An Evolutionary Algorithm for Short Addition Chains

Bahig, Hazem M.; Khaled, Ali; Mohammed, Ahmed O.; AlGhadhban, Amer; Hatem, Muntaha Abudlzahra

doi:10.14569/ijacsa.2020.0111258

IJACSA

2020

DOI: 10.14569/ijacsa.2020.0111258

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An Evolutionary Algorithm for Short Addition Chains

Hazem M. Bahig¹,

Ali Khaled²,

Ahmed O. Mohammed³

et al.

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2024

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Cited by 1 publication

References 32 publications

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An efficient simulated annealing algorithm for short addition sequences

Bahig,

Hazber,

Bahig

2024

MATH

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<abstract> <p>Let $ N = \left\{{n}_{1}, {n}_{2}, \;\dots , {n}_{k}\right\} $ be a finite set of positive numbers. The problem of finding the minimal number of additions required to compute all elements of <italic>N</italic> starting from 1 (called the addition sequence problem) is NP-complete. It is equivalent to finding the minimum number of multiplications needed to compute a group exponentiation $ {g}^{{n}_{1}}, {g}^{{n}_{2}}, \;\dots , {g}^{{n}_{k}} $, where <italic>g</italic> is an element in a group. This paper aims to propose a new metaheuristic algorithm using a simulated annealing strategy to generate a short addition sequence. The performance of the proposed algorithm is measured by considering two parameters: The size of <italic>N</italic> and the domain of $ {n}_{\mathrm{i}}, 1\le i\le k $. The proposed algorithm is a new trade-off between the length of the generated addition sequence and the average running time of generating addition sequences. It sometimes produces longer addition sequences than exact algorithms that are slower, and it is slower than suboptimal algorithms that produce longer addition sequences.</p> </abstract>

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An efficient simulated annealing algorithm for short addition sequences

Bahig,

Hazber,

Bahig

2024

MATH

View full text Add to dashboard Cite

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An Evolutionary Algorithm for Short Addition Chains

Cited by 1 publication

References 32 publications

An efficient simulated annealing algorithm for short addition sequences

An efficient simulated annealing algorithm for short addition sequences

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