The Markov network fitness model

Fitness modelling is an area of research which has recently received much interest among the evolutionary computing community. Fitness models can improve the efficiency of optimisation through direct sampling to generate new solutions, guiding of traditional genetic operators or as surrogates for a noisy or long-running fitness functions. In this chapter we discuss the application of Markov networks to fitness modelling of black-box functions within evolutionary computation, accompanied by discussion on the relationship betweenMarkov networks andWalsh analysis of fitness functions.We review alternative fitness modelling and approximation techniques and draw comparisons with the Markov network approach. We discuss the applicability of Markov networks as fitness surrogates which may be used for constructing guided operators or more general hybrid algorithms.We conclude with some observations and issues which arise from work conducted in this area so far

Multivariate Markov networks for fitness modelling in an estimation of distribution algorithm.

A well-known paradigm for optimisation is the evolutionary algorithm (EA). An EA maintains a population of possible solutions to a problem which converges on a global optimum using biologically-inspired selection and reproduction operators. These algorithms have been shown to perform well on a variety of hard optimisation and search problems. A recent development in evolutionary computation is the Estimation of Distribution Algorithm (EDA) which replaces the traditional genetic reproduction operators (crossover and mutation) with the construction and sampling of a probabilistic model. While this can often represent a significant computational expense, the benefit is that the model contains explicit information about the fitness function. This thesis expands on recent work using a Markov network to model fitness in an EDA, resulting in what we call the Markov Fitness Model (MFM). The work has explored the theoretical foundations of the MFM approach which are grounded in Walsh analysis of fitness functions. This has allowed us to demonstrate a clear relationship between the fitness model and the underlying dynamics of the problem. A key achievement is that we have been able to show how the model can be used to predict fitness and have devised a measure of fitness modelling capability called the fitness prediction correlation (FPC). We have performed a series of experiments which use the FPC to investigate the effect of population size and selection operator on the fitness modelling capability. The results and analysis of these experiments are an important addition to other work on diversity and fitness distribution within populations. With this improved understanding of fitness modelling we have been able to extend the framework Distribution Estimation Using Markov networks (DEUM) to use a multivariate probabilistic model. We have proposed and demonstrated the performance of a number of algorithms based on this framework which lever the MFM for optimisation, which can now be added to the EA toolbox. As part of this we have investigated existing techniques for learning the structure of the MFM; a further contribution which results from this is the introduction of precision and recall as measures of structure quality. We have also proposed a number of possible directions that future work could take

Mining Markov Network Surrogates to Explain the Results of Metaheuristic Optimisation

Metaheuristics are randomised search algorithms that are effective at finding ”good enough” solutions to optimisation problems. However, they present no justification for the generated solutions, and are non-trivial to analyse. We propose that identifying which combinations of variables strongly influence solution quality, and the nature of that relationship, represents a step towards explaining the choices made by the algorithm. Here, we present an approach to mining this information from a “surrogate fitness function” within a metaheuristic. The approach is demonstrated with two simple examples and a real-world case study

Mining Markov Network Surrogates to Explain the Results of Metaheuristic Optimisation

Metaheuristics are randomised search algorithms that are effective at finding ”good enough” solutions to optimisation problems. However, they present no justification for the generated solutions, and are non-trivial to analyse. We propose that identifying which combinations of variables strongly influence solution quality, and the nature of that relationship, represents a step towards explaining the choices made by the algorithm. Here, we present an approach to mining this information from a “surrogate fitness function” within a metaheuristic. The approach is demonstrated with two simple examples and a real-world case study

The role of Walsh structure and ordinal linkage in the optimisation of pseudo-Boolean functions under monotonicity invariance.

Optimisation heuristics rely on implicit or explicit assumptions about the structure of the black-box fitness function they optimise. A review of the literature shows that understanding of structure and linkage is helpful to the design and analysis of heuristics. The aim of this thesis is to investigate the role that problem structure plays in heuristic optimisation. Many heuristics use ordinal operators; which are those that are invariant under monotonic transformations of the fitness function. In this thesis we develop a classification of pseudo-Boolean functions based on rank-invariance. This approach classifies functions which are monotonic transformations of one another as equivalent, and so partitions an infinite set of functions into a finite set of classes. Reasoning about heuristics composed of ordinal operators is, by construction, invariant over these classes. We perform a complete analysis of 2-bit and 3-bit pseudo-Boolean functions. We use Walsh analysis to define concepts of necessary, unnecessary, and conditionally necessary interactions, and of Walsh families. This helps to make precise some existing ideas in the literature such as benign interactions. Many algorithms are invariant under the classes we define, which allows us to examine the difficulty of pseudo-Boolean functions in terms of function classes. We analyse a range of ordinal selection operators for an EDA. Using a concept of directed ordinal linkage, we define precedence networks and precedence profiles to represent key algorithmic steps and their interdependency in terms of problem structure. The precedence profiles provide a measure of problem difficulty. This corresponds to problem difficulty and algorithmic steps for optimisation. This work develops insight into the relationship between function structure and problem difficulty for optimisation, which may be used to direct the development of novel algorithms. Concepts of structure are also used to construct easy and hard problems for a hill-climber

