An efficient optimization model and tabu search-based global optimization approach for continuous p-dispersion problem
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913364114931712 |
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| author | Lai, Xiangjing Lin, Zhenheng Hao, Jin-Kao Wu, Qinghua |
| author_facet | Lai, Xiangjing Lin, Zhenheng Hao, Jin-Kao Wu, Qinghua |
| contents | Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and operations research. In this work, we concentrate on general cases with a non-convex multiply-connected region that are rarely studied in the literature due to their intractability and the absence of an efficient optimization model. Using the penalty function approach, we design a unified and almost everywhere differentiable optimization model for these complex problems and propose a tabu search-based global optimization (TSGO) algorithm for solving them. Computational results over a variety of benchmark instances show that the proposed model works very well, allowing popular local optimization methods (e.g., the quasi-Newton methods and the conjugate gradient methods) to reach high-precision solutions due to the differentiability of the model. These results further demonstrate that the proposed TSGO algorithm is very efficient and significantly outperforms several popular global optimization algorithms in the literature, improving the best-known solutions for several existing instances in a short computational time. Experimental analyses are conducted to show the influence of several key ingredients of the algorithm on computational performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An efficient optimization model and tabu search-based global optimization approach for continuous p-dispersion problem Lai, Xiangjing Lin, Zhenheng Hao, Jin-Kao Wu, Qinghua Optimization and Control Discrete Mathematics Mathematical Software Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and operations research. In this work, we concentrate on general cases with a non-convex multiply-connected region that are rarely studied in the literature due to their intractability and the absence of an efficient optimization model. Using the penalty function approach, we design a unified and almost everywhere differentiable optimization model for these complex problems and propose a tabu search-based global optimization (TSGO) algorithm for solving them. Computational results over a variety of benchmark instances show that the proposed model works very well, allowing popular local optimization methods (e.g., the quasi-Newton methods and the conjugate gradient methods) to reach high-precision solutions due to the differentiability of the model. These results further demonstrate that the proposed TSGO algorithm is very efficient and significantly outperforms several popular global optimization algorithms in the literature, improving the best-known solutions for several existing instances in a short computational time. Experimental analyses are conducted to show the influence of several key ingredients of the algorithm on computational performance. |
| title | An efficient optimization model and tabu search-based global optimization approach for continuous p-dispersion problem |
| topic | Optimization and Control Discrete Mathematics Mathematical Software |
| url | https://arxiv.org/abs/2405.16618 |