Adaptive Simulated Annealing with Greedy Search for the Circle Bin Packing Problem

TL;DR

This paper introduces a new circle bin packing problem with circular items, proposing an adaptive simulated annealing algorithm with greedy search that significantly improves packing efficiency and solution quality over existing methods.

Contribution

The paper presents a novel problem formulation, a greedy constructive algorithm, and an adaptive simulated annealing approach with new local perturbation strategies for efficient packing.

Findings

ASA-GS outperforms the greedy algorithm in all tested instances.

Packing density in top bins is significantly higher with ASA-GS.

The algorithm is size-agnostic and scales well with problem size.

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 the 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, the packing density of ASA-GS on the top few dense bins is much higher than that of the state-of-the-art algorithm for the single circle packing problem, inferring the high quality of the packing solutions for CBPP-CI.