Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs for the first time in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast evolutionary as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.
We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex objectives. First, it implements a simultaneous search by using variational posteriors, such as, mixtures of Gaussians. Second, it applies annealing to gradually trade off exploration for exploitation. Finally, it learns the variational search distribution using natural-gradient learning where updates resemble well-known and easy-to-implement algorithms. The three concepts come together in NVA giving rise to new algorithms and also allowing us to incorporate "fitness shaping", a core concept from evolutionary algorithms. We assess the quality of search on simulations and compare them to methods using gradient descent and evolution strategies. We also provide an application to a real-world inverse problem in planetary science.
Evolutionary Algorithms (EAs) are widely employed tools for complex search and optimization tasks; however, the absence of an overarching operational framework that permits a systematic regulation of the exploration-exploitation tradeoff--critical for efficient convergence--restricts the full actualization of their potential, leading to the so-called exploration-exploitation dilemma in algorithm design. A systematic resolution to this dilemma requires: (1) an independent yet coordinated control over exploration and exploitation, and (2) an explicit, computationally feasible, adaptive regulation mechanism. The current, almost decentralized, traditional parameter tuning-centeric approach--lacks the foundation to satisfy these requirements under encoding-imposed structural constraints. We propose a Human-Centered Two-Phase Search (HCTPS) framework, in which the actualization of (1) and (2) is enabled through an external configuration variable--the Search Space Control Parameter (SSCP). As the sole control knob of HCTPS, the SSCP centralizes exploration adjustments, sparing users from micromanaging traditional parameters with unintelligible interdependencies. To this construct, the human user serves as a meta-parameter, adaptively steering the regulatory process via SSCP adjustments. We prove that the HCTPS strictly surpasses the current approach in terms of search space coverage without disrupting the EAs' inherent convergence mechanisms, demonstrate a concrete instantiation of it--using the Genetic Algorithm as the underlying heuristic on a suite of global benchmark unconstrained optimization problems, provide a through assessment of the proposed framework, and envision future research directions. Any search algorithm prone to this dilemma can be applied in light of the proposed framework, being algorithm-agnostic by design.
In the domain of multi-objective optimization, evolutionary algorithms are distinguished by their capability to generate a diverse population of solutions that navigate the trade-offs inherent among competing objectives. This has catalyzed the ascension of evolutionary multi-objective optimization (EMO) as a prevalent approach. Despite the effectiveness of the EMO paradigm, the analysis of resultant solution sets presents considerable challenges. This is primarily attributed to the high-dimensional nature of the data and the constraints imposed by static visualization methods, which frequently culminate in visual clutter and impede interactive exploratory analysis. To address these challenges, this paper introduces ParetoLens, a visual analytics framework specifically tailored to enhance the inspection and exploration of solution sets derived from the multi-objective evolutionary algorithms. Utilizing a modularized, algorithm-agnostic design, ParetoLens enables a detailed inspection of solution distributions in both decision and objective spaces through a suite of interactive visual representations. This approach not only mitigates the issues associated with static visualizations but also supports a more nuanced and flexible analysis process. The usability of the framework is evaluated through case studies and expert interviews, demonstrating its potential to uncover complex patterns and facilitate a deeper understanding of multi-objective optimization solution sets. A demo website of ParetoLens is available at https://dva-lab.org/paretolens/.
Evolutionary algorithms (EAs) maintain populations through evolutionary operators to discover diverse solutions for complex tasks while gathering valuable knowledge, such as historical population data and fitness evaluations. However, traditional EAs face challenges in dynamically adapting to expanding knowledge bases, hindering the efficient exploitation of accumulated information and limiting adaptability to new situations. To address these issues, we introduce an Optimization Knowledge Adaptation Evolutionary Model (OKAEM), which features dynamic parameter adjustment using accumulated knowledge to enhance its optimization capabilities. OKAEM employs attention mechanisms to model the interactions among individuals, fitness landscapes, and genetic components separately, thereby parameterizing the evolutionary operators of selection, crossover, and mutation. These powerful learnable operators enable OKAEM to benefit from pre-learned extensive prior knowledge and self-tune with real-time evolutionary insights. Experimental results demonstrate that OKAEM: 1) exploits prior knowledge for significant performance gains across various knowledge transfer settings; 2) achieves competitive performance through self-tuning alone, even without prior knowledge; 3) outperforms state-of-the-art black-box baselines in a vision-language model tuning case; 4) can improve its optimization capabilities with growing knowledge; 5) is capable of emulating principles of natural selection and genetic recombination.
