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

Group Properties of Crossover and Mutation

It is supposed that the finite search space Ω has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Ω are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Ω to induce a group structure on Ω itself

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

An application of genetic algorithms to chemotherapy treatment.

The present work investigates methods for optimising cancer chemotherapy within the bounds of clinical acceptability and making this optimisation easily accessible to oncologists. Clinical oncologists wish to be able to improve existing treatment regimens in a systematic, effective and reliable way. In order to satisfy these requirements a novel approach to chemotherapy optimisation has been developed, which utilises Genetic Algorithms in an intelligent search process for good chemotherapy treatments. The following chapters consequently address various issues related to this approach. Chapter 1 gives some biomedical background to the problem of cancer and its treatment. The complexity of the cancer phenomenon, as well as the multi-variable and multi-constrained nature of chemotherapy treatment, strongly support the use of mathematical modelling for predicting and controlling the development of cancer. Some existing mathematical models, which describe the proliferation process of cancerous cells and the effect of anti-cancer drugs on this process, are presented in Chapter 2. Having mentioned the control of cancer development, the relevance of optimisation and optimal control theory becomes evident for achieving the optimal treatment outcome subject to the constraints of cancer chemotherapy. A survey of traditional optimisation methods applicable to the problem under investigation is given in Chapter 3 with the conclusion that the constraints imposed on cancer chemotherapy and general non-linearity of the optimisation functionals associated with the objectives of cancer treatment often make these methods of optimisation ineffective. Contrariwise, Genetic Algorithms (GAs), featuring the methods of evolutionary search and optimisation, have recently demonstrated in many practical situations an ability to quickly discover useful solutions to highly-constrained, irregular and discontinuous problems that have been difficult to solve by traditional optimisation methods. Chapter 4 presents the essence of Genetic Algorithms, as well as their salient features and properties, and prepares the ground for the utilisation of Genetic Algorithms for optimising cancer chemotherapy treatment. The particulars of chemotherapy optimisation using Genetic Algorithms are given in Chapter 5 and Chapter 6, which present the original work of this thesis. In Chapter 5 the optimisation problem of single-drug chemotherapy is formulated as a search task and solved by several numerical methods. The results obtained from different optimisation methods are used to assess the quality of the GA solution and the effectiveness of Genetic Algorithms as a whole. Also, in Chapter 5 a new approach to tuning GA factors is developed, whereby the optimisation performance of Genetic Algorithms can be significantly improved. This approach is based on statistical inference about the significance of GA factors and on regression analysis of the GA performance. Being less computationally intensive compared to the existing methods of GA factor adjusting, the newly developed approach often gives better tuning results. Chapter 6 deals with the optimisation of multi-drug chemotherapy, which is a more practical and challenging problem. Its practicality can be explained by oncologists' preferences to administer anti-cancer drugs in various combinations in order to better cope with the occurrence of drug resistant cells. However, the imposition of strict toxicity constraints on combining various anticancer drugs together, makes the optimisation problem of multi-drug chemotherapy very difficult to solve, especially when complex treatment objectives are considered. Nevertheless, the experimental results of Chapter 6 demonstrate that this problem is tractable to Genetic Algorithms, which are capable of finding good chemotherapeutic regimens in different treatment situations. On the basis of these results a decision has been made to encapsulate Genetic Algorithms into an independent optimisation module and to embed this module into a more general and user-oriented environment - the Oncology Workbench. The particulars of this encapsulation and embedding are also given in Chapter 6. Finally, Chapter 7 concludes the present work by summarising the contributions made to the knowledge of the subject treated and by outlining the directions for further investigations. The main contributions are: (1) a novel application of the Genetic Algorithm technique in the field of cancer chemotherapy optimisation, (2) the development of a statistical method for tuning the values of GA factors, and (3) the development of a robust and versatile optimisation utility for a clinically usable decision support system. The latter contribution of this thesis creates an opportunity to widen the application domain of Genetic Algorithms within the field of drug treatments and to allow more clinicians to benefit from utilising the GA optimisation

Evolutionary algorithms in artificial intelligence: a comparative study through applications

