In optimization and machine learning, the divide between discrete and continuous problems and methods is deep and persistent. We attempt to remove this distinction by training neural network autoencoders that embed discrete candidate solutions in continuous latent spaces. This allows us to take advantage of state-of-the-art continuous optimization methods for solving discrete optimization problems, and mitigates certain challenges in discrete optimization, such as design of bias-free search operators. In the experimental part, we consider program synthesis as the special case of combinatorial optimization. We train an autoencoder network on a large sample of programs in a problem-agnostic, unsupervised manner, and then use it with an evolutionary continuous optimization algorithm (CMA-ES) to map the points from the latent space to programs. We propose also a variant in which semantically similar programs are more likely to have similar embeddings. Assessment on a range of benchmarks in two domains indicates the viability of this approach and the usefulness of involving program semantics.

Employee scheduling problems are of critical importance to large businesses. These problems are hard to solve due to large numbers of conflicting constraints. While many approaches address a subset of these constraints, there is no single approach for simultaneously addressing all of them. We hybridise 'Evolutionary Ruin & Stochastic Recreate' and 'Variable Neighbourhood Search' metaheuristics to solve a real world instance of the employee scheduling problem to near optimality. We compare this with Simulated Annealing, exploring the algorithm configuration space using the irace software package to ensure fair comparison. The hybrid algorithm generates schedules that reduce unmet demand by over 28% compared to the baseline. All data used, where possible, is either directly from the real world engineer scheduling operation of around 25,000 employees, or synthesised from a related distribution where data is unavailable.

Metaheuristics are an effective and diverse class of optimization algorithms: a means of obtaining solutions of acceptable quality for otherwise intractable problems. The selection, construction, and configuration of a metaheuristic for a given problem has historically been a manually intensive process based on experience, experimentation, and reasoning by metaphor. More recently, there has been interest in automating the process of algorithm configuration. In this article, we identify shared state as an inhibitor of progress for such automation. To solve this problem, we introduce the Automated Open-Closed Principle (AOCP), which stipulates design requirements for unintrusive reuse of algorithm frameworks and automated assembly of algorithms from an extensible palette of components. We demonstrate how the AOCP enables a greater degree of automation than previously possible via an example implementation.

In 2016-2018 at the IEEE Conference on Computational Intelligence in Games, the authors of this paper ran a competition for agents that can play classic text-based adventure games. This competition fills a gap in existing game artificial intelligence (AI) competitions that have typically focused on traditional card/board games or modern video games with graphical interfaces. By providing a platform for evaluating agents in textbased adventures, the competition provides a novel benchmark for game AI with unique challenges for natural language understanding and generation. This paper summarizes the three competitions ran in 2016-2018 (including details of open-source implementations of both the competition framework and our competitors) and presents the results of an improved evaluation of these competitors across 20 games.

There is increasing impetus towards 'Industry 4.0', a recently proposed roadmap for process automation across a broad spectrum of manufacturing industries. The proposed approach uses Evolutionary Computation to optimise real-world metrics. Features of the proposed approach are that it is generic (i.e. applicable across multiple problem domains) and decentralised, i.e. hosted remotely from the physical system upon which it operates. In particular, by virtue of being serverless, the project goal is that computation can be performed 'just in time' in a scalable fashion. We describe a case study for value-based optimisation, applicable to a wide range of manufacturing processes. In particular, value is expressed in terms of Overall Equipment Effectiveness (OEE), grounded in monetary units. We propose a novel online stopping condition that takes into account the predicted utility of further computational effort. We apply this method to scheduling problems in the (max, +) algebra, and compare against a baseline stopping criterion with no prediction mechanism. Near optimal profit is obtained by the proposed approach, across multiple problem instances.

Genetic programming is an effective technique for inductive synthesis of programs from tests, i.e. training examples of desired input-output behavior. Programs synthesized in this way are not guaranteed to generalize beyond the training set, which is unacceptable in many applications. We present Counterexample-Driven Genetic Programming (CDGP) that employs evolutionary search to synthesize provably correct programs from formal specifications. CDGP employs a Satisfiability Modulo Theories (SMT) solver to formally verify programs in the evaluation phase. A failed verification produces counterexamples that are in turn used to calculate fitness and thereby drive the search process. When compared with a range of approaches on a suite of state-of-the-art specification-based synthesis benchmarks, CDGP systematically outperforms them, typically synthesizing correct programs faster and using fewer tests.

