A survey of computational approaches to three-dimensional layout problems

Abstract

Component layout plays an important role in the design and usability of many engineering products. The layout problem is also classified under the headings of packing, packaging, configuration, container stuffing, pallet loading or spatial arrangement in the literature. The problem involves the placement of components in an available space such that a set of objectives can be optimized while satisfying optional spatial or performance constraints. Whereas the technologies for circuit board and IC chip layout have advanced significantly during the past two decades and many commercial CAD tools have been available, the same is not to be said for three-dimensional mechanical layout methods and tools. While the number of components to be placed in a mechanical system is modest compared to that of a VLSI system, the increased combinatorial complexity over the two-dimensional layout problem and the geometric complexity of 3-D non-uniform components and container spaces make the mechanical layout synthesis a challenging task. Current tools available in practice to designers to aid in the general mechanical layout process mostly remain at the stages of physical or electronic models with the assistance of manual adjustment and visual feedback. The needs arising in the product layout and rapid prototyping for compact and complex products, quick turnaround time and efficient use of resources justify the development of effective layout synthesis methods for 3-D components of complex geometry. The difficulty in automating the mechanical and electro-mechanical layout process stems from 1) the modeling of the design objectives and constraints, 2) the efficient calculation of the objectives and constraints, 3) the identification of appropriate optimization search strategies. optimization search algorithm exploratory moves evaluations / simulations decision making accept, reject moves stop criteria topological connections attachment points route definition constraints non-overlap proximity alignment components geometric representation rigid body transformation design variables location orientation objectives packing density center of gravity configuration cost routing cost bracket cost performance constraints non-overlap proximity alignment constraints non-overlap proximity alignment components geometric representation rigid body transformation design variables location orientation objectives packing density center of gravity configuration cost routing cost bracket cost performance objectives packing density center of gravity configuration cost routing cost bracket cost performance optimization search algorithm exploratory moves evaluations / simulations decision making accept, reject moves stop criteria Figure 1. Major constituent parts for generic layout synthesis.

Optimizing Design Teams Based on Problem Properties: Computational Team Simulations and an Applied Empirical Test

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Application of layout and topology optimization using pattern gradation for the conceptual design of buildings

“…The spatial arrangement of material, often known in the literature as the layout problem, is of key importance for the design and usability of many engineering products [Cagan et al, 2002]. Specifically, in building design, the manner in which material is distributed is significant for engineers to develop a lateral bracing system or create a conceptual design for structural members.…”

A Universal CAD System for Cutting Stock Problem

“…Most of these problems are geometry-dependent (e.g., facility layout, vehicle routing, packing, or cutting stock problems) [4][5][6][7][8][9]. Solving them calls for a colourful variability of geometry representation, search methods (i.e., algorithms), and objectives selection.…”

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