Inspired by Fisher's geometric approach to study beneficial mutations, we analyse probabilities of beneficial mutation and crossover recombination of strings in a general Hamming space with arbitrary finite alphabet. Mutations and recombinations that reduce the distance to an optimum are considered as beneficial. Geometric and combinatorial analysis is used to derive closed-form expressions for transition probabilities between spheres around an optimum giving a complete description of Markov evolution of distances from an optimum over multiple generations. This paves the way for optimization of parameters of mutation and recombination operators. Here we derive optimality conditions for mutation and recombination radii maximizing the probabilities of mutation and crossover into the optimum. The analysis highlights important differences between these evolutionary operators. While mutation can potentially reach any part of the search space, the probability of beneficial mutation decreases with distance to an optimum, and the optimal mutation radius or rate should also decrease resulting in a slow-down of evolution near the optimum. Crossover recombination, on the other hand, acts in a subspace of the search space defined by the current population of strings. However, probabilities of beneficial and deleterious crossover are balanced, and their characteristics, such as variance, are translation invariant in a Hamming space, suggesting that recombination may complement mutation and boost the rate of evolution near the optimum.

Evolutionary robot systems are usually affected by the properties of the environment indirectly through selection. In this paper, we present and investigate a system where the environment also has a direct effect: through regulation. We propose a novel robot encoding method where a genotype encodes multiple possible phenotypes, and the incarnation of a robot depends on the environmental conditions taking place in a determined moment of its life. This means that the morphology, controller, and behavior of a robot can change according to the environment. Importantly, this process of development can happen at any moment of a robot lifetime, according to its experienced environmental stimuli. We provide an empirical proof-of-concept, and the analysis of the experimental results shows that Plasticoding improves adaptation (task performance) while leading to different evolved morphologies, controllers, and behaviour.

One of the common artificial intelligence applications in electronic games consists of making an artificial agent learn how to execute some determined task successfully in a game environment. One way to perform this task is through machine learning algorithms capable of learning the sequence of actions required to win in a given game environment. There are several supervised learning techniques able to learn the correct answer for a problem through examples. However, when learning how to play electronic games, the correct answer might only be known by the end of the game, after all the actions were already taken. Thus, not being possible to measure the accuracy of each individual action to be taken at each time step. A way for dealing with this problem is through Neuroevolution, a method which trains Artificial Neural Networks using evolutionary algorithms. In this article, we introduce a framework for testing optimization algorithms with artificial agent controllers in electronic games, called EvoMan, which is inspired in the action-platformer game Mega Man II. The environment can be configured to run in different experiment modes, as single evolution, coevolution and others. To demonstrate some challenges regarding the proposed platform, as initial experiments we applied Neuroevolution using Genetic Algorithms and the NEAT algorithm, in the context of competitively coevolving two distinct agents in this game.

Despite the recent advancements in artificial intelligence technologies have shown great potential in improving transport efficiency and safety, autonomous vehicles(AVs) still face great challenge of driving in time-varying traffic flow, especially in dense and interactive situations. Meanwhile, human have free wills and usually do not make the same decisions even situate in the exactly same scenarios, leading to the data-driven methods suffer from poor migratability and high search cost problems, decreasing the efficiency and effectiveness of the behavior policy. In this research, we propose a safety-first human-like decision-making framework(SF-HLDM) for AVs to drive safely, comfortably, and social compatiblely in effiency. The framework integrates a hierarchical progressive framework, which combines a spatial-temporal attention (S-TA) mechanism for other road users' intention inference, a social compliance estimation module for behavior regulation, and a Deep Evolutionary Reinforcement Learning(DERL) model for expanding the search space efficiently and effectively to make avoidance of falling into the local optimal trap and reduce the risk of overfitting, thus make human-like decisions with interpretability and flexibility. The SF-HLDM framework enables autonomous driving AI agents dynamically adjusts decision parameters to maintain safety margins and adhering to contextually appropriate driving behaviors at the same time.

Differential Evolution (DE) is a widely used evolutionary algorithm for black-box optimization problems. However, in modern DE implementations, a major challenge lies in the limited population diversity caused by the fixed population size enforced by the generational replacement. Population size is a critical control parameter that significantly affects DE performance. Larger populations inherently contain a more diverse set of individuals, thereby facilitating broader exploration of the search space. Conversely, when the maximum evaluation budgets is constrained, smaller populations focusing on a limited number of promising candidates may be more suitable. Many state-of-the-art DE variants incorporate an archive mechanism, in which a subset of discarded individuals is preserved in an archive during generation replacement and reused in mutation operations. However, maintaining what is essentially a secondary population via an archive introduces additional design considerations, such as policies for insertion, deletion, and appropriate sizing. To address these limitations, we propose a novel DE framework called Unbounded Differential Evolution (UDE), which adds all generated candidates to the population without discarding any individual based on fitness. Unlike conventional DE, which removes inferior individuals during generational replacement, UDE eliminates replacement altogether, along with the associated complexities of archive management and dynamic population sizing. UDE represents a fundamentally new approach to DE, relying solely on selection mechanisms and enabling a more straightforward yet powerful search algorithm.

