Heuristics for Job-Shop Scheduling

Two methods of obtaining approximate solutions to the classic General Job-shop Scheduling Program are investigated. The first method is iterative. A sampling of the solution space is used to decide which of a collection of space pruning constraints are consistent with "good" schedules. The selected space pruning constraints are then used to reduce the search space and the sampling is repeated. This approach can be used either to verify whether some set of space pruning constraints can prune with discrimination or to generate solutions directly. Schedules can be represented as trajectories through a Cartesian space. Under the objective criteria of Minimum maximum Lateness family of "good" schedules (trajectories) are geometric neighbors (reside with some "tube") in this space. This second method of generating solutions takes advantage of this adjacency by pruning the space from the outside in thus converging gradually upon this "tube." One the average this methods significantly outperforms an array of the Priority Dispatch rules when the object criteria is that of Minimum Maximum Lateness. It also compares favorably with a recent relaxation procedure.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Internet Fish

I have invented "Internet Fish," a novel class of resource-discovery tools designed to help users extract useful information from the Internet. Internet Fish (IFish) are semi-autonomous, persistent information brokers; users deploy individual IFish to gather and refine information related to a particular topic. An IFish will initiate research, continue to discover new sources of information, and keep tabs on new developments in that topic. As part of the information-gathering process the user interacts with his IFish to find out what it has learned, answer questions it has posed, and make suggestions for guidance. Internet Fish differ from other Internet resource discovery systems in that they are persistent, personal and dynamic. As part of the information-gathering process IFish conduct extended, long-term conversations with users as they explore. They incorporate deep structural knowledge of the organization and services of the net, and are also capable of on-the-fly reconfiguration, modification and expansion. Human users may dynamically change the IFish in response to changes in the environment, or IFish may initiate such changes itself. IFish maintain internal state, including models of its own structure, behavior, information environment and its user; these models permit an IFish to perform meta-level reasoning about its own structure. To facilitate rapid assembly of particular IFish I have created the Internet Fish Construction Kit. This system provides enabling technology for the entire class of Internet Fish tools; it facilitates both creation of new IFish as well as additions of new capabilities to existing ones. The Construction Kit includes a collection of encapsulated heuristic knowledge modules that may be combined in mix-and-match fashion to create a particular IFish; interfaces to new services written with the Construction Kit may be immediately added to "live" IFish. Using the Construction Kit I have created a demonstration IFish specialized for finding World-Wide Web documents related to a given group of documents. This "Finder" IFish includes heuristics that describe how to interact with the Web in general, explain how to take advantage of various public indexes and classification schemes, and provide a method for discovering similarity relationships among documents.

Basis Reduction Algorithms and Subset Sum Problems

This thesis investigates a new approach to lattice basis reduction suggested by M. Seysen. Seysen's algorithm attempts to globally reduce a lattice basis, whereas the Lenstra, Lenstra, Lovasz (LLL) family of reduction algorithms concentrates on local reductions. We show that Seysen's algorithm is well suited for reducing certain classes of lattice bases, and often requires much less time in practice than the LLL algorithm. We also demonstrate how Seysen's algorithm for basis reduction may be applied to subset sum problems. Seysen's technique, used in combination with the LLL algorithm, and other heuristics, enables us to solve a much larger class of subset sum problems than was previously possible.

A System for Representing and Using Real-World Knowledge

This report describes a knowledge-base system in which the information is stored in a network of small parallel processing elements ??de and link units ??ich are controlled by an external serial computer. This network is similar to the semantic network system of Quillian, but is much more tightly controlled. Such a network can perform certain critical deductions and searches very quickly; it avoids many of the problems of current systems, which must use complex heuristics to limit and guided their searches. It is argued (with examples) that the key operation in a knowledge-base system is the intersection of large explicit and semi-explicit sets. The parallel network system does this in a small, essentially constant number of cycles; a serial machine takes time proportional to the size of the sets, except in special cases.

ADEPT: A Heuristic Program for Proving Theorems of Group Theory

A computer program, named ADEPT (A Distinctly Empirical Prover of Theorems), has been written which proves theorems taken from the abstract theory of groups. Its operation is basically heuristic, incorporating many of the techniques of the human mathematician in a "natural" way. This program has proved almost 100 theorems, as well as serving as a vehicle for testing and evaluating special-purpose heuristics. A detailed description of the program is supplemented by accounts of its performance on a number of theorems, thus providing many insights into the particular problems inherent in the design of a procedure capable of proving a variety of theorems from this domain. Suggestions have been formulated for further efforts along these lines, and comparisons with related work previously reported in the literature have been made.

