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.

翻译：带边界约束与不带边界约束的连续p-分散问题均属于NP难优化问题，在设施选址、圆填充等诸多现实场景中具有广泛应用，是数学与运筹学领域广泛研究的课题。本文聚焦于具有非凸多连通区域的一般情形，该类问题因其难解性及缺乏高效优化模型，在现有文献中鲜有研究。采用罚函数方法，我们为这类复杂问题设计了一个统一且几乎处处可微的优化模型，并提出一种基于禁忌搜索的全局优化（TSGO）算法用于求解。在多种基准算例上的计算结果表明，所提模型效果优异，得益于模型的可微性，主流的局部优化方法（如拟牛顿法、共轭梯度法）能够获得高精度解。这些结果进一步表明，所提出的TSGO算法效率极高，显著优于文献中多种主流全局优化算法，在较短计算时间内改进了多个现有算例的已知最优解。实验分析展示了算法中若干关键要素对计算性能的影响。