Redundant Representations in Evolutionary Computation

Redundanz , Evolutionary programmin

Discovering Representations for Black-box Optimization

The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Variational Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions -- but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinematics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.Comment: Presented at GECCO 2020 -- v2 (Previous title 'Automating Representation Discovery with MAP-Elites'

Unifying a Geometric Framework of Evolutionary Algorithms and Elementary Landscapes Theory

Evolutionary algorithms (EAs) are randomised general-purpose strategies, inspired by natural evolution, often used for finding (near) optimal solutions to problems in combinatorial optimisation. Over the last 50 years, many theoretical approaches in evolutionary computation have been developed to analyse the performance of EAs, design EAs or measure problem difficulty via fitness landscape analysis. An open challenge is to formally explain why a general class of EAs perform better, or worse, than others on a class of combinatorial problems across representations. However, the lack of a general unified theory of EAs and fitness landscapes, across problems and representations, makes it harder to characterise pairs of general classes of EAs and combinatorial problems where good performance can be guaranteed provably. This thesis explores a unification between a geometric framework of EAs and elementary landscapes theory, not tied to a specific representation nor problem, with complementary strengths in the analysis of population-based EAs and combinatorial landscapes. This unification organises around three essential aspects: search space structure induced by crossovers, search behaviour of population-based EAs and structure of fitness landscapes. First, this thesis builds a crossover classification to systematically compare crossovers in the geometric framework and elementary landscapes theory, revealing a shared general subclass of crossovers: geometric recombination P-structures, which covers well-known crossovers. The crossover classification is then extended to a general framework for axiomatically analysing the population behaviour induced by crossover classes on associated EAs. This shows the shared general class of all EAs using geometric recombination P-structures, but no mutation, always do the same abstract form of convex evolutionary search. Finally, this thesis characterises a class of globally convex combinatorial landscapes shared by the geometric framework and elementary landscapes theory: abstract convex elementary landscapes. It is formally explained why geometric recombination P-structure EAs expectedly can outperform random search on abstract convex elementary landscapes related to low-order graph Laplacian eigenvalues. Altogether, this thesis paves a way towards a general unified theory of EAs and combinatorial fitness landscapes

Talking Helps: Evolving Communicating Agents for the Predator-Prey Pursuit Problem

We analyze a general model of multi-agent communication in which all agents communicate simultaneously to a message board. A genetic algorithm is used to evolve multi-agent languages for the predator agents in a version of the predator-prey pursuit problem. We show that the resulting behavior of the communicating multi-agent system is equivalent to that of a Mealy finite state machine whose states are determined by the agents’ usage of the evolved language. Simulations show that the evolution of a communication language improves the performance of the predators. Increasing the language size (and thus increasing the number of possible states in the Mealy machine) improves the performance even further. Furthermore, the evolved communicating predators perform significantly better than all previous work on similar preys. We introduce a method for incrementally increasing the language size which results in an effective coarse-to-fine search that significantly reduces the evolution time required to find a solution. We present some observations on the effects of language size, experimental setup, and prey difficulty on the evolved Mealy machines. In particular, we observe that the start state is often revisited, and incrementally increasing the language size results in smaller Mealy machines. Finally, a simple rule is derived that provides a pessimistic estimate on the minimum language size that should be used for any multi-agent problem

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..

Genetic Algorithm Design for Constrained Optimization

School of Electrical and Computer Engineerin