Hypothesis Formation and Evaluation in Medical Diagnosis

This thesis describes some aspects of a computer system for doing medical diagnosis in the specialized field of kidney disease. Because such a system faces the spectre of combinatorial explosion, this discussion concentrates on heuristics which control the number of concurrent hypotheses and efficient "compiled" representations of medical knowledge. In particular, the differential diagnosis of hematuria (blood in the urine) is discussed in detail. A protocol of a simulated doctor/patient interaction is presented and analyzed to determine the crucial structures and processes involved in the diagnosis procedure. The data structure proposed for representing medical information revolves around elementary hypotheses which are activated when certain disposing of findings, activating hypotheses, evaluating hypotheses locally and combining hypotheses globally is examined for its heuristic implications. The thesis attempts to fit the problem of medical diagnosis into the framework of other Artifcial Intelligence problems and paradigms and in particular explores the notions of pure search vs. heuristic methods, linearity and interaction, local vs. global knowledge and the structure of hypotheses within the world of kidney disease.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.

Causal and Teleological Reasoning in Circuit Recognition

This thesis presents a theory of human-like reasoning in the general domain of designed physical systems, and in particular, electronic circuits. One aspect of the theory, causal analysis, describes how the behavior of individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to aid this causal analysis. The theory is implemented as a computer program, which, given a circuit topology, can construct by qualitative causal analysis a mechanism graph describing the functional topology of the system. This functional topology is then parsed by a grammar for common circuit functions. Ambiguities are introduced into the analysis by the approximate qualitative nature of the analysis. For example, there are often several possible mechanisms which might describe the circuit's function. These are disambiguated by teleological analysis. The requirement that each component be assigned an appropriate purpose in the functional topology imposes a severe constraint which eliminates all the ambiguities. Since both analyses are based on heuristics, the chosen mechanism is a rationalization of how the circuit functions, and does not guarantee that the circuit actually does function. This type of coarse understanding of circuits is useful for analysis, design and troubleshooting.

Finding Edges and Lines in Images

The problem of detecting intensity changes in images is canonical in vision. Edge detection operators are typically designed to optimally estimate first or second derivative over some (usually small) support. Other criteria such as output signal to noise ratio or bandwidth have also been argued for. This thesis is an attempt to formulate a set of edge detection criteria that capture as directly as possible the desirable properties of an edge operator. Variational techniques are used to find a solution over the space of all linear shift invariant operators. The first criterion is that the detector have low probability of error i.e. failing to mark edges or falsely marking non-edges. The second is that the marked points should be as close as possible to the centre of the true edge. The third criterion is that there should be low probability of more than one response to a single edge. The technique is used to find optimal operators for step edges and for extended impulse profiles (ridges or valleys in two dimensions). The extension of the one dimensional operators to two dimentions is then discussed. The result is a set of operators of varying width, length and orientation. The problem of combining these outputs into a single description is discussed, and a set of heuristics for the integration are given.

From Genetic Algorithms to Efficient Organization

The work described in this thesis began as an inquiry into the nature and use of optimization programs based on "genetic algorithms." That inquiry led, eventually, to three powerful heuristics that are broadly applicable in gradient-ascent programs: First, remember the locations of local maxima and restart the optimization program at a place distant from previously located local maxima. Second, adjust the size of probing steps to suit the local nature of the terrain, shrinking when probes do poorly and growing when probes do well. And third, keep track of the directions of recent successes, so as to probe preferentially in the direction of most rapid ascent. These algorithms lie at the core of a novel optimization program that illustrates the power to be had from deploying them together. The efficacy of this program is demonstrated on several test problems selected from a variety of fields, including De Jong's famous test-problem suite, the traveling salesman problem, the problem of coordinate registration for image guided surgery, the energy minimization problem for determining the shape of organic molecules, and the problem of assessing the structure of sedimentary deposits using seismic data.

The Benefits of Re-Evaluating Real-Time Fulfillment Decisions

At the time of a customer order, the e-tailer assigns the order to one or more of its order fulfillment centers, and/or to drop shippers, so as to minimize procurement and transportation costs, based on the available current information. However this assignment is necessarily myopic as it cannot account for all future events, such as subsequent customer orders or inventory replenishments. We examine the potential benefits from periodically re-evaluating these real-time order-assignment decisions. We construct near-optimal heuristics for the re-assignment for a large set of customer orders with the objective to minimize the total number of shipments. We investigate how best to implement these heuristics for a rolling horizon, and discuss the effect of demand correlation, customer order size, and the number of customer orders on the nature of the heuristics. Finally, we present potential saving opportunities by testing the heuristics on sets of order data from a major e-tailer.