Scatter Search and Path-Relinking: Fundamentals, Advances, and Applications

Scatter search is an evolutionary metaheuristic that explores solution spaces by evolving a set of reference points, operating on a small set of solutions while making only limited use of randomization. We give a comprehensive description of the elements and methods that make up its template, including the most recent elements incorporated in successful applications in both global and combinatorial optimization. Path-relinking is an intensification strategy to explore trajectories connecting elite solutions obtained by heuristic methods such as scatter search, tabu search, and GRASP. We describe its mechanics, implementation issues, randomization, the use of pools of high-quality solutions to hybridize path-relinking with other heuristic methods, and evolutionary path-relinking. We also describe the hybridization of path-relinking with genetic algorithms to implement a progressive crossover operator. Some successful applications of scatter search and of path-relinking are also reported.