Automated design of boolean satisfiability solvers employing evolutionary computation

Modern society gives rise to complex problems which sometimes lend themselves to being transformed into Boolean satisfiability (SAT) decision problems; this thesis presents an example from the program understanding domain. Current conflict-driven clause learning (CDCL) SAT solvers employ all-purpose heuristics for making decisions when finding truth assignments for arbitrary logical expressions called SAT instances. The instances derived from a particular problem class exhibit a unique underlying structure which impacts a solver\u27s effectiveness. Thus, tailoring the solver heuristics to a particular problem class can significantly enhance the solver\u27s performance; however, manual specialization is very labor intensive. Automated development may apply hyper-heuristics to search program space by utilizing problem-derived building blocks. This thesis demonstrates the potential for genetic programming (GP) powered hyper-heuristic driven automated design of algorithms to create tailored CDCL solvers, in this case through custom variable scoring and learnt clause scoring heuristics, with significantly better performance on targeted classes of SAT problem instances. As the run-time of GP is often dominated by fitness evaluation, evaluating multiple offspring in parallel typically reduces the time incurred by fitness evaluation proportional to the number of parallel processing units. The naive synchronous approach requires an entire generation to be evaluated before progressing to the next generation; as such, heterogeneity in the evaluation times will degrade the performance gain, as parallel processing units will have to idle until the longest evaluation has completed. This thesis shows empirical evidence justifying the employment of an asynchronous parallel model for GP powered hyper-heuristics applied to SAT solver space, rather than the generational synchronous alternative, for gaining speed-ups in evolution time. Additionally, this thesis explores the use of a multi-objective GP to reveal the trade-off surface between multiple CDCL attributes --Abstract, page iii

Evolving comprehensible and scalable solvers using CGP for solving some real-world inspired problems

My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative Cartesian Genetic Programming can encode loops and nested loop with their termination criteria, making susceptible to evolutionary modification the whole programming construct. This newly developed extension and its application to metaheuristics are demonstrated to discover effective solvers for NP-hard and discrete problems. This thesis also extends Cartesian Genetic Programming and Iterative Cartesian Genetic Programming to adapt a hyper-heuristic reproductive operator at the same time of exploring the automatic design space. It is demonstrated the exploration of an automated design space can be improved when specific types of active and non-active genes are mutated. \\ A series of rigorous empirical investigations demonstrate that lowering the comprehension barrier of automatically designed algorithms can help communicating and identifying an effective and ineffective pattern of primitives. The complete evolution of loops and nested loops without imposing a hard limit on the number of recursive calls is shown to broaden the automatic design space. Finally, it is argued the capability of a learning objective function to assess the scalable potential of a generated algorithm can be beneficial to a generative hyper-heuristic

Evolved parameterized selection for evolutionary algorithms

Selection functions enable Evolutionary Algorithms (EAs) to apply selection pressure to a population of individuals, by regulating the probability that an individual\u27s genes survive, typically based on fitness. Various conventional fitness based selection functions exist, each providing a unique method of selecting individuals based on their fitness, fitness ranking within the population, and/or various other factors. However, the full space of selection algorithms is only limited by max algorithm size, and each possible selection algorithm is optimal for some EA configuration applied to a particular problem class. Therefore, improved performance is likely to be obtained by tuning an EA\u27s selection algorithm to the problem at hand, rather than employing a conventional selection function. This thesis details an investigation of the extent to which performance can be improved by tuning the selection algorithm. We do this by employing a Hyper-heuristic to explore the space of algorithms which determine the methods used to select individuals from the population. We show, with both a conventional EA and a Covariance Matrix Adaptation Evolutionary Strategy, the increase in performance obtained with a tuned selection algorithm, versus conventional selection functions. Specifically, we measure performance on instances from several benchmark problem classes, including separate testing instances to show generalization of the improved performance. This thesis consists of work that was presented at the Genetic and Evolutionary Computation Conference (GECCO) in 2018, as well as work that will be submitted to GECCO in 2019 --Abstract, page iii

Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the `Rush to Heuristics'

In the power and energy systems area, a progressive increase of literature contributions that contain applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods that are based on weak comparisons. This ‘rush to heuristics’ does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems and aims at providing a comprehensive view of the main issues that concern the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls that are found in literature contributions are identified, and specific guidelines are provided regarding how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde

Evolutionary methods for the design of dispatching rules for complex and dynamic scheduling problems

Three methods, based on Evolutionary Algorithms (EAs), to support and automate the design of dispatching rules for complex and dynamic scheduling problems are proposed in this thesis. The first method employs an EA to search for problem instances on which a given dispatching rule performs badly. These instances can then be analysed to reveal weaknesses of the tested rule, thereby providing guidelines for the design of a better rule. The other two methods are hyper-heuristics, which employ an EA directly to generate effective dispatching rules. In particular, one hyper-heuristic is based on a specific type of EA, called Genetic Programming (GP), and generates a single rule from basic job and machine attributes, while the other generates a set of work centre-specific rules by selecting a (potentially) different rule for each work centre from a number of existing rules. Each of the three methods is applied to some complex and dynamic scheduling problem(s), and the resulting dispatching rules are tested against benchmark rules from the literature. In each case, the benchmark rules are shown to be outperformed by a rule (set) that results from the application of the respective method, which demonstrates the effectiveness of the proposed methods