Pearl Y. Wang

Diagnostic Expert Systems Based on a Set Covering Model

This paper proposes that a generalization of the set covering problem can be used as an intuitively plausible model for diagnostic problem solving. Such a model is potentially useful as a basis for expert systems in that it provides a solution to the difficult problem of multiple simultaneous disorders. We briefly introduce the theoretical model and then illustrate its application in diagnostic expert systems. Several challenging issues arise in adopting the set covering model to real-world problems, and these are also discussed along with the solutions we have adopted.

Cutting and packing

Over a decade ago, the European Journal of Operational Research published its first special issue on Cutting and Packing [1] in conjunction with the founding of SICUP, the Special Interest Group on Cutting and Packing. The majority of the papers in the first special issue were focused on cutting problems in the aluminium, paper, and canvas industry, as well as container loading problems. In 1995, a second special issue appeared [2]. As before, the issue included a number of papers on traditional oneand two-dimensional cutting stock problems and container/pallet loading problems, but it also reported new research in nesting problems and introduced the use of metaheuristics such as simulated annealing and genetic algorithms for solving packing problems. Interest in solving these problems continues to grow: an increasing number of papers are being published in the literature each year on a range of cutting, packing, loading, and layout problems. Following the trend, this third special issue of EJOR reports current research that addresses a variety of cutting, packing and related problems where classical, as well heuristic approaches are applied. A first cluster of papers is dedicated to one-dimensional cutting and packing. De Carvalho reviews several models for problems of the cutting stock and bin packing type and analyses the relationship between them as grounds for the development of branch-and-price algorithms. In the two succeeding papers, new methods for the generation of integer solutions to the one-dimensional cutting stock problem with different standard lengths are presented. Belov and Scheithauer introduced an exact approach which uses Chvatal– Gomory cutting planes to tighten up the continuous relaxation of the classic model formulation. Despite the impressive computational results given, the suggested method may still not be applicable to all practical problems due to its computational requirements. In such cases, the heuristic solution method developed and evaluated by Holthaus may represent a feasible alternative. Important aspects of many real-world problems are considered in another two papers. Zak looks at cutting processes which extend over several stages. He proposes a solution method which is based on the classic column-generation procedure by Gilmore and Gomory and dynamically generates both rows (intermediate sizes) and columns (cutting patterns). However, the method does not guarantee that an optimal solution is found. In practice, the question of how to cut down orders from stock lengths is often interconnected with the problem of sequencing the cutting patterns in the most economical way. Armbruster describes such a problem at a steel service centre and suggests a European Journal of Operational Research 141 (2002) 239–240

A formal model of diagnostic inference. I. Problem formulation and decomposition

Abstract This paper, which is Part I of a two-part series, introduces a new model of diagnostic problem solving based on a generalization of the set-covering problem. The model formalizes the concepts of 1. (1) whether or not a set of one or more disorders is sufficient to explain a set of occurring manifestations, 2. (2) what a solution is for a diagnostic problem, and 3. (3) how to generate all of the alternative explanations in a problems solution. In addition, conditions for decomposing a diagnostic problem into independent subproblems are stated and proven. This model is of interest because it captures several intuitively plausible features of human diagnostic inference, it directly addresses the issue of multiple simultaneous causative disorders, it can serve as a theoretical basis for expert systems for diagnostic problem solving, and it provides a conceptual framework within which to view some recent AI work on diagnostic problem solving in general. In Part II, the concepts developed in this paper will be used to present algorithms for diagnostic problem solving.

VLSI placement and area optimization using a genetic algorithm to breed normalized postfix expressions

We present a genetic algorithm (GA) that uses a slicing tree construction process for the placement and area optimization of soft modules in very large scale integration floorplan design. We have overcome the serious representational problems usually associated with encoding slicing floorplans into GAs and have obtained excellent (often optimal) results for module sets with up to 100 rectangles. The slicing tree construction process used by our GA to generate the floorplans has a runtime scaling of O(n lg n). This compares very favorably with other recent approaches based on nonslicing floorplans that require much longer runtimes. We demonstrate that our GA outperforms a simulated annealing implementation with the same representation and mutation operators as the GA.

