While crossover is a critical and often indispensable component in other forms of Genetic Programming, such as Linear- and Tree-based, it has consistently been claimed that it deteriorates search performance in CGP. As a result, a mutation-alone $(1+λ)$ evolutionary strategy has become the canonical approach for CGP. Although several operators have been developed that demonstrate an increased performance over the canonical method, a general solution to the problem is still lacking. In this paper, we compare basic crossover methods, namely one-point and uniform, to variants in which nodes are ``preserved,'' including the subgraph crossover developed by Roman Kalkreuth, the difference being that when ``node preservation'' is active, crossover is not allowed to break apart instructions. We also compare a node mutation operator to the traditional point mutation; the former simply replaces an entire node with a new one. We find that node preservation in both mutation and crossover improves search using symbolic regression benchmark problems, moving the field towards a general solution to CGP crossover.

While large language models (LLMs) are increasingly used as automated heuristic designers for vehicle routing problems (VRPs), current state-of-the-art methods predominantly rely on prompting massive, general-purpose models like GPT-4. This work challenges that paradigm by demonstrating that a smaller, specialized LLM, when meticulously fine-tuned, can generate components that surpass expert-crafted heuristics within advanced solvers. We propose RFTHGS, a novel Reinforcement learning (RL) framework for Fine-Tuning a small LLM to generate high-performance crossover operators for the Hybrid Genetic Search (HGS) solver, applied to the Capacitated VRP (CVRP). Our method employs a multi-tiered, curriculum-based reward function that progressively guides the LLM to master generating first compilable, then executable, and finally, superior-performing operators that exceed human expert designs. This is coupled with an operator caching mechanism that discourages plagiarism and promotes diversity during training. Comprehensive experiments show that our fine-tuned LLM produces crossover operators which significantly outperform the expert-designed ones in HGS. The performance advantage remains consistent, generalizing from small-scale instances to large-scale problems with up to 1000 nodes. Furthermore, RFTHGS exceeds the performance of leading neuro-combinatorial baselines, prompt-based methods, and commercial LLMs such as GPT-4o and GPT-4o-mini.

The rapid advancement of Large Language Models (LLMs) poses a significant challenge to existing mathematical reasoning benchmarks. However, these benchmarks tend to become easier over time as LLMs can learn from the published benchmarks. This limitation hinder the precise evaluation of the true capabilities of SOTA models. To address this challenge, this paper introduces EvolMathEval, an automated mathematical benchmark generation and evolution framework based on evolutionary testing. Experimental results demonstrate that EvolMathEval can not only generate a large volume of high-difficulty problems through continuous self-iteration, but it can also significantly enhance the complexity of public datasets like GSM8K through evolution, reducing model accuracy by an average of 48\%. Deeper investigation reveals that when solving these evolved problems, LLMs tend to bypass complex multi-step logical reasoning by relying on simplistic and fuzzy conditions, consequently leading to incorrect solutions. We define this phenomenon as the ``Pseudo Aha Moment", which we find accounts for 77\% to 100\% of errors on targeted problems. Code and resources are available at: https://anonymous.4open.science/r/EvolMathEval

This study introduces an innovative crossover operator named Particle Swarm Optimization-inspired Crossover (PSOX), which is specifically developed for real-coded genetic algorithms. Departing from conventional crossover approaches that only exchange information between individuals within the same generation, PSOX uniquely incorporates guidance from both the current global best solution and historical optimal solutions across multiple generations. This novel mechanism enables the algorithm to maintain population diversity while simultaneously accelerating convergence toward promising regions of the search space. The effectiveness of PSOX is rigorously evaluated through comprehensive experiments on 15 benchmark test functions with diverse characteristics, including unimodal, multimodal, and highly complex landscapes. Comparative analysis against five state-of-the-art crossover operators reveals that PSOX consistently delivers superior performance in terms of solution accuracy, algorithmic stability, and convergence speed, especially when combined with an appropriate mutation strategy. Furthermore, the study provides an in-depth investigation of how different mutation rates influence PSOX's performance, yielding practical guidelines for parameter tuning when addressing optimization problems with varying landscape properties.

Recently, Meta-Black-Box-Optimization (MetaBBO) methods significantly enhance the performance of traditional black-box optimizers through meta-learning flexible and generalizable meta-level policies that excel in dynamic algorithm configuration (DAC) tasks within the low-level optimization, reducing the expertise required to adapt optimizers for novel optimization tasks. Though promising, existing MetaBBO methods heavily rely on human-crafted feature extraction approach to secure learning effectiveness. To address this issue, this paper introduces a novel MetaBBO method that supports automated feature learning during the meta-learning process, termed as RLDE-AFL, which integrates a learnable feature extraction module into a reinforcement learning-based DE method to learn both the feature encoding and meta-level policy. Specifically, we design an attention-based neural network with mantissa-exponent based embedding to transform the solution populations and corresponding objective values during the low-level optimization into expressive landscape features. We further incorporate a comprehensive algorithm configuration space including diverse DE operators into a reinforcement learning-aided DAC paradigm to unleash the behavior diversity and performance of the proposed RLDE-AFL. Extensive benchmark results show that co-training the proposed feature learning module and DAC policy contributes to the superior optimization performance of RLDE-AFL to several advanced DE methods and recent MetaBBO baselines over both synthetic and realistic BBO scenarios. The source codes of RLDE-AFL are available at https://github.com/GMC-DRL/RLDE-AFL.

