Abstract
The capacitated clustering problem (CCP) divides the vertices of the undirected graph into several disjoint clusters so that the sum of the node weights in each cluster meets the capacity limit while maximizing the sum of the weight of the edges between nodes in the same cluster. CCP is a typical NP-hard problem with a wide range of engineering applications. In recent years, heuristic algorithms represented by greedy random adaptive search program (GRASP) and variable neighborhood search (VNS) have achieved excellent results in solving CCP. To improve the efficiency and quality of the CCP solution, this study proposes a new hybrid algorithm HA-CCP. In HA-CCP, a feasible solution construction method is designed to adapt to the CCP with stricter upper and lower bound constraints and an adaptive local solution destruction and reconstruction method is designed to increase population diversity and improve convergence speed. Experiments on 90 instances of 4 types show that the best average solution obtained by HA-CCP on 58 instances is better than all comparison algorithms, indicating that HA-CCP has better solution stability. HA-CCP is also superior to all comparison algorithms in average solving efficiency.
Highlights
Background and LiteratureReview is section introduces the concept of the capacitated clustering problem (CCP) and the stateof-the-art CCP algorithms in the literature
To improve the efficiency and quality of CCP solutions, this study proposes a new hybrid algorithm HA-CCP, which intelligently combines iterative greedy (IG)-greedy random adaptive search program (GRASP) and skewed general VNS (SGVNS) algorithms
HA-CCP uses a process based on the combination of greediness and randomization to construct the initial solution, uses the variable neighborhood descent (VND) method to perform a local search to find the local optimal solution, and uses the destruction and reconstruction partial solution to shake the current solution
Summary
HA-CCP uses a process based on the combination of greediness and randomization to construct the initial solution, uses the VND method to perform a local search to find the local optimal solution, and uses the destruction and reconstruction partial solution to shake the current solution. Because the three processes of partial destruction, reconstruction, and local search have a certain degree of randomness, each iteration will produce a different new solution. Algorithm 1 jumps out of the local optimization after the preset number of iterations without any improvement (Algorithm 1, Line 8), but Algorithm 2 appropriately accepts the suboptimal solution as the current solution to moving the search to other areas of the solution space (Algorithm 2, line 19). (2) In terms of introducing diversity for search, HACCP adopts the strategy of destructing and reconstructing the current solution, and the VNS-based SGVNS adopts a completely random shake process. (3) In terms of perturbation strength, HA-CCP controls the number of the deleted nodes of the destructive method according to the number of nodes, clusters, and the parameter d max of the current instance, while SGNVS adjusts the perturbation strength according to the solution obtained in the search process
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