An algorithm for approximating global optimal solution of optimization problems using clustering technique of data mining

Subject Areas : تحقیق در عملیات

محمد علی نژادمفرد ¹ , مهتاب حدادپور ² , محمد دهقان نیری ³

1 - Department of Basic sciences. University of Bojnord. Bojnord. Iran
2 - Department of Basic sciences. University of Bojnord. Bojnord. Iran
3 - Department of Basic sciences. University of Bojnord. Bojnord. Iran

Received: 2023-02-01 Accepted : 2023-12-12 Published : 2025-06-11

Keywords: داده‌کاوی, فضای جستجوی کاهش‌یافته, خوشه‌بندی, جواب بهینه سراسری, بهینه‌سازی سراسری,

Abstract :

Finding the global optimal solution is very important in some optimization problems. If the search space of the problem can be iteratively reduced in such a way that it most probably includes the global optimal solution, then a suitable approximation for the optimal solution of the problem can be obtained. In this article, the clustering technique of data mining is used to reduce the search space. By iteratively using this technique together with the uniform design of the good lattice points type to produce a suitable distribution of points on the boundaries and within the feasible region in each iteration, a stochastic algorithm is proposed that is able to find a suitable approximation of the global optimal solution. The comparison of the results of this algorithm with the genetic algorithm for three nonlinear unconstrained optimization problems shows that the proposed algorithm can obtain those approximations with a lower number of iterations and computational time; Furthermore, when the global optimal solution is located on the boundaries, the convergence speed, compared to the genetic algorithm, is significantly higher.

References:

[1] R. Horst, and P. M. Pardalos. Handbook of Global Optimization. Springer (1995)

[2] A. Zhigljavsky, A. Zilinskas. Stochastic global optimization. Springer (2008)

[3] R. Horst, H. Tuy. Global Optimization (Deterministic Approaches). Springer (1996)

[4] A. Torn, A. Zilinskas. Global optimization. Springer (1989)

[5] M. Haddadpour, M. Alinejadmofrad, M. Dehghan Nayyeri. Reducing search space in optimization problems with data mining techniques. Towards Mathematical Sciences 2 (1): 110-121 (2022). Doi: 10.22067/tmsj.2022.42824

[6] T. Y. Chen, J. H. Huang. An efficient and practical approach to obtain a better optimum solution for structural optimization. Engineering Optimization 45 (8): 1005–26 (2013)

[7] T. Y. Chen, J. H. Huang. Application of data mining in a global optimization algorithm. Advances in Engineering Software 66: 24–33 (2013)

[8] J. Han, M. Kamber, J. Pei. Data Mining: Concepts and Techniques, 3rd ed.. Morgan Kaufmann (2011)

[9] K. T. Fang, Y. Wang. Number-Theoretic Methods in Statistics. Chapman and Hall. London (1994)

[10] K. T. Fang, Y. Wang, P. M. Bentler. Some applications of number-theoretic methods in statistics. Statistical Science 9 (3): 416–28 (1994)

[11] K. T. Fang, D. K. J. Lin. Uniform Experimental Designs and Their Application in Industry. Vol. 22. Handbook of Statistics. Elsevier Science (2003)

[12] W. Hopkins. Uniform Space-Filling Designs and Their Applications in Designed Experiments. M.Sc. thesis, Department of Mathematical Sciences. Montana State University (2018)

[13] J. Nocedal, and S. Wright. Numerical Optimization, 2nd.ed.. Springer (2006)

[14] Z. Tu‎, ‎ Y. Lu. ‎A robust stochastic genetic algorithm (StGA) for global numerical ‎optimization‎. ‎IEEE Transactions on Evolutionary Computation 8 (5): ‎456–70 (2004)