Franz Oppacher

HARP: a tableau-based theorem prover

This paper presents HARP, a complete, tableau-based theorem prover for first order logic, which is intended to be used both interactively and as an inference engine for Artificial Intelligence applications. Accordingly, HARPs construction is influenced by the design goals of ‘naturalness’, efficiency, usefulness in an Artificial Intelligence environment, and modifiability of the control structure by heuristics. To achieve these goals, HARP accepts the entire language of first order logic, i.e. avoids conversion to any kind of normal form, and combines a proof condensation procedure with explicitly represented, declaratively formulated heuristics to construct and communicate its proofs in a format congenial to people. The proof condensation procedure makes proof shorter and more readable by excising redundancies from proof trees. Domain-independent heuristics are formulated to capture efficient and human-like deduction strategies and to rapidly detect certain types of nontheorems. Domain-dependent heuristics can be used to implement specific control regimes, e.g. to efficiently support inheritance. HARPs architecture-and the concomitant ready extensibility of its control structure by declarative heuristic rules-renders it easy to let extralogical information, e.g. semantic and world knowledge, guide the search for proofs and help eliminate irrelevant premisses.

Program Search with a Hierarchical Variable Lenght Representation: Genetic Programming, Simulated Annealing and Hill Climbing

This paper emphasizes the general value of a hierarchical variable length representation for program induction by demonstrating that different search strategies and operators complementary to them can be used to obtain solutions. It presents a comparison of Genetic Programming (GP) with Simulated Annealing (SA) and Stochastic Iterated Hill Climbing (SIHC). All three search algorithms employ the hierarchical variable length representation for programs brought into recent prominence with the GP paradigm [K-92]. We experiment with three GP crossover operators and a new hierarchical variable length mutation operator developed for use in SA and SIHC. The results do not favor any one search technique which bears out the observation that a search strategy should be chosen in view of the landscape determined by fitness function and representation.

Hybridized crossover-based search techniques for program discovery

Addresses the problem of program discovery as defined by genetic programming. By combining a hierarchical crossover operator with two traditional single-point search algorithms (simulated annealing and stochastic iterated hill climbing), we have solved some problems by processing fewer candidate solutions and with a greater probability of success than genetic programming. We have also enhanced genetic programming by hybridizing it with the simple idea of hill climbing from a few individuals, at a fixed interval of generations.

An Analysis of Koza's Computational Effort Statistic for Genetic Programming

As research into the theory of genetic programming progresses, more effort is being placed on systematically comparing results to give an indication of the effectiveness of sundry modifications to traditional GP. The statistic that is commonly used to report the amount of computational effort to solve a particular problem with 99% probability is Kozas I(M, i, z) statistic. This paper analyzes this measure from a statistical perspective. In particular, Kozas I tends to underestimate the true computational effort, by 25% or more for commonly used GP parameters and run sizes. The magnitude of this underestimate is nonlinearly decreasing with increasing run count, leading to the possibility that published results based on few runs may in fact be unmatchable when replicated at higher resolution. Additional analysis shows that this statistic also underreports the generation at which optimal results are achieved.

Adaptive Crossover Using Automata

Genetic Algorithms (GAs) have traditionally required the specification of a number of parameters that control the evolutionary process. In the classical model, the mutation and crossover operator probabilities are specified before the start of a GA run and remain unchanged; a so-called static model. This paper extends the conventional representation by using automata in order to allow the adaptation of the crossover operator probability as the run progresses in order to facilitate schema identification and reduce schema disruption. Favourable results have been achieved for a wide range of function minimization problems and these are described.

The underlying similarity of diversity measures used in evolutionary computation

In this paper we compare and analyze the various diversity measures used in the Evolutionary Computation field. While each measure looks quite different from the others in form, we surprisingly found that the same basic method underlies all of them: the distance between all possible pairs of chromosomes/ organisms in the population. This is true even of the Shannon entropy of gene frequencies. We then associate the different varieties of EC diversity measures to different diversity measures used in Biology. Finally we give an O(n) implementation for each of the diversity measures (where n is the population size), despite their basis in an O(n2) number of comparisons.

Low-Level Visual Homing

We present a variant of the snapshot model [1] for insect visual homing. In this model a snapshot image is taken by an agent at the goal position. The disparity between current and snapshot images is subsequently used to guide the agent’s return. A matrix of local low-level processing elements is applied here to compute this disparity and transform it into a motion vector. This scheme contrasts with other variants of the snapshot model which operate on one-dimensional images, generally taken as views from a synthetic or simplified real world setting. Our approach operates directly on two-dimensional images of the real world. Although this system is not a model of any known neural structure, it hopes to offer more biological plausibility than competing techniques because the processing applied is low-level, and because the information processed appears to be of the same sort of information that is processed by insects. We present a comparison of results obtained on a set of real-world images.

A Representation Scheme To Perform Program Induction in a Canonical Genetic Algorithm

This paper studies Genetic Programming (GP) and its relation to the Genetic Algorithm (GA). GP uses a GA approach to breed successive populations of programs, represented in the chromosomes as parse trees, until a program that solves the problem emerges. However, parse trees are not naturally homologous, consequently changes had to be introduced into GP. To better understand these changes it would be instructive if a canonical GA could also be used to perform program induction. To this end an appropriate GA representation scheme is developed (called EP-I for Evolutionary Programming with Introns). EP-I has been tested on three problems and performed identically to GP, thus demonstrating that the changes introduced by GP do not have any properties beyond those of a canonical GA for program induction. EP-I is also able to simulate GP exactly thus gaining further insights into the nature of GP as a GA.

Distance between populations

Gene space, as it is currently formulated, cannot provide a solid basis for investigating the behavior of the GA. We instead propose an approach that takes population effects into account. Starting from a discussion of diversity, we develop a distance measure between populations and thereby a population metric space. We finally argue that one specific parameterization of this measure is particularly appropriate for use with GAs.

A General Model of Co-evolution for Genetic Algorithms

Compared with natural systems, Genetic Algorithms have a limited adaptive capacity, i.e. they get quite frequently trapped at local optima and they are poor at tracking moving optima in dynamic environments. This paper describes a general, formal model of co-evolution, the Linear Model of Symbiosis, that allows for the concise, unified expression of all types of co-evolutionary relations studied in ecology. Experiments on several difficult problems support our assumption that the addition of the Linear Model of Symbiosis to a canonical Genetic Algorithm can remedy the above shortcomings.