The discovery of symbolic solutions—mathematical expressions, logical rules, and algorithmic structures—is fundamental to advancing scientific and engineering progress. However, traditional methods often struggle with search efficiency and fail to integrate knowledge effectively. While recent large language model-based (LLM-based) approaches have demonstrated improvements in search efficiency, they lack the ability to continually refine and expand upon discovered solutions and their underlying knowledge, limiting their potential for \textit{open-ended innovation}. To address these limitations, we introduce CoEvo, a novel framework that leverages large language models within an evolutionary search methodology to continually generate and refine symbolic solutions. CoEvo integrates a dynamic knowledge library, enabling open-ended innovation of solutions through effective knowledge management. Additionally, CoEvo leverages multiple representations of solutions—including natural language, mathematical expressions, and code—to further enhance search efficiency. By combining the reasoning capabilities of LLMs with the exploratory power of evolutionary algorithms, CoEvo significantly improves the efficiency and scope of symbolic discovery. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing LLMs in the perpetual pursuit of scientific and engineering breakthroughs.

In recent years, a number of dynamic multiobjective evolutionary algorithms (DMOEAs) have been proposed for tackling dynamic multiobjective optimization problems (DMOPs). Most of DMOEAs adopt learning methods to extract search experiences from past environments, trying to predict a promising initial population in new environments. However, they often ignore the use of search experiences to guide the evolutionary trajectory in new environments, which is also important to accelerate their convergence. Thus, this paper proposes a historical search-guided evolutionary (HSGE) framework for tackling DMOPs, which designs a neural network-based pattern learning (NNPL) strategy and a historical direction-guided evolutionary (HDGE) strategy. First, the NNPL strategy trains a neural network to effectively extract search experiences from historical environments. Then, based on these search experiences, the HDGE strategy is designed to steer the evolutionary direction of population, aiming to speed up its convergence in new environments. After embedding four dynamic response mechanisms into the HSGE framework, the corresponding DMOEAs have shown superior performance over the original DMOEAs on most test DMOPs. Moreover, the experimental results also validate the advantages of HSGE over two state-of-the-art optimization frameworks for tackling DMOPs.

As the initial phase of evolutionary multi-objective optimization (EMO), population initialization is always essential for subsequent evolutionary processes aimed at solving multi-objective optimization problems. While random initialization (i.e., random sampling) remains the most frequently used initialization method in EMO algorithms, many studies have indicated that the utilization of alternative initialization methods instead of random initialization can significantly improve the performance of the original EMO algorithms. Some studies have also investigated the effects of different initialization techniques or parameters (e.g., methods and population size). However, there is a scarcity of recent reviews focusing on population initialization for EMO algorithms. To bridge this research gap in the EMO research community, this paper provides a short review on this crucial topic. Specifically, the current choice of initialization methods is briefly summarized by using some representative EMO algorithms. The effects of population initialization and new initialization method design are then extensively reviewed. Insights into population initialization are also provided. This study aims to provide a comprehensive understanding of population initialization for newcomers to the EMO community.

Crafting adversarial examples is crucial for evaluating and enhancing the robustness of Deep Neural Networks (DNNs), presenting a challenge equivalent to maximizing a non-differentiable 0-1 loss function. However, existing single objective methods, namely adversarial attacks focus on a surrogate loss function, do not fully harness the benefits of engaging multiple loss functions, as a result of insufficient understanding of their synergistic and conflicting nature. To overcome these limitations, we propose the Multi-Objective Set-Based Attack (MOS Attack), a novel adversarial attack framework leveraging multiple loss functions and automatically uncovering their interrelations. The MOS Attack adopts a set-based multi-objective optimization strategy, enabling the incorporation of numerous loss functions without additional parameters. It also automatically mines synergistic patterns among various losses, facilitating the generation of potent adversarial attacks with fewer objectives. Extensive experiments have shown that our MOS Attack outperforms single-objective attacks. Furthermore, by harnessing the identified synergistic patterns, MOS Attack continues to show superior results with a reduced number of loss functions. Our code is available at https://github.com/pgg3/MOS-Attack.

Recently, performance comparison results of evolutionary multi-objective optimization (EMO) algorithms have been reported in many studies. However, EMO algorithms have not been compared with mathematical programming-based methods in those studies. To demonstrate the usefulness of EMO algorithms, it is needed to clearly show their advantages over mathematical programming-based methods in solving multi-objective optimization problems since those methods are usually highly efficient and effective. In this paper, a novel improved linear programming-based relaxation method, named ILP-R, is proposed for addressing multi-objective knapsack problems (MOKP), which are used as the test problems for performance comparison. Extensive experimental results show that ILP-R outperforms a basic linear programming-based relaxation method and EMO algorithms. Nevertheless, EMO algorithms exhibit the ability to further improve the solutions generated by the ILP-R method. Furthermore, a knowledge-based mutation method is explored to demonstrate its effectiveness in further improving the performance of EMO algorithms that use the heuristic ILP-R solutions as the initial population.

Optimizing Register Transfer Level (RTL) code is crucial for improving the efficiency and performance of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper introduces SymRTLO, a neuron-symbolic framework that integrates LLMs with symbolic reasoning for the efficient and effective optimization of RTL code. Our method incorporates a retrieval-augmented system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods. We will release the code as open source upon the paper's acceptance.

Hypervolume subset selection (HSS) has received significant attention since it has a strong connection with evolutionary multiobjective optimization (EMO), such as environment selection and post-processing to identify representative solutions for decision-makers. The goal of HSS is to find the optimal subset that maximizes the hypervolume (HV) indicator subject to a given cardinality constraint. However, existing HSS algorithms or related methods are not efficient in achieving good performance in high-dimensional objective spaces. This is primarily because HSS problems become NP-hard when the number of objectives exceeds two, and the calculation of HV contribution (HVC) is very time-consuming. To efficiently solve HSS problems while maintaining a good solution quality, we propose a fast and scalable HSS method for many-objective optimization based on the determinantal point process (DPP), named DPP-HSS, which is fully free of HVC calculation. Specifically, DPP-HSS constructs an HV kernel matrix by extracting the convergence and diversity representations of each solution for a given HSS problem. This matrix is then used to build a DPP model. Subsequently, the original HSS problem is reformulated as a new maximization optimization problem based on the constructed model. A greedy DPP-based HSS algorithm is implemented to solve this transformed problem. Extensive experiments show that the proposed DPP-HSS achieves significant speedup and good HV performance in comparison with state-of-the-art HSS algorithms on benchmark problems. Furthermore, DPP-HSS demonstrates very good scalability with respect to the number of objectives.