Directed Intervention Crossover Approaches in Genetic Algorithms with Application to Optimal Control Problems

Genetic Algorithms (GAs) are a search heuristic modeled on the processes of evolution. They have been used to solve optimisation problems in a wide variety of fields. When applied to the optimisation of intervention schedules for optimal control problems, such as cancer chemotherapy treatment scheduling, GAs have been shown to require more fitness function evaluations than other search heuristics to find fit solutions. This thesis presents extensions to the GA crossover process, termed directed intervention crossover techniques, that greatly reduce the number of fitness function evaluations required to find fit solutions, thus increasing the effectiveness of GAs for problems of this type. The directed intervention crossover techniques use intervention scheduling information from parent solutions to direct the offspring produced in the GA crossover process towards more promising areas of a search space. By counting the number of interventions present in parents and adjusting the number of interventions for offspring schedules around it, this allows for highly fit solutions to be found in less fitness function evaluations. The validity of these novel approaches are illustrated through comparison with conventional GA crossover approaches for optimisation of intervention schedules of bio-control application in mushroom farming and cancer chemotherapy treatment. These involve optimally scheduling the application of a bio-control agent to combat pests in mushroom farming and optimising the timing and dosage strength of cancer chemotherapy treatments to maximise their effectiveness. This work demonstrates that significant advantages are gained in terms of both fitness function evaluations required and fitness scores found using the proposed approaches when compared with traditional GA crossover approaches for the production of optimal control schedules

TEDA: A Targeted Estimation of Distribution Algorithm

This thesis discusses the development and performance of a novel evolutionary algorithm, the Targeted Estimation of Distribution Algorithm (TEDA). TEDA takes the concept of targeting, an idea that has previously been shown to be effective as part of a Genetic Algorithm (GA) called Fitness Directed Crossover (FDC), and introduces it into a novel hybrid algorithm that transitions from a GA to an Estimation of Distribution Algorithm (EDA). Targeting is a process for solving optimisation problems where there is a concept of control points, genes that can be said to be active, and where the total number of control points found within a solution is as important as where they are located. When generating a new solution an algorithm that uses targeting must first of all choose the number of control points to set in the new solution before choosing which to set. The hybrid approach is designed to take advantage of the ability of EDAs to exploit patterns within the population to effectively locate the global optimum while avoiding the tendency of EDAs to prematurely converge. This is achieved by initially using a GA to effectively explore the search space before transitioning into an EDA as the population converges on the region of the global optimum. As targeting places an extra restriction on the solutions produced by specifying their size, combining it with the hybrid approach allows TEDA to produce solutions that are of an optimal size and of a higher quality than would be found using a GA alone without risking a loss of diversity. TEDA is tested on three different problem domains. These are optimal control of cancer chemotherapy, network routing and Feature Subset Selection (FSS). Of these problems, TEDA showed consistent advantage over standard EAs in the routing problem and demonstrated that it is able to find good solutions faster than untargeted EAs and non evolutionary approaches at the FSS problem. It did not demonstrate any advantage over other approaches when applied to chemotherapy. The FSS domain demonstrated that in large and noisy problems TEDA’s targeting derived ability to reduce the size of the search space significantly increased the speed with which good solutions could be found. The routing domain demonstrated that, where the ideal number of control points is deceptive, both targeting and the exploitative capabilities of an EDA are needed, making TEDA a more effective approach than both untargeted approaches and FDC. Additionally, in none of the problems was TEDA seen to perform significantly worse than any alternative approaches

Directed intervention crossover approaches in genetic algorithms with application to optimal control problems

Genetic Algorithms (GAs) are a search heuristic modeled on the processes of evolution. They have been used to solve optimisation problems in a wide variety of fields. When applied to the optimisation of intervention schedules for optimal control problems, such as cancer chemotherapy treatment scheduling, GAs have been shown to require more fitness function evaluations than other search heuristics to find fit solutions. This thesis presents extensions to the GA crossover process, termed directed intervention crossover techniques, that greatly reduce the number of fitness function evaluations required to find fit solutions, thus increasing the effectiveness of GAs for problems of this type. The directed intervention crossover techniques use intervention scheduling information from parent solutions to direct the offspring produced in the GA crossover process towards more promising areas of a search space. By counting the number of interventions present in parents and adjusting the number of interventions for offspring schedules around it, this allows for highly fit solutions to be found in less fitness function evaluations. The validity of these novel approaches are illustrated through comparison with conventional GA crossover approaches for optimisation of intervention schedules of bio-control application in mushroom farming and cancer chemotherapy treatment. These involve optimally scheduling the application of a bio-control agent to combat pests in mushroom farming and optimising the timing and dosage strength of cancer chemotherapy treatments to maximise their effectiveness. This work demonstrates that significant advantages are gained in terms of both fitness function evaluations required and fitness scores found using the proposed approaches when compared with traditional GA crossover approaches for the production of optimal control schedules.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Gaining Insight into Determinants of Physical Activity using Bayesian Network Learning

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