A local search algorithm with movement gap and adaptive configuration checking for the maximum weighted s-plex problem

The maximum weighted s-plex problem (MWSP) is an important generalization of the maximum s-plex problem and has a wide range of applications in many fields such as social network analysis. In this paper, we propose an efficient local search algorithm based on movement gap and adaptive configuration checking. Firstly, we use flip to construct the initial solution and select more suitable vertices to jump out of the local optimum. Secondly, we propose a novel variant of configuration checking with stronger automatic adjustment capability, called adaptive configuration checking (ACC), which can effectively avoid the cycling problem in local search. Besides, we use three operators Add, Swap, and Drop to improve the solution. Our algorithm determines the operator by the increment and judges which vertices are more likely to appear in the solution based on the movement gap (MG) of each vertex. In the perturbation phase, we use the Jump operator to escape the local optimum and adopt the best from multiple selections based on the dynamic parameter (DPBMS) heuristic to improve the search efficiency. By comparing the current state-of-the-art algorithms, we demonstrate that our method performs well. In addition, we validate the effectiveness of the ACC and MG strategies throughout the algorithm and the role of the DPBMS heuristic in the perturbation procedure.