Multi-objective evolutionary algorithms (MOEAs) are widely used for searching optimal solutions in complex multi-component applications. Traditional MOEAs for multi-component deep learning (MCDL) systems face challenges in enhancing the search efficiency while maintaining the diversity. To combat these, this paper proposes $\mu$MOEA, the first LLM-empowered adaptive evolutionary search algorithm to detect safety violations in MCDL systems. Inspired by the context-understanding ability of Large Language Models (LLMs), $\mu$MOEA promotes the LLM to comprehend the optimization problem and generate an initial population tailed to evolutionary objectives. Subsequently, it employs adaptive selection and variation to iteratively produce offspring, balancing the evolutionary efficiency and diversity. During the evolutionary process, to navigate away from the local optima, $\mu$MOEA integrates the evolutionary experience back into the LLM. This utilization harnesses the LLM's quantitative reasoning prowess to generate differential seeds, breaking away from current optimal solutions. We evaluate $\mu$MOEA in finding safety violations of MCDL systems, and compare its performance with state-of-the-art MOEA methods. Experimental results show that $\mu$MOEA can significantly improve the efficiency and diversity of the evolutionary search.
Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE_code.
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use of evolutionary algorithms for such optimization, specifically for time-series forecasting. We perform a comparison, for diverse instances of real-world data, between gradient-descent parameter optimization and covariant-matrix adaptation evolutionary strategy. We observe that gradient descent becomes permanently trapped in local minima that have been avoided by evolutionary algorithms in all tested datasets, reaching up to a six-fold decrease in prediction error. Finally, the combined use of evolutionary and gradient-based techniques is explored, aiming at retaining advantages of both. The results are particularly applicable in scenarios sensitive to gains in accuracy.
In this paper, we reveal the intrinsic duality between graph neural networks (GNNs) and evolutionary algorithms (EAs), bridging two traditionally distinct fields. Building on this insight, we propose Graph Neural Evolution (GNE), a novel evolutionary algorithm that models individuals as nodes in a graph and leverages designed frequency-domain filters to balance global exploration and local exploitation. Through the use of these filters, GNE aggregates high-frequency (diversity-enhancing) and low-frequency (stability-promoting) information, transforming EAs into interpretable and tunable mechanisms in the frequency domain. Extensive experiments on benchmark functions demonstrate that GNE consistently outperforms state-of-the-art algorithms such as GA, DE, CMA-ES, SDAES, and RL-SHADE, excelling in complex landscapes, optimal solution shifts, and noisy environments. Its robustness, adaptability, and superior convergence highlight its practical and theoretical value. Beyond optimization, GNE establishes a conceptual and mathematical foundation linking EAs and GNNs, offering new perspectives for both fields. Its framework encourages the development of task-adaptive filters and hybrid approaches for EAs, while its insights can inspire advances in GNNs, such as improved global information propagation and mitigation of oversmoothing. GNE's versatility extends to solving challenges in machine learning, including hyperparameter tuning and neural architecture search, as well as real-world applications in engineering and operations research. By uniting the dynamics of EAs with the structural insights of GNNs, this work provides a foundation for interdisciplinary innovation, paving the way for scalable and interpretable solutions to complex optimization problems.
Community structures are critical for understanding the mesoscopic organization of networks, bridging local and global patterns. While methods such as DeepWalk and node2vec capture local positional information through random walks, they fail to preserve community structures. Other approaches like modularized nonnegative matrix factorization and evolutionary algorithms address this gap but are computationally expensive and unsuitable for large-scale networks. To overcome these limitations, we propose Two Layer Walk (TLWalk), a novel graph embedding algorithm that incorporates hierarchical community structures. TLWalk balances intra- and inter-community relationships through a community-aware random walk mechanism without requiring additional parameters. Theoretical analysis demonstrates that TLWalk effectively mitigates locality bias. Experiments on benchmark datasets show that TLWalk outperforms state-of-the-art methods, achieving up to 3.2% accuracy gains for link prediction tasks. By encoding dense local and sparse global structures, TLWalk proves robust and scalable across diverse networks, offering an efficient solution for network analysis.
