This paper describes the development of OM-Darwin, a generalized system for composing with genetic algorithms (GA), realized as a library for OpenMusic. It provides a simple GA engine, along with sophisticated devices for genotype encoding, phenotype mapping and modular fitness function design, while offering a collection of objects that represent common musical forms and rules. A comparison with other optimization methods reveals some advantages in the GA approach, in particular the capability of defining frequency-based rules and producing partial solutions to difficult musical problems. Reference is made to the author's Future Perfect (2010) for 13 instruments, composed entirely using OM-Darwin.

Lau Chun Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 122-125). / Chapter Chapter 1: --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Static Plant Layout Problem --- p.1 / Chapter 1.3 --- Dynamic Plant Layout Problem --- p.3 / Chapter 1.4 --- Example Problem of SPLP --- p.4 / Chapter 1.5 --- Formulation of SPLP --- p.7 / Chapter 1.6 --- Example Problem of DPLP --- p.8 / Chapter 1.7 --- Mathematical Model of DPLP --- p.12 / Chapter 1.8 --- Characteristics of the DPLP --- p.13 / Chapter 1.9 --- Constrained Dynamic Plant Layout Problem (CDPLP) --- p.14 / Chapter 1.10 --- Mathematical Model of CDPLP --- p.14 / Chapter 1.11 --- Objective of the Research --- p.15 / Chapter 1.12 --- Conclusion --- p.16 / Chapter Chapter 2: --- Literature Review --- p.17 / Chapter 2.1 --- Overview --- p.17 / Chapter 2.2 --- Static Plant Layout Problem (SPLP) --- p.17 / Chapter 2.2.1 --- The optimal algorithms / Chapter 2.2.2 --- The sub-optimal algorithms / Chapter 2.2.3 --- Construction algorithms / Chapter 2.2.4 --- Improvement algorithms / Chapter 2.3 --- Dynamic Plant Layout Problem (DPLP) --- p.21 / Chapter 2.4 --- Conclusion: --- p.26 / Chapter Chapter 3: --- Genetic Algorithms in DPLP --- p.27 / Chapter 3.1 --- Introduction of Genetic Algorithms --- p.27 / Chapter 3.2 --- Genetic Algorithms in DPLP --- p.28 / Chapter 3.2.1 --- Encoding of a solution / Chapter 3.2.2 --- Fitness function / Chapter 3.2.3 --- Crossover operator / Chapter 3.2.4 --- Selection scheme / Chapter 3.2.5 --- Replacement and reproduction / Chapter 3.2.6 --- Mutation / Chapter 3.2.7 --- Initialization of parent pool / Chapter 3.2.8 --- Termination criterion / Chapter 3.3 --- Summary of the Proposed Method --- p.50 / Chapter Chapter 4: --- Computational Result of GA in DPLP --- p.51 / Chapter 4.1 --- Overview --- p.51 / Chapter 4.2 --- Characteristics of the Testing Problems --- p.51 / Chapter 4.3 --- Mathematical Model of DPLP for the Testing Problem --- p.52 / Chapter 4.4 --- The Design of Experiment --- p.53 / Chapter 4.4.1 --- The experiment / Chapter 4.4.2 --- Generating the initial layouts: / Chapter 4.5 --- Result: --- p.56 / Chapter 4.6 --- Analysis of Results --- p.60 / Chapter 4.6.1 --- 6department problems / Chapter 4.6.2 --- 15and 30 department problems / Chapter 4.7 --- Conclusion --- p.66 / Chapter Chapter 5: --- Constrained Dynamic Plant Layout Problem --- p.68 / Chapter 5.1 --- Overview --- p.68 / Chapter 5.2 --- The Mathematical Model of CDPLP --- p.69 / Chapter 5.3 --- Properties of CDPLP --- p.69 / Chapter 5.4 --- The Proposed GA on CDPLP --- p.71 / Chapter 5.4.1 --- Introduction / Chapter 5.4.2 --- Procedure / Chapter 5.4.3 --- Properties of dynamic programming under the dummy periods / Chapter 5.4.4 --- Properties of the proposed GA under the dummy periods / Chapter 5.4.5 --- The maximum number of iteration for the procedure / Chapter 5.5 --- Design of Experiment --- p.78 / Chapter 5.6 --- Result of Experiment on CDPLP --- p.81 / Chapter 5.7 --- Analysis of Results --- p.91 / Chapter 5.7.1 --- Type 1 budget (self): / Chapter 5.7.2 --- The average cost of the test / Chapter 5.8 --- Conclusion: --- p.93 / Chapter Chapter 6: --- Conclusion --- p.94 / Appendix A: The Improved Implementation for Conway and Venkataramanan's GA --- p.96 / Appendix B: Computational Result for CDPLP --- p.98 / Bibliography --- p.122

