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A new benchmark optimization problem of adaptable difficulty: theoretical considerations and practical testing

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  • D. K. Karpouzos

    (Aristotle University of Thessaloniki)

  • K. L. Katsifarakis

    (Aristotle University of Thessaloniki)

Abstract

In this paper, we present a new benchmark problem for testing both local and global optimization techniques. This problem is based on ideas from groundwater hydraulics and simple Euclidian geometry and has the following attractive features: (a) known values of the infinite global optima, which can be classified in a restricted number of sets, with known location in the search space (b) simple form and (c) quick computation of objective function values. Moreover, the number of local optima sets, their location in the search space and thus the respective values of the objective function can be easily determined by the user, without affecting the global optimum value. In this way, the difficulty of finding the global optimum can be changed from quite small to almost insurmountable, as demonstrated by applying five widely used optimization methods, namely genetic algorithms, sequential quadratic programming, simulated annealing, Knitro and branch and bound. Moreover, some observations on the different behavior of optimization methods are discussed.

Suggested Citation

  • D. K. Karpouzos & K. L. Katsifarakis, 2021. "A new benchmark optimization problem of adaptable difficulty: theoretical considerations and practical testing," Operational Research, Springer, vol. 21(1), pages 231-250, March.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:1:d:10.1007_s12351-019-00462-8
    DOI: 10.1007/s12351-019-00462-8
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    References listed on IDEAS

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    1. Lei-Hong Zhang & Li-Zhi Liao, 2012. "An alternating variable method for the maximal correlation problem," Journal of Global Optimization, Springer, vol. 54(1), pages 199-218, September.
    2. Dimitrios Karpouzos & Konstantinos Katsifarakis, 2013. "A Set of New Benchmark Optimization Problems for Water Resources Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(9), pages 3333-3348, July.
    3. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
    4. Rafael Martí & Gerhard Reinelt & Abraham Duarte, 2012. "A benchmark library and a comparison of heuristic methods for the linear ordering problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1297-1317, April.
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