A Simulated Annealing approach for the Circle Bin Packing Problem with Rectangular Items

Abstract

We introduce a new variant of Bin Packing Problem (BPP) called the Circular Bin Packing Problem with Rectangular Items (CBPP-RI). CBPP-RI involves the dense orthogonal packing of rectangular items into a minimum number of bins. To our knowledge, there is no existing literature addressing this NP-hard problem. To fill this gap, we study CBPP-RI and propose an algorithm consisting of two stages, an initialization stage and an improvement stage. We propose a first-fit grid search (FGS) algorithm to generate the initial solution, then we design a Simulated Annealing (SA) algorithm to explore the solution space from the initial solution by the proposed novel local neighborhood search strategy called the circular quadrant perturbation (CQP). The SA algorithm always accepts the current solution if it is better than the previous one, and otherwise accepts based on a probability function. Experimental results show that the proposed algorithm is effective for not only the introduced CBPP-RI problem, but also other related packing problems.