Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of algorithms for symbolic regression have been based on evolutionary algorithms. However, there has been a recent surge of new proposals that instead utilize approaches such as enumeration algorithms, mixed linear integer programming, neural networks, and Bayesian optimization. In order to assess how well these new approaches behave on a set of common challenges often faced in real-world data, we hosted a competition at the 2022 Genetic and Evolutionary Computation Conference consisting of different synthetic and real-world datasets which were blind to entrants. For the real-world track, we assessed interpretability in a realistic way by using a domain expert to judge the trustworthiness of candidate models.We present an in-depth analysis of the results obtained in this competition, discuss current challenges of symbolic regression algorithms and highlight possible improvements for future competitions.

In this paper, we try to improve exploration in Blackbox methods, particularly Evolution strategies (ES), when applied to Reinforcement Learning (RL) problems where intermediate waypoints/subgoals are available. Since Evolutionary strategies are highly parallelizable, instead of extracting just a scalar cumulative reward, we use the state-action pairs from the trajectories obtained during rollouts/evaluations, to learn the dynamics of the agent. The learnt dynamics are then used in the optimization procedure to speed-up training. Lastly, we show how our proposed approach is universally applicable by presenting results from experiments conducted on Carla driving and UR5 robotic arm simulators.

A large challenge in Artificial Intelligence (AI) is training control agents that can properly adapt to variable environments. Environments in which the conditions change can cause issues for agents trying to operate in them. Building algorithms that can train agents to operate in these environments and properly deal with the changing conditions is therefore important. NeuroEvolution of Augmenting Topologies (NEAT) was a novel Genetic Algorithm (GA) when it was created, but has fallen aside with newer GAs outperforming it. This paper furthers the research on this subject by implementing various versions of improved NEAT in a variable environment to determine if NEAT can perform well in these environments. The improvements included, in every combination, are: recurrent connections, automatic feature selection, and increasing population size. The recurrent connections improvement performed extremely well. The automatic feature selection improvement was found to be detrimental to performance, and the increasing population size improvement lowered performance a small amount, but decreased computation requirements noticeably.

While evolutionary computation is well suited for automatic discovery in engineering, it can also be used to gain insight into how humans and organizations could perform more effectively. Using a real-world problem of innovation search in organizations as the motivating example, this article first formalizes human creative problem solving as competitive multi-agent search (CMAS). CMAS is different from existing single-agent and team search problems in that the agents interact through knowledge of other agents' searches and through the dynamic changes in the search landscape that result from these searches. The main hypothesis is that evolutionary computation can be used to discover effective strategies for CMAS; this hypothesis is verified in a series of experiments on the NK model, i.e.\ partially correlated and tunably rugged fitness landscapes. Different specialized strategies are evolved for each different competitive environment, and also general strategies that perform well across environments. These strategies are more effective and more complex than hand-designed strategies and a strategy based on traditional tree search. Using a novel spherical visualization of such landscapes, insight is gained about how successful strategies work, e.g.\ by tracking positive changes in the landscape. The article thus provides a possible framework for studying various human creative activities as competitive multi-agent search in the future.

Many state-of-the-art automated machine learning (AutoML) systems use greedy ensemble selection (GES) by Caruana et al. (2004) to ensemble models found during model selection post hoc. Thereby, boosting predictive performance and likely following Auto-Sklearn 1's insight that alternatives, like stacking or gradient-free numerical optimization, overfit. Overfitting in Auto-Sklearn 1 is much more likely than in other AutoML systems because it uses only low-quality validation data for post hoc ensembling. Therefore, we were motivated to analyze whether Auto-Sklearn 1's insight holds true for systems with higher-quality validation data. Consequently, we compared the performance of covariance matrix adaptation evolution strategy (CMA-ES), state-of-the-art gradient-free numerical optimization, to GES on the 71 classification datasets from the AutoML benchmark for AutoGluon. We found that Auto-Sklearn's insight depends on the chosen metric. For the metric ROC AUC, CMA-ES overfits drastically and is outperformed by GES -- statistically significantly for multi-class classification. For the metric balanced accuracy, CMA-ES does not overfit and outperforms GES significantly. Motivated by the successful application of CMA-ES for balanced accuracy, we explored methods to stop CMA-ES from overfitting for ROC AUC. We propose a method to normalize the weights produced by CMA-ES, inspired by GES, that avoids overfitting for CMA-ES and makes CMA-ES perform better than or similar to GES for ROC AUC.

Bayesian Optimization (BO) is a class of surrogate-based, sample-efficient algorithms for optimizing black-box problems with small evaluation budgets. The BO pipeline itself is highly configurable with many different design choices regarding the initial design, surrogate model, and acquisition function (AF). Unfortunately, our understanding of how to select suitable components for a problem at hand is very limited. In this work, we focus on the definition of the AF, whose main purpose is to balance the trade-off between exploring regions with high uncertainty and those with high promise for good solutions. We propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let the exploration-exploitation trade-off self-adjust in a data-driven manner, based on a convergence criterion for BO. On the noise-free black-box BBOB functions of the COCO benchmarking platform, our method exhibits a favorable any-time performance compared to handcrafted baselines and serves as a robust default choice for any problem structure. The suitability of our method also transfers to HPOBench. With SAWEI, we are a step closer to on-the-fly, data-driven, and robust BO designs that automatically adjust their sampling behavior to the problem at hand.

Differential privacy (DP), as a promising privacy-preserving model, has attracted great interest from researchers in recent years. Currently, the study on combination of machine learning and DP is vibrant. In contrast, another widely used artificial intelligence technique, the swarm intelligence (SI) algorithm, has received little attention in the context of DP even though it also triggers privacy concerns. For this reason, this paper attempts to combine DP and SI for the first time, and proposes a general differentially private swarm intelligence algorithm framework (DPSIAF). Based on the exponential mechanism, this framework can easily develop existing SI algorithms into the private versions. As examples, we apply the proposed DPSIAF to four popular SI algorithms, and corresponding analyses demonstrate its effectiveness. More interestingly, the experimental results show that, for our private algorithms, their performance is not strictly affected by the privacy budget, and one of the private algorithms even owns better performance than its non-private version in some cases. These findings are different from the conventional cognition, which indicates the uniqueness of SI with DP. Our study may provide a new perspective on DP, and promote the synergy between metaheuristic optimization community and privacy computing community.

Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizational problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples -- Burgers equation, wave equation, and Korteweg - de Vries equation.

We provide partial implementations of von Neumann's universal constructor and universal copier, starting out with three types of simple building blocks using minimal assumptions. Using the same principles, we also construct Turing machines. Combining both, we arrive at a proposal for a self-replicating Turing machine. Our construction allows for mutations if desired, and we give a simple description language.

For a robot to be both autonomous and collaborative requires the ability to adapt its movement to a variety of external stimuli, whether these come from humans or other robots. Typically, legged robots have oscillation periods explicitly defined as a control parameter, limiting the adaptability of walking gaits. Here we demonstrate a virtual quadruped robot employing a bio-inspired central pattern generator (CPG) that can spontaneously synchronize its movement to a range of rhythmic stimuli. Multi-objective evolutionary algorithms were used to optimize the variation of movement speed and direction as a function of the brain stem drive and the center of mass control respectively. This was followed by optimization of an additional layer of neurons that filters fluctuating inputs. As a result, a range of CPGs were able to adjust their gait pattern and/or frequency to match the input period. We show how this can be used to facilitate coordinated movement despite differences in morphology, as well as to learn new movement patterns.