GRASP with Evolutionary Path Relinking for the conditional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si88.svg" display="inline" id="d1e1412"><mml:mi>p</mml:mi></mml:math>-Dispersion problem

In this paper, we propose a new heuristic method that hybridizes GRASP with Path Relinking to solve the conditional p -Dispersion problem. Given n elements, from which q < n have been already selected, this problem seeks to select p < n additional unselected elements to maximize the minimum dissimilarity among them. The conditional p -dispersion problem models a facility location problem motivated by a real situation faced in many practical settings arising when some facilities have been already located. The algorithm includes a novel proposal based on an efficient interplay between search intensification and diversification provided by the Path Relinking component, and it also incorporates an intelligent way to measure the diversity among solutions. An extensive computational experimentation is carried out to compare the performance of our heuristic with the state of the art method. The comparison shows that our proposal is competitive with the existing method, since it is able to identify 17 best-known values. Additionally, our experimentation includes a real practical case solved for a Spanish company in its expansion process. This case illustrates both the applicability of the conditional p -dispersion model, and the suitability of our algorithm to efficiently solve practical instances. • Resolution of a new optimization problem: the conditional p-dispersion problem. • A new diversity metric for min-max and max-min problems has been defined. • Different variants of the GRASP with Path Relinking have been tested. • A novel Path Relinking (PR) variant combining interior and exterior PR is proposed. • Perform numerical experiments that disclose the best strategies.