Adaptive Large Neighborhood Search for Circle Bin Packing Problem

Abstract: We address a new variant of packing problem called the circle bin packing problem (CBPP), which is to find a dense packing of circle items to multiple square bins so as to minimize the number of used bins. 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 search that depends on the stochastic annealing schedule to avoid getting stuck in local minimum traps. Specifically, ALNS perturbs the current layout to jump out of a local optimum by iteratively reassigns some circles and accepts the new layout with some probability during the search. The acceptance probability is adjusted adaptively using simulated annealing that fine-tunes the search direction in order to reach the global optimum. We benchmark computational results against GACOA in heterogeneous instances. ALNS always outperforms GACOA in improving the objective function, and in several cases, there is a significant reduction on the number of bins used in the packing.