Adaptive simulated annealing with greedy search for the circle bin packing problem

Abstract

We introduce a new bin packing problem, termed the circle bin packing problem with circular items (CBPP-CI). The problem involves packing all the circular items into multiple identical circle bins as compact as possible with the objective of minimizing the number of used bins. We first define the tangent occupying action (TOA) and propose a constructive greedy algorithm that sequentially packs the items into places tangent to the packed items or the bin boundaries. Moreover, to avoid falling into a local minimum trap and efficiently judge whether an optimal solution has been established, we continue to present an adaptive simulated annealing with greedy search (ASA-GS) algorithm that explores and exploits the search space efficiently. Specifically, we offer two novel local perturbation strategies to jump out of the local optimum and incorporate the greedy search to achieve faster convergence. The parameters of ASA-GS are adaptive according to the number of items so that they can be size-agnostic across the problem scale. We design two sets of new benchmark instances, and the empirical results show that ASA-GS completely outperforms the constructive greedy algorithm. Moreover, for the problem of packing unequal circles to a fixed size circular container to maximize the area of circles packed, ASA-GS outperforms the advanced formulation space search (FSS) algorithm in terms of solution quality and computational cost, inferring that our approach is not only adapted to CBPP-CI but also works well when the number of bins is reduced to one to become a typical circle packing problem.