Greedy Randomized Adaptive Search Procedures with Path Relinking. An analytical review of designs and implementations

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR). GRASP with PR has become a widely adopted approach for solving hard optimization problems since its proposal in 1999. The paper covers the historical development of GRASP with PR and its theoretical foundations, as well as recent advances in its implementation and application. The review includes a careful analysis of PR variants, paying special attention to memory-based and randomized designs, with a total of ten different implementations. It identifies the design questions that are still open in the scientific literature. The experimental section applies advanced PR implementations on two well-known combinatorial optimization problems, linear ordering and max-cut, in an effort to answer these open questions. The paper also explores the hybridization of PR and other metaheuristics, such as tabu search, scatter search, and random-keys genetic algorithms. Overall, this review provides valuable insights for researchers and practitioners seeking to implement GRASP with PR for solving optimization problems. • Path Relinking efficiently explores paths between quality GRASP solutions. • We present and test Path Relinking variants and GRASP hybridizations. • We analyze and test strategies for elite set management. • We review previous research on GRASP with Path Relinking. • We present a critical review comparing variants empirically and theoretically.