An Adaptive Large Neighborhood Search for Two-Dimensional Packing with Conflict Penalty

Abstract

Many problems in the real world can be modeled as two-dimensional packing problems with conflict penalty, and the existing theoretical research on this problem is not enough. Considering the variable conflict penalty between items, an adaptive large neighborhood search (ALNS) algorithm is proposed to approximately solve the problem. An explicit structure is defined in ALNS to represent the solution. An efficient bin packing method based on Best Fit is designed to generate the initial solution of ALNS, so that ALNS can start to search from a better solution. Three destroy operators and two repair operators are used to guide the solution search process. The objective is to minimize the number of bins combining with the packing penalty. Finally, the exact solver gurobi is used to measure the gap between the solution obtained by the heuristic algorithm and the optimal solution. The results show that ALNS found the optimal solutions in a reasonable time for the small-scale cases and found the better solutions in a short time than what gurobi got in a hour for the medium- and large-scale cases.