Construction Heuristics for three-dimensional packing problems

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K12981
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Social systems engineering/Safety system
• Research Institution: Nagoya University
• Principal Investigator: HU YANNAN 名古屋大学, 情報学研究科, 助教 (00778326)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 三次元配置問題 / 組合せ最適化 / アルゴリズム設計

Outline of Final Research Achievements

In this research, we approximately represent a general three-dimensional items by a three-dimensional rectilinear polyhedron, which can be treated as a set of cuboids with fixed relative positions. We propose construction heuristics for the rectilinear polyhedron packing problem, which asks to pack a set of rectilinear polyhedrons into a large cuboid container without overlap so as to minimize the depth of the container.
We adopt the deepest-bottom-left (DBL) strategy, in which each polyhedron is packed at the position having the smallest y-coordinate among those having the smallest x-coordinate in the surface with the smallest z-coordinate. We utilize a concept called no-fit cube (NFC) to determine overlaps between items and design efficient implementations by storing NFCs dynamically with advanced data structure. We performed computational experiments and the results show that our algorithms run fast and obtain solutions for instances with more than 3000 items in 72 seconds.

Free Research Field

組合せ最適化

Academic Significance and Societal Importance of the Research Achievements

従来の３次元配置問題はほとんど直方体に焦点をあてて研究が進められて，一般形状の3D物体の形状の取り扱いが難しいためほとんど検討されていない．本研究では，一般の物体を3Dレクトリニア多面体に近似する手法を提案し，2D図形配置問題に対する知見を3D物体に拡張した．本研究の解法は，直方体配置問題や一般の多面体配置問題も特別な場合として扱えるという性質を持つため，様々な形状を持つ製品の配置問題に適用可能な汎用解法となる．提案した方法論が配置問題の基盤技術となり，配置を決定することが求められる問題に対するアルゴリズム設計に導入されることが期待できる．