Randomized search heuristics have been applied successfully to a plethora of problems. This success is complemented by a large body of theoretical results. Unfortunately, the vast majority of these results regard problems with binary or continuous decision variables -- the theoretical analysis of randomized search heuristics for unbounded integer domains is almost nonexistent. To resolve this shortcoming, we start the runtime analysis of multi-objective evolutionary algorithms, which are among the most successful randomized search heuristics, for unbounded integer search spaces. We analyze single- and full-dimensional mutation operators with three different mutation strengths, namely changes by plus/minus one (unit strength), random changes following a law with exponential tails, and random changes following a power-law. The performance guarantees we prove on a recently proposed natural benchmark problem suggest that unit mutation strengths can be slow when the initial solutions are far from the Pareto front. When setting the expected change right (depending on the benchmark parameter and the distance of the initial solutions), the mutation strength with exponential tails yields the best runtime guarantees in our results -- however, with a wrong choice of this expectation, the performance guarantees quickly become highly uninteresting. With power-law mutation, which is an essentially parameter-less mutation operator, we obtain good results uniformly over all problem parameters and starting points. We complement our mathematical findings with experimental results that suggest that our bounds are not always tight. Most prominently, our experiments indicate that power-law mutation outperforms the one with exponential tails even when the latter uses a near-optimal parametrization. Hence, we suggest to favor power-law mutation for unknown problems in integer spaces.
Existing research on AI-based traffic management systems, utilizing techniques such as fuzzy logic, reinforcement learning, deep neural networks, and evolutionary algorithms, demonstrates the potential of AI to transform the traffic landscape. This article endeavors to review the topics where AI and traffic management intersect. It comprises areas like AI-powered traffic signal control systems, automatic distance and velocity recognition (for instance, in autonomous vehicles, hereafter AVs), smart parking systems, and Intelligent Traffic Management Systems (ITMS), which use data captured in real-time to keep track of traffic conditions, and traffic-related law enforcement and surveillance using AI. AI applications in traffic management cover a wide range of spheres. The spheres comprise, inter alia, streamlining traffic signal timings, predicting traffic bottlenecks in specific areas, detecting potential accidents and road hazards, managing incidents accurately, advancing public transportation systems, development of innovative driver assistance systems, and minimizing environmental impact through simplified routes and reduced emissions. The benefits of AI in traffic management are also diverse. They comprise improved management of traffic data, sounder route decision automation, easier and speedier identification and resolution of vehicular issues through monitoring the condition of individual vehicles, decreased traffic snarls and mishaps, superior resource utilization, alleviated stress of traffic management manpower, greater on-road safety, and better emergency response time.
We propose EVOlutionary Selector (EVOS), an efficient training paradigm for accelerating Implicit Neural Representation (INR). Unlike conventional INR training that feeds all samples through the neural network in each iteration, our approach restricts training to strategically selected points, reducing computational overhead by eliminating redundant forward passes. Specifically, we treat each sample as an individual in an evolutionary process, where only those fittest ones survive and merit inclusion in training, adaptively evolving with the neural network dynamics. While this is conceptually similar to Evolutionary Algorithms, their distinct objectives (selection for acceleration vs. iterative solution optimization) require a fundamental redefinition of evolutionary mechanisms for our context. In response, we design sparse fitness evaluation, frequency-guided crossover, and augmented unbiased mutation to comprise EVOS. These components respectively guide sample selection with reduced computational cost, enhance performance through frequency-domain balance, and mitigate selection bias from cached evaluation. Extensive experiments demonstrate that our method achieves approximately 48%-66% reduction in training time while ensuring superior convergence without additional cost, establishing state-of-the-art acceleration among recent sampling-based strategies.
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal multigrid components using machine learning techniques, we adopt a complementary strategy here, employing evolutionary algorithms to construct efficient multigrid cycles from available individual components. This technology is applied to finite element simulations of the laser beam welding process. The thermo-elastic behavior is described by a coupled system of time-dependent thermo-elasticity equations, leading to nonlinear and ill-conditioned systems. The nonlinearity is addressed using Newton's method, and iterative solvers are accelerated with an algebraic multigrid (AMG) preconditioner using hypre BoomerAMG interfaced via PETSc. This is applied as a monolithic solver for the coupled equations. To further enhance solver efficiency, flexible AMG cycles are introduced, extending traditional cycle types with level-specific smoothing sequences and non-recursive cycling patterns. These are automatically generated using genetic programming, guided by a context-free grammar containing AMG rules. Numerical experiments demonstrate the potential of these approaches to improve solver performance in large-scale laser beam welding simulations.
Recent advances in Meta-learning for Black-Box Optimization (MetaBBO) have shown the potential of using neural networks to dynamically configure evolutionary algorithms (EAs), enhancing their performance and adaptability across various BBO instances. However, they are often tailored to a specific EA, which limits their generalizability and necessitates retraining or redesigns for different EAs and optimization problems. To address this limitation, we introduce ConfigX, a new paradigm of the MetaBBO framework that is capable of learning a universal configuration agent (model) for boosting diverse EAs. To achieve so, our ConfigX first leverages a novel modularization system that enables the flexible combination of various optimization sub-modules to generate diverse EAs during training. Additionally, we propose a Transformer-based neural network to meta-learn a universal configuration policy through multitask reinforcement learning across a designed joint optimization task space. Extensive experiments verify that, our ConfigX, after large-scale pre-training, achieves robust zero-shot generalization to unseen tasks and outperforms state-of-the-art baselines. Moreover, ConfigX exhibits strong lifelong learning capabilities, allowing efficient adaptation to new tasks through fine-tuning. Our proposed ConfigX represents a significant step toward an automatic, all-purpose configuration agent for EAs.
