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A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables

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  • Deb, Kalyanmoy
  • Myburgh, Christie

Abstract

Among various complexities affecting the performance of an optimization algorithm, the search space dimension is a major factor. Another key complexity is the discreteness of the search space. When these two complexities are present in a single problem, optimization algorithms have been demonstrated to be inefficient, even in linear programming (LP) problems. In this paper, we consider a specific resource allocation problem constituting to an integer linear programming (ILP) problem which, although comes from a specific industry, is similar to other practical resource allocation and assignment problems. Based on a population based optimization approach, we present a computationally fast method to arrive at a near-optimal solution. Compared to two popular softwares (glpk,Makhorin, 2012 and CPLEX,Gay, 2015), which are not able to handle around 300 and 2000 integer variables while continuing to run for hours, respectively, our proposed method is able to find a near-optimal solution in less than second on the same computer. Moreover, the main highlight of this study is to propose a customized population based optimization algorithm that scales in almost a linear computational complexity in handling 50,000 to one billion (109) variables. We believe that this is the first time such a large-sized real-world constrained problem is ever handled using any optimization algorithm. We perform sensitivity studies of our method for different problem parameters and these studies clearly demonstrate the reasons for such a fast and scale-up application of the proposed method.

Suggested Citation

  • Deb, Kalyanmoy & Myburgh, Christie, 2017. "A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables," European Journal of Operational Research, Elsevier, vol. 261(2), pages 460-474.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:460-474
    DOI: 10.1016/j.ejor.2017.02.015
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    References listed on IDEAS

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    1. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    2. Stelios H. Zanakis & James R. Evans, 1981. "Heuristic “Optimization”: Why, When, and How to Use It," Interfaces, INFORMS, vol. 11(5), pages 84-91, October.
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    Cited by:

    1. Andrea Ferigo & Giovanni Iacca, 2020. "A GPU-Enabled Compact Genetic Algorithm for Very Large-Scale Optimization Problems," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    2. Andrea Ponti & Antonio Candelieri & Ilaria Giordani & Francesco Archetti, 2023. "Intrusion Detection in Networks by Wasserstein Enabled Many-Objective Evolutionary Algorithms," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    3. Maskooki, Alaleh & Deb, Kalyanmoy & Kallio, Markku, 2022. "A customized genetic algorithm for bi-objective routing in a dynamic network," European Journal of Operational Research, Elsevier, vol. 297(2), pages 615-629.

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