Conventional genetic programming (GP) can guarantee only that synthesized programs pass tests given by the provided input-output examples. The alternative to such a test-based approach is synthesizing programs by formal specification, typically realized with exact, nonheuristic algorithms. In this article, we build on our earlier study on Counterexample-Based Genetic Programming (CDGP), an evolutionary heuristic that synthesizes programs from formal specifications. The candidate programs in CDGP undergo formal verification with a Satisfiability Modulo Theory (SMT) solver, which results in counterexamples that are subsequently turned into tests and used to calculate fitness. The original CDGP is extended here with a fitness threshold parameter that decides which programs should be verified, a more rigorous mechanism for turning counterexamples into tests, and other conceptual and technical improvements. We apply it to 24 benchmarks representing two domains: the linear integer arithmetic (LIA) and the string manipulation (SLIA) problems, showing that CDGP can reliably synthesize provably correct programs in both domains. We also confront it with two state-of-the art exact program synthesis methods and demonstrate that CDGP effectively trades longer synthesis time for smaller program size.

Search Based Software Engineering techniques are emerging as important tools for software maintenance. Foremost among these is Genetic Improvement, which has historically applied the stochastic techniques of Genetic Programming to optimize pre-existing program code. Previous work in this area has not generally preserved program semantics and this article describes an alternative to the traditional mutation operators used, employing deterministic proof search in the sequent calculus to yield semantics-preserving transformations on algebraic data types. Two case studies are described, both of which are applicable to the recently-introduced 'grow and graft' technique of Genetic Improvement: the first extends the expressiveness of the 'grafting' phase and the second transforms the representation of a list data type to yield an asymptotic efficiency improvement.

Combinatorial optimization problems such as the Travelling Salesman Problem, Quadratic Assignment Problem and Sliding-Tile Puzzle have structure that can be described algebraically and exploited to improve search quality. In particular, heuristic functions for these problems can be described in terms of symmetric groups. By employing techniques from the emerging field of algebraic machine learning, we investigate the harmonic decomposition of popular sliding-tile puzzle heuristics via the extension of the Fourier Transform to noncommutative groups. The Fourier-space representation for these heuristics can then be manipulated by multiplication with a real-valued weight vector. By performing such a reweighting and then taking the inverse transform, we obtain a `filtered' version of the original heuristic. Taking the 8-puzzle as a case study, we demonstrate that heuristic accuracy is related to harmonic spectral density and further that the heuristic functions given by the Hamming and Manhattan distance metrics on puzzle state can be transformed into significantly better heuristics by performing a search in the weight space.

Genetic programming is an effective technique for inductive synthesis of programs from training examples of desired input-output behavior (tests). Programs synthesized in this way are not guaranteed to generalize beyond the training set, which is unacceptable in many applications. We present Counterexample-Driven Genetic Programming (CDGP) that employs evolutionary search to synthesize provably correct programs from formal specifications. CDGP employs a Satisfiability Modulo Theories (SMT) solver to formally verify programs in the evaluation phase. A failed verification produces counterexamples that are in turn used to calculate fitness and so drive the search process. When compared against a range of approaches on a suite of state-of-the-art specification-based synthesis benchmarks, CDGP systematically outperforms them, typically synthesizing correct programs faster and using fewer tests.

Online progress in search and optimization is often hindered by neutrality in the fitness landscape, when many genotypes map to the same fitness value. We propose a method for imposing a gradient on the fitness function of a metaheuristic (in this case, Genetic Programming) via a metric (Minimum Description Length) induced from patterns detected in the trajectory of program execution. These patterns are induced via a decision tree classifier. We apply this method to a range of integer and boolean-valued problems, significantly outperforming the standard approach. The method is conceptually straightforward and applicable to virtually any metaheuristic that can be appropriately instrumented.