Deep Neural Crossover leverages the capabilities of deep reinforcement learning and an encoder-decoder architecture to select offspring genes. BERT mutation masks multiple gp-tree nodes and then tries to replace these masks with nodes that will most likely improve the individual's fitness. We show the efficacy of both operators through experimentation.

There are many combinatorial optimization problems whose solutions are best represented by permutations. The classic traveling salesperson seeks an optimal ordering over a set of cities. Scheduling problems often seek optimal orderings of tasks or activities. Although some evolutionary approaches to such problems utilize the bit strings of a genetic algorithm, it is more common to directly represent solutions with permutations. Evolving permutations directly requires specialized evolutionary operators. Over the years, many crossover and mutation operators have been developed for solving permutation problems with evolutionary algorithms. In this paper, we survey the breadth of evolutionary operators for permutations. We implemented all of these in Chips-n-Salsa, an open source Java library for evolutionary computation. Finally, we empirically analyze the crossover operators on artificial fitness landscapes isolating different permutation features.

Evolutionary algorithms (EAs) have emerged as a powerful framework for optimization, especially for black-box optimization. This paper first focuses on automated EA: Automated EA exploits structure in the problem of interest to automatically generate update rules (optimization strategies) for generating and selecting potential solutions so that it can move a random population near the optimal solution. However, current EAs cannot achieve this goal due to the poor representation of the optimization strategy and the weak interaction between the optimization strategy and the target task. We design a deep evolutionary convolution network (DECN) to realize the move from hand-designed EAs to automated EAs without manual interventions. DECN has high adaptability to the target task and can obtain better solutions with less computational cost. DECN is also able to effectively utilize the low-fidelity information of the target task to form an efficient optimization strategy. The experiments on nine synthetics and two real-world cases show the advantages of learned optimization strategies over the state-of-the-art human-designed and meta-learning EA baselines. In addition, due to the tensorization of the operations, DECN is friendly to the acceleration provided by GPUs and runs 102 times faster than EA.

The training of generative adversarial networks (GANs) is usually vulnerable to mode collapse and vanishing gradients. The evolutionary generative adversarial network (E-GAN) attempts to alleviate these issues by optimizing the learning strategy with multiple loss functions. It uses a learning-based evolutionary framework, which develops new mutation operators specifically for general deep neural networks. However, the evaluation mechanism in the fitness function of E-GAN cannot truly reflect the adaptability of individuals to their environment, leading to an inaccurate assessment of the diversity of individuals. Moreover, the evolution step of E-GAN only contains mutation operators without considering the crossover operator jointly, isolating the superior characteristics among individuals. To address these issues, we propose an improved E-GAN framework called IE-GAN, which introduces a new fitness function and a generic crossover operator. In particular, the proposed fitness function, from an objective perspective, can model the evolutionary process of individuals more accurately. The crossover operator, which has been commonly adopted in evolutionary algorithms, can enable offspring to imitate the superior gene expression of their parents through knowledge distillation. Experiments on various datasets demonstrate the effectiveness of our proposed IE-GAN in terms of the quality of the generated samples and time efficiency.

Extensive research has been conducted, over recent years, on various ways of enhancing heuristic search for combinatorial optimization problems with machine learning algorithms. In this study, we investigate the use of predictions from graph neural networks (GNNs) in the form of heatmaps to improve the Hybrid Genetic Search (HGS), a state-of-the-art algorithm for the Capacitated Vehicle Routing Problem (CVRP). The crossover and local-search components of HGS are instrumental in finding improved solutions, yet these components essentially rely on simple greedy or random choices. It seems intuitive to attempt to incorporate additional knowledge at these levels. Throughout a vast experimental campaign on more than 10,000 problem instances, we show that exploiting more sophisticated strategies using measures of node relatedness (heatmaps, or simply distance) within these algorithmic components can significantly enhance performance. However, contrary to initial expectations, we also observed that heatmaps did not present significant advantages over simpler distance measures for these purposes. Therefore, we faced a common -- though rarely documented -- situation of overkill: GNNs can indeed improve performance on an important optimization task, but an ablation analysis demonstrated that simpler alternatives perform equally well.