Adaptive large neighborhood search for solving the circle bin packing problem

Abstract

We address a new packing problem variant known as the 2D circle bin packing problem (2D-CBPP), which involves packing circles into multiple square bins as densely as possible so as to minimize the number of bins used. To this end, we propose an adaptive large neighborhood search (ALNS) algorithm, which uses our Greedy Algorithm with Corner Occupying Action (GACOA) to construct an initial layout. The greedy solution is usually in a local optimum trap, and ALNS enables multiple neighborhood searches that depend on a stochastic annealing schedule to avoid local minimum traps. Specifically, ALNS perturbs the current layout to escape local optima by iteratively reassigning some circles and accepting the new layout with some probability during the search. The acceptance probability is adjusted adaptively using simulated annealing, which fine-tunes the search direction in order to reach the global optimum. We benchmark computational results against GACOA in heterogeneous instances. In all cases, ALNS outperforms GACOA in improving the objective function, and in several cases, the number of bins used for packing is significantly reduced.