Greedy Randomized Adaptive Search Procedure (GRASP)

In this article, we introduce the Greedy Randomized Adaptive Search Procedure (GRASP) algorithm. The algorithm initiates the problem-solving process by generating an initial solution through a randomized min-min completion time approach, which creates a restricted candidate list of promising solutions using probabilistic selection criteria. Subsequently, it employs a variable neighborhood descent (VND) method to iteratively improve this solution by systematically exploring multiple neighborhood structures through local search operations. This methodology enables broader exploration of the solution space and achieves superior outcomes in optimization objectives. Implementation of GRASP typically involves two phases: a constructive phase with adaptive greedy randomized functions, and an improvement phase with neighborhood swap/shake operations. The algorithm has demonstrated significant effectiveness in solving complex combinatorial problems across various domains including transportation, scheduling, manufacturing, and planning applications. Understanding GRASP's operational mechanism, particularly its balance between randomization and local search intensification, is essential for professionals working in these optimization-intensive fields.