to serve as benchmarks. Our results indicate that the proposed approach is a very promising alternative to deal with this problem.

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Acknowledgments

This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-4882. The second author gratefully acknowledges support from CONACyT project no. 221551. In addition, this work was supported in part by the Research Council KU Leuven (C16/15/058) and IOF project EDA-DSE (HB/13/020).

Author information

Authors and Affiliations

  1. ESAT/COSIC and iMinds, KU Leuven, Kasteelpark Arenberg 10, Bus 2452, 3001, Leuven-Heverlee, Belgium

    Stjepan Picek & Nele Mentens

  2. Department of Computer Science, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, Mexico D.F., 07360, Mexico

    Carlos A. Coello Coello

  3. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

    Domagoj Jakobovic

Authors
  1. Stjepan Picek
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  2. Carlos A. Coello Coello
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  3. Domagoj Jakobovic
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  4. Nele Mentens
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Corresponding author

Correspondence to Stjepan Picek .

Editor information

Editors and Affiliations

  1. University of Málaga, Málaga, Spain

    Francisco Chicano

  2. Austrian Insttitute of Technology, Vienna, Austria

    Bin Hu

  3. University of Granada, Granada, Spain

    Pablo García-Sánchez

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Picek, S., Coello Coello, C.A., Jakobovic, D., Mentens, N. (2016). Evolutionary Algorithms for Finding Short Addition Chains: Going the Distance. In: Chicano, F., Hu, B., García-Sánchez, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2016. Lecture Notes in Computer Science(), vol 9595. Springer, Cham. https://doi.org/10.1007/978-3-319-30698-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-30698-8_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30697-1

  • Online ISBN: 978-3-319-30698-8

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