Sit, Loi Yuk. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 64-65). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Introduction to Genetic Algorithm --- p.5 / Chapter 2.1 --- The Basic Genetic Algorithm --- p.5 / Chapter 2.1.1 --- Selection Mechanisms --- p.7 / Chapter 2.1.2 --- Variation Operators --- p.8 / Chapter 2.2 --- Implementation of Genetic Algorithm --- p.10 / Chapter 2.3 --- Examples of Combinatorial Optimization --- p.12 / Chapter 2.3.1 --- Max-Cut Problem --- p.12 / Chapter 2.3.2 --- Transportation Problem --- p.15 / Chapter 2.3.3 --- Travelling Salesman Problem --- p.23 / Chapter 3 --- Model Building --- p.27 / Chapter 3.1 --- Introduction --- p.27 / Chapter 3.2 --- Sampling Mechanism --- p.28 / Chapter 3.3 --- Sampling Algorithm --- p.34 / Chapter 3.4 --- Parameters Estimation --- p.35 / Chapter 3.4.1 --- Parameters α and β of f(y) --- p.36 / Chapter 3.4.2 --- "Parameters p of f(z\x1,x2)" --- p.38 / Chapter 4 --- Design and Results of the Simulation Study --- p.40 / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- Selection Mechanism --- p.41 / Chapter 4.3 --- Choice of Parameters' Values --- p.42 / Chapter 4.4 --- Performance Index --- p.43 / Chapter 4.5 --- Results and Interpretation --- p.48 / Chapter 5 --- Empirical Checking of the Selection Rule --- p.54 / Chapter 5.1 --- Introduction --- p.54 / Chapter 5.2 --- Max-Cut Problem --- p.54 / Chapter 5.3 --- Transportation Problem --- p.56 / Chapter 5.4 --- Travelling Salesman Problem --- p.57 / Chapter 6 --- Conclusion and Discussion --- p.60 / Bibliography --- p.64

Genetic algorithms are an evolutionary technique that use crossover and mutation operators to solve optimization problems using a survival of the fittest idea. They have been used successfully in a variety of different problems, including the traveling salesman problem. In the traveling salesman problem we wish to find a tour of all nodes in a weighted graph so that the total weight is minimized. The traveling salesman problem is NP-hard but has many real world applications so a good solution would be useful. Many different crossover and mutation operators have been devised for the traveling salesman problem and each give different results. We compare these results and find that operators that use heuristic information or a matrix representation of the graph give the best results.

"July 2002." Bibliography: leaves 119-126. !. Introduction -- 2. Preliminiaries -- 3. Genetic algorithms -- 4. Equilibria and stability in economic models -- 5. Stochastic representation of economic models -- 6. Two population models -- 7. Overview. The aim of this dissertation is to provide a mathematical foundation for the application of genetic algorithms to economic models.

The basis of this thesis is the presumption that while neural networks are useful structures that can be used to model complex, highly non-linear systems, current methods of training the neural networks are inadequate in some problem domains. Genetic algorithms have been used to optimise both the weights and architectures of neural networks, but these approaches do not treat the neural network in a sensible manner. In this thesis, I define the basis of computation within a neural network as a single neuron and its associated input connections. Sets of these neurons, stored in a matrix representation, comprise the building blocks that are transferred during one or more epochs of a genetic algorithm. I develop the concept of a Neural Building Block and two new genetic algorithms are created that utilise this concept. The first genetic algorithm utilises the micro neural building block (micro-NBB); a unit consisting of one or more neurons and their input connections. The micro-NBB is a unit that is transmitted through the process of crossover and hence requires the introduction of a new crossover operator. However the micro NBB can not be stored as a reusable component and must exist only as the product of the crossover operator. The macro neural building block (macro-NBB) is utilised in the second genetic algorithm, and encapsulates the idea that fit neural networks contain fit sub-networks, that need to be preserved across multiple epochs. A macro-NBB is a micro-NBB that exists across multiple epochs. Macro-NBBs must exist across multiple epochs, and this necessitates the use of a genetic store, and a new operator to introduce macro-NBBs back into the population at random intervals. Once the theoretical presentation is completed the newly developed genetic algorithms are used to evolve weights for a variety of architectures of neural networks to demonstrate the feasibility of the approach. Comparison of the new genetic algorithm with other approaches is very favourable on two problems: a multiplexer problem and a robot control problem.

