Evolutionary Computation最新文献

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.

Symbolic regression is a challenging task in machine learning that aims to automatically discover highly interpretable mathematical equations from limited data. Keen efforts have been devoted to addressing this issue, yielding promising results. However, there are still bottlenecks that current methods struggle with, especially when dealing with the datasets that characterize intricate mathematical expressions. In this work, we propose a novel Geometric Evolution Symbolic Regression algorithm. Leveraging geometric semantics, the process of symbolic regression in GESR is transformed into an approximation to an unimodal target in n-dimensional semantic space. Then, three key modules are presented to enhance the approximation: (1) a new semantic gradient concept, proposed from the observation of inaccurate approximation results within semantic backpropagation, to assist the exploration in the semantic space and improve the accuracy of semantic approximation; (2) a new geometric semantic search operator, tailored for efficiently approximating the target formula directly in the sparse semantic space, to obtain more accurate and interpretable solutions under strict program size constraints; (3) the Levenberg-Marquardt algorithm with L1 regularization, used for the adjustment of expression structures and the optimization of global subtree weights to assist the proposed geometric semantic search operator. Assisted with these modules, GESR achieves state-of-the-art accuracy performance on SRSD benchmark datasets. The implementation is available at https://github.com/MZT-srcount/GESR.

Submodular optimization problems play a key role in artificial intelligence as they allow to capture many important problems in machine learning, data science, and social networks. Pareto optimization using evolutionary multi-objective algorithms such as GSEMO (also called POMC) has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good approximations is the population size of the algorithms which usually grows with the number of trade-offs that the algorithms encounter. In this paper, we introduce a sliding window speed up technique for recently introduced algorithms. We first examine the setting of deterministic constraints for which bi-objective formulations have been proposed in the literature. We prove that our technique eliminates the population size as a crucial factor negatively impacting the runtime bounds of the classical GSEMO algorithm and achieves the same theoretical performance guarantees as previous approaches within less computation time. Our experimental investigations for the classical maximum coverage problem confirm that our sliding window technique clearly leads to better results for a wide range of instances and constraint settings. After we have shown that the sliding approach leads to significant improvements for bi-objective formulations, we examine how to speed up a recently introduced 3-objective formulation for stochastic constraints. We show through theoretical and experimental investigations that the sliding window approach also leads to significant improvements for such 3-objective formulations as it allows for a more tailored parent selection that matches the optimization progress of the algorithm.