Heuristics for large strip packing problems with guillotine patterns: an empirical study

In this paper, we undertake an empirical study which examines the effectiveness of eight simple strip packing heuristics on data sets of different sizes with various characteristics and known optima. We restrict this initial study to techniques that produce guillotine patterns (also known as slicing floor plans) which are important industrially. Our chosen heuristics are simple to code, have very fast execution times, and provide a good starting point for our research. In particular, we examine the performance of the eight heuristics as the problems become larger, and demonstrate the effectiveness of a preprocessing routine that rotates some of the rectangles by 90 degrees before the heuristics are applied. We compare the heuristic results to those obtained by using a good genetic algorithm (GA) that also produces guillotine patterns. Our findings suggest that the GA is better on problems of up to about 200 rectangles, but thereafter certain of the heuristics become increasingly effective as the problem size becomes larger, producing better results much more quickly than the GA.

Data set generation for rectangular placement problems

Abstract This paper describes a recursive process for generating data sets of rigid rectangles that can be placed into rectangular regions with zero waste. The generation procedure can be modified to guarantee that the aspect and area ratios of the rectangles in the generated data sets satisfy user-specified parameters. This recursive process can thus be employed to create a variety of data sets that can be used to evaluate the efficiency and scalability of rectangular cutting and packing algorithms.

A Survey Of Parallel Algorithms For One-Dimensional Integer Knapsack Problems

AbstractThis article surveys several methods that can be used to solve integer knapsack problems on a variety of parallel computing architectures. Parallel algorithms designed for a variety of one-dimensional knapsack problems on both theoretical PRAM models of computation and existing parallel architectures are examined. First, exact parallel algorithms for one-dimensional exact sum, unbounded, and 0/1 knapsack problems are reviewed. These algorithms were developed from sequential table-based approaches, dynamic programming formulations, and reduction to circuit-valued or prefix convolution problems. Next, greedy algorithms and approximation algorithms for the one-dimensional subset sum, subset product, and 0/1 knapsack problems are also discussed. Experimental results that have been reported in the literature are summarized throughout this report.

A formal model for SIMD computation

A formal model for single-instruction multiple-data (SIMD) computation is presented that captures the essential operating features of current SIMD computers, yet allows for extensions and variations of existing architectures. The fundamental components of the model are a host computer, a set of processing elements, a set of control units, a set of input/output controllers, and a set of external devices. Each component sends or receives data or instructions to/from other components are described by six networks, each of which governs the communication between a single pair of components. The networks are represented as functions or collections of functions with formally specified mathematical properties that have natural interpretations in the context of SIMD computation. Using the functional approach, a set of four assumptions for SIMD computers is proposed, and consequences of these assumptions are explored.<<ETX>>

Analysis of competition-based spreading activation in connectionist models

Abstract In this paper we analyse a connectionist model of information processing in which the spread of activity in the network is controlled by the nodes actively competing for available activation. This model meets the needs of various artificial-intelligence tasks and has demonstrated several useful properties, including circumscribed spread of activation, stability of network activation following termination of external influences, and context-sensitive “winner-take-all” phenomena without explicit inhibitory links between nodes representing mutually exclusive concepts. We examine three instances of the competition-based connectionist model. For each instance, we show that the differential equations modelling the changes in the activation level of each node has a solution, and we prove that given any initial activity values of the nodes, certain equilibrium activation levels are reached. In particular, we demonstrate that lateral inhibition, i.e. mutually exclusive activity for nodes in the same layer, is possible without explicitly including links between nodes in the same layer. We believe that our results for these instances of the model give important insights into the behaviour observed in the general model.

A formal model of diagnostic inference. II. Algorithmic solution and application

Abstract This paper and a preceding companion paper present the generalized set-covering (GSC) formalization of diagnostic inference. In the current paper, the GSC model is used as the basis for algorithms modeling the “hypothesize-and-test” nature of diagnostic problem solving. Two situations are addressed: “concurrent” problem solving, in which all occurring manifestations are already known, and sequential problem solving, in which the manifestations are discovered one at a time. Each algorithm is explained and its correctness within the GSC framework is proven. The utility of the GSC model is illustrated by using it to describe and analyze some recent abductive expert systems for diagnostic problem solving. The limitations of the basic form of the GSC model are then discussed. A more general notion of “parsimonious covering” that includes the GSC model as a special case is then identified and some important directions for further research are presented.