A survey of computational approaches to three-dimensional layout problems

Abstract

The component layout or packaging problem requires efficient search of large, discontinuous spaces. This survey paper reviews the state-of-the-art in product layout algorithms. The focus on optimization and geometric interference calculation strategies addresses the common aspects of the layout problem for all applications.

Introduction

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 3-D 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.

A number of design goals can be modeled as layout objectives. Simulations may be necessary to test the thermal, stress or vibration properties of the package. In addition, a set of constraints often has to be satisfied to ensure the applicability of the layouts. Efficient calculations of objectives and constraints are necessary to solve the layout problem in reasonable time since the analyses of objectives and constraints can be computationally expensive and a large number of evaluations may be required to achieve convergence. The search space of the layout problem is non-linear and multi-modal, making it vital to identify a suitable algorithm to navigate the space and find good quality solutions.

Fig. 1 illustrates the major constituent parts for solving a generic layout problem. Geometric representations of components and the container space are necessary for the check of interference and clearance. Since the interference calculation between components of complex geometry is computationally expensive, different levels of detail may be desirable for coarse and refined evaluations at different stages of the problem solving process. The locations and orientations of components are the design variables to be determined. Rigid body transformation is utilized to record the position and orientation of each component in the global coordinate frame. The layout and packaging goals are usually formulated as objective functions. The objectives may reflect the cost, quality, performance and service requirements. Various constraints may be necessary to specify spatial relationships between components. A common constraint is no component overlap and no container protrusion. Other constraints may include the proximity or alignment between components. Topological connections are necessary if tube routing, for example, is involved in addition to the component placement. The specifications of components, objectives, constraints, and topological connections define a layout problem and an optimization search algorithm takes the problem formulation and identifies promising solutions by evaluating design alternatives and evolving design states. Analyses of objectives and constraints vary from problem to problem. However, the optimization search technique and geometric representation and the resulting interference evaluation are problem independent and are, thus, the focus for a generic layout tool.

This paper examines the characteristics of the layout space and provides a survey of the current state-of-the-art in technologies for the 3-D layout problem. The paper is organized as follows: Section 2 shows a fractal analysis of the layout space and a continuum of optimization search algorithms as a basis for further discussions on various search techniques and their effectiveness. Section 3 reviews the optimization algorithms and geometric representations utilized in the layout problem, the advantages and limitations of different methods, and suitable areas of applications. Section 4 discusses the key issues and strategies in building an effective and efficient layout synthesis tool.