A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

New Evolutionary Theory Via Simulation

Simulation modelling is very common in evolutionary approaches to economics, strategy, and technological innovation. A well-established simulation framework is the NK model of fitness landscapes, which is particularly useful for modelling the processes of technological adaptation, whose difficulty is reflected into how a fitness landscape behaves as a function of the number of components and internal interdependencies of a technology. However, classical NK models become problematic when modelling different types of processes, such as technological exaptation, unless a broader family of NK models is considered. After reviewing the classical NK model, this chapter explores the potential of ‘generalized’ NK landscapes, followed by a review of other important simulation frameworks in evolutionary theory, such as holey landscapes, quantum-like approaches, and history-friendly models.

Analysis of statistical correlations between properties of adaptive walks in fitness landscapes

The fitness landscape metaphor has been central in our way of thinking about adaptation. In this scenario, adaptive walks are idealized dynamics that mimic the uphill movement of an evolving population towards a fitness peak of the landscape. Recent works in experimental evolution have demonstrated that the constraints imposed by epistasis are responsible for reducing the number of accessible mutational pathways towards fitness peaks. Here, we exhaustively analyse the statistical properties of adaptive walks for two empirical fitness landscapes and theoretical NK landscapes. Some general conclusions can be drawn from our simulation study. Regardless of the dynamics, we observe that the shortest paths are more regularly used. Although the accessibility of a given fitness peak is reasonably correlated to the number of monotonic pathways towards it, the two quantities are not exactly proportional. A negative correlation between predictability and mean path divergence is established, and so the decrease of the number of effective mutational pathways ensures the convergence of the attraction basin of fitness peaks. On the other hand, other features are not conserved among fitness landscapes, such as the relationship between accessibility and predictability.

The MODES Toolbox: Measurements of Open-Ended Dynamics in Evolving Systems

Building more open-ended evolutionary systems can simultaneously advance our understanding of biology, artificial life, and evolutionary computation. In order to do so, however, we need a way to determine when we are moving closer to this goal. We propose a set of metrics that allow us to measure a system's ability to produce commonly-agreed-upon hallmarks of open-ended evolution: change potential, novelty potential, complexity potential, and ecological potential. Our goal is to make these metrics easy to incorporate into a system, and comparable across systems so that we can make coherent progress as a field. To this end, we provide detailed algorithms (including C++ implementations) for these metrics that should be easy to incorporate into existing artificial life systems. Furthermore, we expect this toolbox to continue to grow as researchers implement these metrics in new languages and as the community reaches consensus about additional hallmarks of open-ended evolution. For example, we would welcome a measurement of a system's potential to produce major transitions in individuality. To confirm that our metrics accurately measure the hallmarks we are interested in, we test them on two very different experimental systems: NK landscapes and the Avida digital evolution platform. We find that our observed results are consistent with our prior knowledge about these systems, suggesting that our proposed metrics are effective and should generalize to other systems.

The MODES toolbox: Measurements of Open-ended Dynamics in Evolving Systems

Building more open-ended evolutionary systems can simultaneously advance our understanding of biology, artificial life, and evolutionary computation. In order to do so, however, we need a way to determine when we are moving closer to this goal. We propose a set of metrics that allow us to measure a system's ability to produce commonly-agreed-upon hallmarks of open-ended evolution: change potential, novelty potential, complexity potential, and ecological potential. Our goal is to make these metrics easy to incorporate into a system, and comparable across systems so that we can make coherent progress as a field. To this end, we provide detailed algorithms (including C++ implementations) for these metrics that should be easy to incorporate into existing artificial life systems. Furthermore, we expect this toolbox to continue to grow as researchers implement these metrics in new languages and as the community reaches consensus about additional hallmarks of open-ended evolution. For example, we would welcome a measurement of a system's potential to produce major transitions in individuality. To confirm that our metrics accurately measure the hallmarks we are interested in, we test them on two very different experimental systems: NK Landscapes and the Avida Digital Evolution Platform. We find that our observed results are consistent with our prior knowledge about these systems, suggesting that our proposed metrics are effective and should generalize to other systems.

The MODES toolbox: Measurements of Open-ended Dynamics in Evolving Systems

Building more open-ended evolutionary systems can simultaneously advance our understanding of biology, artificial life, and evolutionary computation. In order to do so, however, we need a way to determine when we are moving closer to this goal. We propose a set of metrics that allow us to measure a system's ability to produce commonly-agreed-upon hallmarks of open-ended evolution: change potential, novelty potential, complexity potential, and ecological potential. Our goal is to make these metrics easy to incorporate into a system, and comparable across systems so that we can make coherent progress as a field. To this end, we provide detailed algorithms (including C++ implementations) for these metrics that should be easy to incorporate into existing artificial life systems. Furthermore, we expect this toolbox to continue to grow as researchers implement these metrics in new languages and as the community reaches consensus about additional hallmarks of open-ended evolution. For example, we would welcome a measurement of a system's potential to produce major transitions in individuality. To confirm that our metrics accurately measure the hallmarks we are interested in, we test them on two very different experimental systems: NK Landscapes and the Avida Digital Evolution Platform. We find that our observed results are consistent with our prior knowledge about these systems, suggesting that our proposed metrics are effective and should generalize to other systems.