An efficient optimization model and tabu search-based global optimization approach for continuous p-dispersion problem

TL;DR

This paper introduces a new differentiable optimization model and a tabu search-based algorithm to efficiently solve complex continuous p-dispersion problems, significantly improving solution quality and computational speed.

Contribution

It presents a unified, differentiable optimization model for non-convex, multiply-connected regions and a tabu search-based algorithm that outperforms existing methods on benchmark instances.

Findings

The model enables high-precision solutions with local optimization methods.

The TSGO algorithm outperforms several existing global optimization algorithms.

It improves the best-known solutions for multiple benchmark instances.

Abstract

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.