Evolutionary Computation最新文献

We introduce a population-based approach to solving parameterized graph problems for which the goal is to identify a small set of vertices subject to a feasibility criterion. The idea is to evolve a population of individuals where each individual corresponds to an optimal solution to a subgraph of the original problem. The crossover operation then combines both solutions and subgraphs with the hope to generate an optimal solution for a slightly larger graph. In order to correctly combine solutions and subgraphs, we propose a new crossover operator called generalized allelic crossover which generalizes uniform crossover by associating a probability at each locus depending on the combined alleles of the parents. We prove for graphs with nvertices and medges, the approach solves the k-vertex cover problem in expected time O(4km+m4logn)using a simple RLS-style mutation. This bound can be improved to O(4km+m2nklogn)by using standard mutation constrained to the vertices of the graph. We also prove that a slight modification of the algorithm can be used to find k-coverable subgraphs of arbitrary graphs that are maximal under edge inclusion. We prove that a runtime budget of Ω(2km3log2n)suffices to generate a maximal k-coverable subgraph with high probability. Finally, we empirically show that these subgraphs often retain a number of structural properties of the source graph. This has direct implications for benchmarking, as it allows for the generation of graphs that maintain certain correlation properties while controlling for the optimal cover size.

To address optimization problems that involve expensive evaluations with unknown and heterogeneous costs, cost-aware Bayesian optimization (BO) emerges as a prominent solution in many real-world scenarios. However, as a critical step in developing BO algorithms, the design of efficient cost-aware acquisition functions (AFs) remains a significant challenge. This paper introduces EvolCAF, a novel framework that integrates large language models (LLMs) with evolutionary computation (EC) to automatically design cost-aware AFs. Leveraging the crossover and mutation in the algorithmic space, EvolCAF offers a novel design fashion, significantly reducing the reliance on domain expertise and labor-intensive trial-and-error process in the traditional manual design paradigm. We find the best AF designed by EvolCAF effectively utilizes the available information, including historical data, surrogate models and budget details. It introduces novel ideas not previously explored in the existing literature on acquisition function design, allowing for clear interpretations to provide insights into its behavior and decision-making process. In comparison to the well-known EIpu and EI-cool methods designed by human experts, our approach showcases remarkable efficiency and generalization across various synthetic and real-world tasks.

Special Issue PPSN 2024: Algorithm-selection (AS) methods are essential in order to obtain the best performance from a portfolio of solvers. When considering large sets of instances that either arrive in a stream or in a single batch, there is significant potential to save the function evaluation budget on some instances and reallocate it to others, thereby improving overall performance. We propose an AS pipeline which (1) identifies easy instances which are solved using the single best solver, avoiding the need to run a selector; (2) curtails runs on both easy and hard instances if they become stalled in the search space and/or are predicted to remain in a stalled state thereby saving budget; (3) reallocates budget saved from both previous steps to downstream instances, using an intelligent strategy to predict which instances will benefit most from extra function evaluations. Experiments using the BBOB dataset in two settings (batch and streaming) show that augmenting an AS pipeline with strategies to save and reallocate budget obtains significantly better results in both settings compared to a standard pipeline.

The XCS Classifier System (XCS), the most prominent Learning Classifier System (LCS), originally focused on Reinforcement Learning (RL) problems. Over time, emphasis shifted heavily to supervised learning, with some applications in unsupervised learning. Following rekindled interest in LCSs for RL domains, we intend to capitalise on the close relationship between Q-learning and XCS. Except for Experience Replay, hardly any advances built on Q-learning have been investigated in XCS variants such as XCSF. Recognising this, we introduce three extensions inspired by Q-learning derivates: Target prediction inspired by DQN's target networks to improve the learning stability and double target prediction inspired by Double DQN as well as a Double Q-learning mechanism as countermeasures against overestimation. Addressing these two issues, aims to improve the performance of XCSF and the high variance between runs. We apply them to the Maze Problem, Frozen Lake, and Cart Pole. Our observations indicate mixed results: The Double Q-learning mechanism leads to no improvement. Target and double target prediction can lead to observable and also significantly improved performance and can provide variance reduction. This underscores that improving the RL capabilities of XCSF is non-trivial but indicates that adapting Deep Reinforcement Learning mechanisms for XCSF can be advantageous.

Diversity optimization is the class of optimization problems in which we aim to find a diverse set of good solutions. One of the frequently-used approaches to solve such problems is to use evolutionary algorithms that evolve a desired diverse population. This approach is called evolutionary diversity optimization (EDO). In this paper, we analyze EDO on a three-objective function LOTZk, which is a modification of the two-objective benchmark function (LeadingOnes, TrailingZeros). We prove that the GSEMO computes a set of all Pareto-optimal solutions in O(kn3) expected iterations. We also analyze the runtime of the GSEMOD algorithm (a modification of the GSEMO for diversity optimization) until it finds a population with the best possible diversity for two different diversity measures: the total imbalance and the sorted imbalances vector. For the first measure we show that the GSEMOD optimizes it in O(kn2log⁡(n)) expected iterations (which is asymptotically faster than the upper bound on the runtime until it finds a Pareto-optimal population), and for the second measure we show an upper bound of O(k2n3log⁡(n)) expected iterations. We complement our theoretical analysis with an empirical study, which shows a very similar behavior for both diversity measures. The results of experiments suggest that our bounds for the total imbalance measure are tight, while the bounds for the imbalances vector are too pessimistic.

Designing algorithms for optimization problems, no matter heuristic or meta-heuristic, often relies on manual design and domain expertise, limiting their scalability and adaptability. The integration of Large Language Models (LLMs) and Evolutionary Algorithms (EAs) presents a promising new way to overcome these limitations to make optimization be more automated, where LLMs function as dynamic agents capable of generating, refining, and interpreting optimization strategies, while EAs explore complex searching spaces efficiently through evolutionary operators. Since this synergy enables a more efficient and creative searching process, we first review important developments in this direction, and then summarize an LLM-EA paradigm for automated optimization algorithm design. We conduct an in-depth analysis on innovative methods for four key EA modules, namely, individual representation, selection, variation operators, and fitness evaluation, addressing challenges related to optimization algorithm design, particularly from the perspective of LLM prompts, analyzing how the prompt flow evolving with the evolutionary process, adjusting based on evolutionary feedback (e.g., population diversity, convergence rate). Furthermore, we analyze how LLMs, through flexible prompt-driven roles, introduce semantic intelligence into fundamental EA characteristics, including diversity, convergence, adaptability, and scalability. Our systematic review and thorough analysis into the paradigm can help researchers better understand the current research and boost the development of synergizing LLMs with EAs for automated optimization algorithm design.