GeoNest: Learning to Select Failure-Aware Neighborhoods for the Irregular Knapsack Problem in a Circular Container

2026-09-29

AI Summary

This study addresses the bottleneck of low space utilization in traditional solvers for the irregular packing problem within circular containers, which arises from spatial fragmentation. To this end, we propose GeoNest, a novel framework that introduces a failure-aware large neighborhood search mechanism. Specifically, it constructs neighborhoods by diagnosing geometric blocking relationships and employs reinforcement learning to train a graph neural network policy that dynamically selects optimal repair subproblems, thereby overcoming late-stage packing difficulties. Evaluated on the CircleNest-Bench benchmark and industrial datasets, GeoNest improves average material utilization by approximately 0.9% and 0.6%, respectively, over existing state-of-the-art methods, significantly optimizing complex geometric packing layouts.

Abstract

The two-dimensional irregular knapsack problem in a fixed circular container is an important combinatorial optimization problem for maximizing material utilization in manufacturing. Conventional geometric packing solvers can produce tightly packed layouts, yet they often partition the residual space into isolated small pockets that cannot fit valuable unplaced polygons. To overcome this late-stage packing bottleneck, we propose a failure-aware large neighborhood search framework named GeoNest, driven by a graph policy trained via reinforcement learning. Specifically, we first construct neighborhoods by pairing failed target polygons with residual pockets. We then use explanatory poses to identify the placed polygons that block candidate insertions. These diagnosed blocking relations define bounded, fixed-item repair subproblems for the underlying geometric solver. Finally, the graph policy selects the most promising subproblem for execution. For evaluation, we introduce CircleNest-Bench, a benchmark comprising 2,391 load-controlled instances from four contour sources, including a held-out industrial CAD source. Experimental results demonstrate that, under the same total time budget, GeoNest improves mean utilization over a state-of-the-art standalone packing solver by about 0.9% on average across the three main test sets and by about 0.6% on the held-out industrial set.

Problem

• irregular knapsack problem
• circular container
• packing optimization
• material utilization

Innovation

• Irregular Knapsack Problem
• Large Neighborhood Search
• Reinforcement Learning
• Graph Policy
• Failure-Aware