This paper presents an evolvable conditional diffusion method such that black-box, non-differentiable multi-physics models, as are common in domains like computational fluid dynamics and electromagnetics, can be effectively used for guiding the generative process to facilitate autonomous scientific discovery. We formulate the guidance as an optimization problem where one optimizes for a desired fitness function through updates to the descriptive statistic for the denois-ing distribution, and derive an evolution-guided approach from first principles through the lens of probabilistic evolution. Interestingly, the final derived update algorithm is analogous to the update as per common gradient-based guided diffusion models, but without ever having to compute any derivatives. We validate our proposed evolvable diffusion algorithm in two AI for Science scenarios: the automated design of fluidic topology and meta-surface. Results demonstrate that this method effectively generates designs that better satisfy specific optimization objectives without reliance on differentiable proxies, providing an effective means of guidance-based diffusion that can capitalize on the wealth of black-box, non-differentiable multi-physics numerical models common across Science.

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific problems or optimizing critical pieces of computational infrastructure. AlphaEvolve orchestrates an autonomous pipeline of LLMs, whose task is to improve an algorithm by making direct changes to the code. Using an evolutionary approach, continuously receiving feedback from one or more evaluators, AlphaEvolve iteratively improves the algorithm, potentially leading to new scientific and practical discoveries. We demonstrate the broad applicability of this approach by applying it to a number of important computational problems. When applied to optimizing critical components of large-scale computational stacks at Google, AlphaEvolve developed a more efficient scheduling algorithm for data centers, found a functionally equivalent simplification in the circuit design of hardware accelerators, and accelerated the training of the LLM underpinning AlphaEvolve itself. Furthermore, AlphaEvolve discovered novel, provably correct algorithms that surpass state-of-the-art solutions on a spectrum of problems in mathematics and computer science, significantly expanding the scope of prior automated discovery methods (Romera-Paredes et al., 2023). Notably, AlphaEvolve developed a search algorithm that found a procedure to multiply two $4 \times 4$ complex-valued matrices using $48$ scalar multiplications; offering the first improvement, after 56 years, over Strassen's algorithm in this setting. We believe AlphaEvolve and coding agents like it can have a significant impact in improving solutions of problems across many areas of science and computation.

The Unit Commitment (UC) problem is a classic challenge in the optimal scheduling of power systems. Years of research and practice have shown that formulating reasonable unit commitment plans can significantly improve the economic efficiency of power systems' operations. In recent years, with the introduction of technologies such as machine learning and the Lagrangian relaxation method, the solution methods for the UC problem have become increasingly diversified, but still face challenges in terms of accuracy and robustness. This paper proposes a Function Space Search (FunSearch) method based on large language models. This method combines pre-trained large language models and evaluators to creatively generate solutions through the program search and evolution process while ensuring their rationality. In simulation experiments, a case of unit commitment with \(10\) units is used mainly. Compared to the genetic algorithm, the results show that FunSearch performs better in terms of sampling time, evaluation time, and total operating cost of the system, demonstrating its great potential as an effective tool for solving the UC problem.

This paper introduces Spectral Fault Receptive Fields (SFRFs), a biologically inspired technique for degradation state assessment in bearing fault diagnosis and remaining useful life (RUL) estimation. Drawing on the center-surround organization of retinal ganglion cell receptive fields, we propose a frequency-domain feature extraction algorithm that enhances the detection of fault signatures in vibration signals. SFRFs are designed as antagonistic spectral filters centered on characteristic fault frequencies, with inhibitory surrounds that enable robust characterization of incipient faults under variable operating conditions. A multi-objective evolutionary optimization strategy based on NSGA-II algorithm is employed to tune the receptive field parameters by simultaneously minimizing RUL prediction error, maximizing feature monotonicity, and promoting smooth degradation trajectories. The method is demonstrated on the XJTU-SY bearing run-to-failure dataset, confirming its suitability for constructing condition indicators in health monitoring applications. Key contributions include: (i) the introduction of SFRFs, inspired by the biology of vision in the primate retina; (ii) an evolutionary optimization framework guided by condition monitoring and prognosis criteria; and (iii) experimental evidence supporting the detection of early-stage faults and their precursors. Furthermore, we confirm that our diagnosis-informed spectral representation achieves accurate RUL prediction using a bagging regressor. The results highlight the interpretability and principled design of SFRFs, bridging signal processing, biological sensing principles, and data-driven prognostics in rotating machinery.

Adaptive Curriculum Sequencing (ACS) is essential for personalized online learning, yet current approaches struggle to balance complex educational constraints and maintain optimization stability. This paper proposes a Memetic Walrus Optimizer (MWO) that enhances optimization performance through three key innovations: (1) an expert-guided strategy with aging mechanism that improves escape from local optima; (2) an adaptive control signal framework that dynamically balances exploration and exploitation; and (3) a three-tier priority mechanism for generating educationally meaningful sequences. We formulate ACS as a multi-objective optimization problem considering concept coverage, time constraints, and learning style compatibility. Experiments on the OULAD dataset demonstrate MWO's superior performance, achieving 95.3% difficulty progression rate (compared to 87.2% in baseline methods) and significantly better convergence stability (standard deviation of 18.02 versus 28.29-696.97 in competing algorithms). Additional validation on benchmark functions confirms MWO's robust optimization capability across diverse scenarios. The results demonstrate MWO's effectiveness in generating personalized learning sequences while maintaining computational efficiency and solution quality.