For many years research in artificial intelligence followed a symbolic paradigm which required a level of knowledge described in terms of rules. More recently subsymbolic approaches have been adopted as a suitable means for studying many problems. There are many search mechanisms which can be used to manipulate subsymbolic components, and in recent years general search methods based on models of natural evolution have become increasingly popular. This thesis examines a hybrid symbolic/subsymbolic approach and the application of evolutionary algorithms to a problem from each of the fields of shape representation (finding an iterated function system for an arbitrary shape), natural language dialogue (tuning parameters so that a particular behaviour can be achieved) and speech recognition (selecting the penalties used by a dynamic programming algorithm in creating a word lattice). These problems were selected on the basis that each should have a fundamentally different interactions at the subsymbolic level. Results demonstrate that for the experiments conducted the evolutionary algorithms performed well in most cases. However, the type of subsymbolic interaction that may occur influences the relative performance of evolutionary algorithms which emphasise either top-down (evolutionary programming - EP) or bottom-up (genetic algorithm - GA) means of solution discovery. For the shape representation problem EP is seen to perform significantly better than a GA, and reasons for this disparity are discussed. Furthermore, EP appears to offer a powerful means of finding solutions to this problem, and so the background and details of the problem are discussed at length. Some novel constraints on the problem's search space are also presented which could be used in related work. For the dialogue and speech recognition problems a GA and EP produce good results with EP performing slightly better. Results achieved with EP have been used to improve the performance of a speech recognition system

Prescriptive formalism for constructing domain-specific evolutionary algorithms

It has been widely recognised in the computational intelligence and machine learning communities that the key to understanding the behaviour of learning algorithms is to understand what representation is employed to capture and manipulate knowledge acquired during the learning process. However, traditional evolutionary algorithms have tended to employ a fixed representation space (binary strings), in order to allow the use of standardised genetic operators. This approach leads to complications for many problem domains, as it forces a somewhat artificial mapping between the problem variables and the canonical binary representation, especially when there are dependencies between problem variables (e.g. problems naturally defined over permutations). This often obscures the relationship between genetic structure and problem features, making it difficult to understand the actions of the standard genetic operators with reference to problem-specific structures. This thesis instead advocates m..

Algoritmos genéticos generalizados : variaciones sobre un tema

[Resumen]Durante las tres últimas décadas se ha incrementado el interés por los Algoritmos Genéticos cuya aplicación cubre un amplio espectro de temas. A pesar de que el llamado Teorema de los Esquemas (generalizado al caso contínuo en esta memoria) justifica, en parte, su buen funcionamiento, el problema de caracterizar las funciones difíciles de optimizar a través de un AG es, todavía, una cuestión pendiente de solución. La presente memoria aborda el tema anterior desde el punto de vista de la epistasis que resulta ser uno de los factores que contribuyen a la dificultad de la optimización de una función. El trabajo contiene un estudio detallado de esta noción tanto en el ámbito de las codificaciones binarias como no binarias (el interés por las cuales se ha venido incrementando recientemente) con especial énfasis en las funciones de peso (unitation)

An Improved Multi-Objective Evolutionary Algorithm with Adaptable Parameters

Multi-Objective Evolutionary Algorithms (MOEAs) are not easy to use because they require parameter tunings of three main parameters - population size, crossover probability, and mutation probability - in order to achieve desirable solutions and performance for an arbitrary complex problem. Moreover, the use of fixed parameter settings may lead to slow convergence and sub-optimal solutions. This dissertation develops a MOEA with self-adaptive crossover, self-adaptive mutation, and adaptive population size parameters for automating the process of adjusting appropriate parameter values in order to make the MOEA more efficient, simple to use and available to more users. The MOEA with adaptable parameters is built on the NSGA-II (Non-dominated Sorting Genetic Algorithm II) and named as ANSGA-JI (Adaptable NSGA-II). The NSGA-II is chosen because it is one of the best-known MOEAs. In the ANSGA-II, the crossover and mutation parameters are attached to each solution in the population and allowed to co-evolve with each solution. This enables the algorithm to carry prior successful crossover and mutation for creating children solutions and for adaptation of the parameters. Since good parameter values are associated with good candidate solutions, better parameter values will survive because they produce better solutions. The ANSGA-II selects the right population size by running several populations with different population sizes simultaneously and allows the smaller populations more time to run. Smaller populations may find diverse non-dominated solution sets close to the Paretooptimal front faster than the larger populations. If a subsequent larger population identifies a better non-dominated solution set then the algorithm stops running the smaller population since it is unlikely to identify better solutions than the larger one due to genetic drift. Two performance metrics are investigated for their effective use in comparing non-dominated solution sets among different populations during the execution of the ANSGA-II. The dissertation evaluates and discusses the performance of the ANSGA-II, in terms of finding a diverse non-dominated solution set and converging to the true Pareto-optimal front, by comparing the results obtained on a suite of thirteen benchmark multi-objective problems with those obtained by the original NSGA-II. The results demonstrate that the ANSGA-II out performs the NSGA-II. The improvement comes with the cost of longer execution time due to overheads of finding good non dominated solutions and learning good parameter values at the same time. However, the execution time appears to be acceptable on all thirteen benchmark multi-objective problems