"July 2002." / Bibliography: leaves 119-126. / xi, 126 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / The aim of this dissertation is to provide a mathematical foundation for the application of genetic algorithms to economic models. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2002

Evolutionary algorithms are based on the principles of biological evolution (Bre- mermann et al., 1966; Fraser, 1957; Box, 1957). Genetic algorithms are a class of evolutionary algorithm applicable to optimisation of a wide range of problems because they do not assume that the problem to be optimised is differentiable or convex. Potential solutions to a problem are encoded by allele sequences (genes) on an artificial genome in a manner analogous to biological DNA. Populations of these artificial genomes are then tested and bred together, combining artificial genetic material by the operation of crossover and mutation of genes, so that encoded solutions which more completely optimise the problem flourish and weaker solutions die out. Genetic algorithms are applied to a very broad range of problems in a variety of industries including financial modeling, manufacturing, data mining, engineering, design and science. Some examples are: • Traveling Salesman Problems such as vehicle routing, • Scheduling Problems such as Multiprocessor scheduling, and • Packing problems such as Shipping Container Operations. However, relative to the total volume of papers on genetic algorithms, few have focused on the theoretical foundations and identification of techniques to build effective genetic algorithms. Recent research has tended to focus on industry applications, rather than design techniques or parameter setting for genetic algorithms. There are of course exceptions to these observations. Nevertheless, the exceptions generally focus on a particular parameter or operator in relative isolation and do not attempt to find a foundation, approach or model which underpins them all. The objective of this Thesis is to establish theoretically sound methods for estimating appropriate parameter settings and structurally appropriate operators for genetic algorithms. The Thesis observes a link between some fundamental ideas in information theory and the relative frequency of alleles in a population. This observation leads to a systematic approach to determining optimum values for genetic algorithm parameters and the use of generational operators such as mutation, selection, crossover and termination criteria. The practical significance of the Thesis is that the outcomes form theoretically justified guidelines for researchers and practitioners. The Thesis establishes a model for the analysis of genetic algorithm be- haviour by applying fundamental concepts from information theory. The use of information theory grounds the model and contributions to a well established mathematical framework making them reliable and reproducible. The model and techniques contribute to the field of genetic algorithms by providing a clear and practical basis for algorithm design and tuning. Two ideas are central to the approach taken. Firstly, that evolutionary processes encode information into a population by altering the relative frequency of alleles. Secondly, that the key difference between a genetic algorithm and other algorithms is the generational operators, selection and crossover. Hence the model maximises a population’s information as represented by the relative frequency of solution alleles in the population, encourages the accumulation of these alleles and maximises the number of generations able to be processed. Information theory is applied to characterise the information sources used for mutation as well as to define selection thresholds in ranked populations. The importance of crossover in distributing alleles throughout a population and in promoting the accumulation of information in populations is analysed, while the Shannon–McMillan theorem is applied to identify practical termination criteria. The concept of ideal alleles as being those symbols in the appropriate loci, which form an optimal solution and the associated solution density of the population is central to this analysis. The term solution density is introduced to refer to the relative frequency of ideal alleles in the population at a particular generation. Solution density so defined represents a measure of a population’s fitness. By analysing the key genetic operators in terms of their effect on solution density, this Thesis identifies ten contributions. • A model for the analysis of genetic algorithm behaviour inspired by information theory. • A static selection threshold in ranked populations. • A dynamic selection threshold in ranked populations. • A maximum limit on the number of loci participating in epistasis is identified whereby more epistatic loci degrade directed search. • A practical limit to the amount of useful crossover is identified as sufficient. • An optimal crossover section length is found. • A cumulative scoring method for identifying solution density. • An entropy profile of ranked lists is described. • A practical termination criteria of most probable individuals based on the Shannon–McMillan theorem is provided. • An alternative genome representation which incorporates job–shop schedule problem knowledge in the genome rather than the algorithm’s generational operators is developed. Each of these contributions is validated by simulations, benchmark problems and application to a real–world problem.

Thesis (M.S.)--University of Nevada, Reno, 2006. / "May, 2006." Includes bibliographical references (leaves 70-72). Online version available on the World Wide Web.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.