A dynamic programming-based local search algorithm for solving the dynamic bipartite drawing problem

The dynamic bipartite drawing problem is a challenging NP-hard combinatorial optimization problem with numerous applications. In this study, we propose a dynamic programming-based local search (DP-LS) algorithm for solving it. Unlike previous metaheuristics reported in the literature, which move just one vertex (or two vertices) at each neighborhood iteration, the proposed DP-LS algorithm selects and performs multiple independent neighborhood moves at the same time to enhance the search efficiency. Generally, starting from a random initial solution, DP-LS iteratively explores the search space by integrating the DP-LS to locate local optima, and then uses a perturbation procedure to escape from the local optima. In addition, the proposed incremental evaluation techniques of the insert and swap moves enhance the efficiency of the neighborhood evaluation. Extensive computational experiments on two sets of 1120 problem instances indicate that the proposed DP-LS is highly competitive with the best-performing algorithms (including the general purpose solver Gurobi) in terms of both solution quality and computational efficiency. We analyzed the dynamic programming mechanism in the proposed DP-LS algorithm to determine its effectiveness (increasing the search efficiency tens of times). Not only can the proposed DP-LS algorithm be used to solve the DBDP, it can also be used as a general methodology for solving other combinatorial optimization problems, especially permutation optimization problems.