计算几何与并行算法

本文首先介绍了计算几何的基本概念,论述了计算几何的四个基本问题,即几何搜索问题、相交问题、邻接问题及凸壳问题。然后重点分析了凸壳构造问题,介绍了其最佳串行算法、及相应的并行算法。接着对一些计算几何的串行及并行算法进行了分析比较。最后提出了笔者对新一代并行计算机系统上设计计算几何并行算法的看法。     

K终端可靠度分解算法中多边形→链简化定理的完善

无向网络K终端可靠度的分解算法中,包括多边形→链简化在内的等可靠度简化和分解定理结合,可以降低算法的复杂度。本文完善了边随机无向网络和混合随机无向网络的4#,6#,7#型多边形→链简化定理。计算机编程验证了其正确性。     

Genetic algorithms for symbolic clustering

This paper introduces a novel methodology for clustering of symbolic objects by making use of Genetic Algorithms (GAs). GAs are a family of computational models inspired by evolution. These algorithms encode potential solutions to specific problems on simple chromosome-like data structures and apply recombination operators to these structures so as to preserve critical information. A new type of representation for chromosome structure is presented here along with a new method for mutation. The efficacy of the proposed method is examined by application to numeric data of known number of classes and also to assertion type of symbolic objects drawn from the domain of fat oil, microcomputers, microprocessors and botany. The validity of the clusters obtained is examined.     

Genetic algorithms for optimal logical database design

The focus of this paper is database design using automated database design tools or more general CASE tools. We present a genetic algorithm for the optimization of (internal) database structures, using a multi-criterion objective function. This function expresses conflicting objectives, reflecting the well-known time/space trade-off. This paper shows how the solution space of the algorithm can be set up in the form of tree structures (forests), and how these are encoded by a simple integer assignation. Genetic operators (database transformations) defined in terms of this encoding behave as if they manipulate tree structures. Some basic experimental results produced by a research prototype are presented.     

On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving

In this paper we analyze the algebraic formulations of certain geometry statements appearing in recent literature related to mechanical geometry theorem proving and give several examples to show that one of these formulations can cause serious problems. We clarify a formulation which is essentially due to W. T. Wu and, in our opinion, is the most satisfactory.This author was supported by NSF Grants DCR-8503498 and CCR-8702108.     

A genetic algorithm for the optimisation of assembly sequences

This paper describes a Genetic Algorithm (GA) designed to optimise the Assembly Sequence Planning Problem (ASPP), an extremely diverse, large scale and highly constrained combinatorial problem. The modelling of the ASPP problem, which has to be able to encode any industrial-size product with realistic constraints, and the GA have been designed to accommodate any type of assembly plan and component. A number of specific modelling issues necessary for understanding the manner in which the algorithm works and how it relates to real-life problems, are succinctly presented, as they have to be taken into account/adapted/solved prior to Solving and Optimising (S/O) the problem. The GA has a classical structure but modified genetic operators, to avoid the combinatorial explosion. It works only with feasible assembly sequences and has the ability to search the entire solution space of full-scale, unabridged problems of industrial size. A case study illustrates the application of the proposed GA for a 25-components product.     

Neural Networks Analysis of Steel Plate Processing Augmented by Multi‐objective Genetic Algorithms

An earlier neural network analysis of processing of steel plates through hot rolling was subjected to a further refined analysis through some flexible neural networks that evolved using a multi‐objective predator‐prey genetic algorithm. The original data set expressing the Yield Strength and Ultimate Tensile Strength of the rolled slabs in terms of a total of 108 process variables were subjected to a systematic pruning through this evolutionary approach, till the nitrogen content of the steel emerged as the most significant input variable. A theoretical explanation is provided for this slightly unexpected result.     

Nonnegative integral subset representations of integer sets

We consider an integer-subset representation problem motivated by a medical application in radiation therapy. We prove NP-completeness, derive nontrivial bounds, and report on the performance of a greedy heuristic.     

Accelerating Refractive Rendering of Transparent Objects

In this paper, a technique is proposed for the rendering of transparent objects interactively using the method of refractive rendering. In the proposed technique, the refractive rendering algorithm is performed in two stages, namely the pre‐computation stage and the shading stage. In the pre‐computation stage, ray‐traced information, including directions and positions of rays, are generated by a ray tracing process and are stored in a set of ray lists. In the shading stage, these data are retrieved from the ray lists for computing the shading of an object. Using the proposed technique, photorealistic image of transparent objects and gemstones with various cuttings, material properties, lighting and background can be rendered interactively. By combining the refractive rendering technique with conventional shading techniques, jewelry and crystal designs can be rendered at a much higher speed comparing with conventional ray tracing techniques.