An Analysis of the Genetic Algorithm and Abstract Search Space Visualisation

The Genetic Algorithm (Holland, 1975) is a powerful search technique based upon the principles of Darwinian evolution. In its simplest form the GA consists of three main operators - crossover, mutation and selection. The principal theoretical treatment of the Genetic Algorithm (GA) is provided by the Schema Theorem and building block hypothesis (Holland, 1975). The building block hypothesis describes the GA search process as the combination, sampling and recombination of fragments of solutions known as building blocks. The crossover operator is responsible for the combination of building blocks, whilst the selection operator allocates increasing numbers of samples to good building blocks. Thus the GA constructs the optimal (or near-optimal) solution from those fragments of solutions which are, in some sense, optimal. The first part of this thesis documents the development of a technique for the isolation of building blocks from the populations of the GA. This technique is shown to extract exactly those building blocks of interest - those which are sampled most regularly by the GA. These building blocks are used to empirically investigate the validity of the building block hypothesis. It is shown that good building blocks do not combine to form significantly better solution fragments than those resulting from the addition of randomly generated building blocks to good building blocks. This results casts some doubt onto the value of the building block hypothesis as an account of the GA search process (at least for the functions used during these experiments). The second part of this thesis describes an alternative account of the action of crossover. This account is an approximation of the geometric effect of crossover upon the population of samples maintained by the GA. It is shown that, for a simple function, this description of the crossover operator is sufficiently accurate to warrant further investigation. A pair of performance models for the GA upon this function are derived and shown to be accurate for a wide range of crossover schemes. Finally, the GA search process is described in terms of this account of the crossover operator and parallels are drawn with the search process of the simulated annealing algorithm (Kirkpatrick et al, 1983). The third and final part of this thesis describes a technique for the visualisation of high dimensional surfaces, such as are defined by functions of many parameters. This technique is compared to the statistical technique of projection pursuit regression (Friedman & Tukey, 1974) and is shown to compare favourably both in terms of computational expense and quantitative accuracy upon a wide range of test functions. A fundamental flaw of this technique is that it may produce poor visualisations when applied to functions with a small high frequency (or order) components

Multidimensional crossover in genetic algorithms

Not available

ADAPTIVE SEARCH AND THE PRELIMINARY DESIGN OF GAS TURBINE BLADE COOLING SYSTEMS

This research concerns the integration of Adaptive Search (AS) technique such as the Genetic Algorithms (GA) with knowledge based software to develop a research prototype of an Adaptive Search Manager (ASM). The developed approach allows to utilise both quantitative and qualitative information in engineering design decision making. A Fuzzy Expert System manipulates AS software within the design environment concerning the preliminary design of gas turbine blade cooling systems. Steady state cooling hole geometry models have been developed for the project in collaboration with Rolls Royce plc. The research prototype of ASM uses a hybrid of Adaptive Restricted Tournament Selection (ARTS) and Knowledge Based Hill Climbing (KBHC) to identify multiple "good" design solutions as potential design options. ARTS is a GA technique that is particularly suitable for real world problems having multiple sub-optima. KBHC uses information gathered during the ARTS search as well as information from the designer to perform a deterministic hill climbing. Finally, a local stochastic hill climbing fine tunes the "good" designs. Design solution sensitivity, design variable sensitivities and constraint sensitivities are calculated following Taguchi's methodology, which extracts sensitivity information with a very small number of model evaluations. Each potential design option is then qualitatively evaluated separately for manufacturability, choice of materials and some designer's special preferences using the knowledge of domain experts. In order to guarantee that the qualitative evaluation module can evaluate any design solution from the entire design space with a reasonably small number of rules, a novel knowledge representation technique is developed. The knowledge is first separated in three categories: inter-variable knowledge, intra-variable knowledge and heuristics. Inter-variable knowledge and intra-variable knowledge are then integrated using a concept of compromise. Information about the "good" design solutions is presented to the designer through a designer's interface for decision support.Rolls Royce plc., Bristol (UK

Conjugate Schema and Basis Representation of Crossover and Mutation Operators

In genetic search algorithms and optimization routines, the representation of the mutation and crossover operators are typically defaulted to the canonical basis. We show that this can be influential in the usefulness of the search algorithm. We then pose the question of how to find a basis for which the search algorithm is most useful. The conjugate schema is introduced as a general mathematical construct and is shown to separate a function into smaller dimensional functions whose sum is the original function. It is shown that conjugate schema, when used on a test suite of functions, improves the performance of the search algorithm on 10 out of 12 of these functions. Finally, a rigorous but abbreviated mathematical derivation is given in the appendices

Saddles and Barrier in Landscapes of Generalized Search Operators

Barrier trees are a convenient way of representing the structure of complex combinatorial landscapes over graphs. Here we generalize the concept of barrier trees to landscapes defined over general multi-parent search operators based on a suitable notion of topological connectedness that depends explicitly on the search operator. We show that in the case of recombination spaces, path-connectedness coincides with connectedness as defined by the mutation operator alone. In contrast, topological connectedness is more general and depends on the details of the recombination operators as well. Barrier trees can be meaningfully defined for both concepts of connectedness

Efficient Incremental View Maintenance for Data Warehousing

Data warehousing and on-line analytical processing (OLAP) are essential elements for decision support applications. Since most OLAP queries are complex and are often executed over huge volumes of data, the solution in practice is to employ materialized views to improve query performance. One important issue for utilizing materialized views is to maintain the view consistency upon source changes. However, most prior work focused on simple SQL views with distributive aggregate functions, such as SUM and COUNT. This dissertation proposes to consider broader types of views than previous work. First, we study views with complex aggregate functions such as variance and regression. Such statistical functions are of great importance in practice. We propose a workarea function model and design a generic framework to tackle incremental view maintenance and answering queries using views for such functions. We have implemented this approach in a prototype system of IBM DB2. An extensive performance study shows significant performance gains by our techniques. Second, we consider materialized views with PIVOT and UNPIVOT operators. Such operators are widely used for OLAP applications and for querying sparse datasets. We demonstrate that the efficient maintenance of views with PIVOT and UNPIVOT operators requires more generalized operators, called GPIVOT and GUNPIVOT. We formally define and prove the query rewriting rules and propagation rules for such operators. We also design a novel view maintenance framework for applying these rules to obtain an efficient maintenance plan. Extensive performance evaluations reveal the effectiveness of our techniques. Third, materialized views are often integrated from multiple data sources. Due to source autonomicity and dynamicity, concurrency may occur during view maintenance. We propose a generic concurrency control framework to solve such maintenance anomalies. This solution extends previous work in that it solves the anomalies under both source data and schema changes and thus achieves full source autonomicity. We have implemented this technique in a data warehouse prototype developed at WPI. The extensive performance study shows that our techniques put little extra overhead on existing concurrent data update processing techniques while allowing for this new functionality