The Online and Offline Single Cylindrical Packing Problems with Cylindrical Items

Abstract

This paper introduces a new three-dimensional (3D) packing problem, the Single Cylindrical Packing Problem with Cylindrical Items (SCPP-CI), that involves packing as many cylindrical items as possible into a cylindrical container so as to maximize the volume utilization. We consider two variants: the online version where items are coming sequentially and need to be packed immediately once coming, and the offline version where all items are given at once. We design a Cylindrical Tangent Occupying Action (CTOA) operator for this problem to obtain dense placements, and design a Compact Level Degree (CLD) metric to evaluate the quality of feasible CTOAs. For the online problem, we design a deterministic greedy heuristic algorithm based on the CTOA operator and CLD metric that packs each coming item greedily. For the offline problem, we design another greedy construction algorithm that chooses an operator greedily over all candidate items, then we propose a top-$N$ Local Search algorithm that considers future benefits during the construction. To utilize existing resources to evaluate the performance of the algorithms, we first degrade the 3D SCPP-CI problem to two-dimensional (2D) circle packing problems and compare our methods with the CPLEX constraint programming solver and an effective unequal circle packing heuristic, FSS, on existing 2D benchmarks. We then generate 10 groups of SCPP-CI instances (100 instances in each group) with increasing heterogeneity, and compare with CPLEX on these instances. Experimental results show that both our algorithms significantly outperform the baselines for both 2D and 3D problems, indicating the excellent performance of the proposed methods.

Keywords: Discrete optimization, 3D cylinder packing, Online and offline packing, Cylindrical tangent occupying action, Compact level degree