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An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

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  • Ghassan Shobaki
  • Jafar Jamal

Abstract

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ghassan Shobaki & Jafar Jamal, 2015. "An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers," Computational Optimization and Applications, Springer, vol. 61(2), pages 343-372, June.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:2:p:343-372
    DOI: 10.1007/s10589-015-9725-9
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    References listed on IDEAS

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    1. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    2. Escudero, L. F., 1988. "An inexact algorithm for the sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 37(2), pages 236-249, November.
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    Cited by:

    1. Chou, Xiaochen & Dell’Amico, Mauro & Jamal, Jafar & Montemanni, Roberto, 2023. "Precedence-Constrained arborescences," European Journal of Operational Research, Elsevier, vol. 307(2), pages 575-589.
    2. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.

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