  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.
