Heuristic Algorithms for the Fair Max-Min Diversity Problem

He ZHENG, Anna Martínez-Gavara, Rafa Martí

Keywords: Fair Max-Min Diversity, GRASP, Probabilistic Tabu Search, Heuristics

Abstract: This paper investigates the Fair Max-min Diversity Problem (FMMD), which seeks to select a subset of elements that maximizes the minimum pairwise distance while ensuring fair representation across predefined groups. We formulate the problem mathematically and propose heuristic approaches to efficiently obtain high-quality solutions. Specifically, we compare the performance of the Greedy Randomized Adaptive Search Procedure (GRASP) and Probabilistic Tabu Search (PTS). GRASP constructs solutions with adaptive randomness and refines them through local search, while PTS integrates probabilistic mechanisms within tabu search to enhance diversification and intensification. Experimental evaluations on synthetic and real-world datasets demonstrate the effectiveness of both approaches, with PTS consistently achieving superior performance in terms of solution quality and computational efficiency.

Submission Number: 27