Recent advances in learnable evolutionary algorithms have demonstrated the importance of leveraging population distribution information and historical evolutionary trajectories. While significant progress has been made in continuous optimization domains, combinatorial optimization problems remain challenging due to their discrete nature and complex solution spaces. To address this gap, we propose SeqMO, a novel learnable multi-objective combinatorial optimization method that integrates sequence-to-sequence models with evolutionary algorithms. Our approach divides approximate Pareto solution sets based on their objective values' distance to the Pareto front, and establishes mapping relationships between solutions by minimizing objective vector angles in the target space. This mapping creates structured training data for pointer networks, which learns to predict promising solution trajectories in the discrete search space. The trained model then guides the evolutionary process by generating new candidate solutions while maintaining population diversity. Experiments on the multi-objective travel salesman problem and the multi-objective quadratic assignment problem verify the effectiveness of the algorithm. Our code is available at: \href{https://github.com/jiaxianghuang/SeqMO}{https://github.com/jiaxianghuang/SeqMO}.
Clustering algorithms are pivotal in data analysis, enabling the organization of data into meaningful groups. However, individual clustering methods often exhibit inherent limitations and biases, preventing the development of a universal solution applicable to diverse datasets. To address these challenges, we introduce a robust clustering framework that integrates the Minimum Description Length (MDL) principle with a genetic optimization algorithm. The framework begins with an ensemble clustering approach to generate an initial clustering solution, which is then refined using MDL-guided evaluation functions and optimized through a genetic algorithm. This integration allows the method to adapt to the dataset's intrinsic properties, minimizing dependency on the initial clustering input and ensuring a data-driven, robust clustering process. We evaluated the proposed method on thirteen benchmark datasets using four established validation metrics: accuracy, normalized mutual information (NMI), Fisher score, and adjusted Rand index (ARI). Experimental results demonstrate that our approach consistently outperforms traditional clustering methods, yielding higher accuracy, improved stability, and reduced bias. The methods adaptability makes it effective across datasets with diverse characteristics, highlighting its potential as a versatile and reliable tool for complex clustering tasks. By combining the MDL principle with genetic optimization, this study offers a significant advancement in clustering methodology, addressing key limitations and delivering superior performance in varied applications.
In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.
Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary algorithms (SAEAs) in EOPs, we discovered an intriguing phenomenon. Because only a limited number of solutions are evaluated in each iteration, relying solely on these evaluated solutions for evolution can lead to reduced disparity in successive populations. This, in turn, hampers the reproduction operators' ability to generate superior solutions, thereby reducing the algorithm's convergence speed. To address this issue, we propose a strategic approach that incorporates high-quality, un-evaluated solutions predicted by surrogate models during the selection phase. This approach aims to improve the distribution of evaluated solutions, thereby generating a superior next generation of solutions. This work details specific implementations of this concept across various reproduction operators and validates its effectiveness using multiple surrogate models. Experimental results demonstrate that the proposed strategy significantly enhances the performance of surrogate-assisted evolutionary algorithms. Compared to mainstream SAEAs and Bayesian optimization algorithms, our approach incorporating the un-evaluated solution strategy shows a marked improvement.
Autonomous Driving Systems (ADSs) rely on Deep Neural Networks, allowing vehicles to navigate complex, open environments. However, the unpredictability of these scenarios highlights the need for rigorous system-level testing to ensure safety, a task usually performed with a simulator in the loop. Though one important goal of such testing is to detect safety violations, there are many undesirable system behaviors, that may not immediately lead to violations, that testing should also be focusing on, thus detecting more subtle problems and enabling a finer-grained analysis. This paper introduces Cooperative Co-evolutionary MEtamorphic test Generator for Autonomous systems (CoCoMEGA), a novel automated testing framework aimed at advancing system-level safety assessments of ADSs. CoCoMEGA combines Metamorphic Testing (MT) with a search-based approach utilizing Cooperative Co-Evolutionary Algorithms (CCEA) to efficiently generate a diverse set of test cases. CoCoMEGA emphasizes the identification of test scenarios that present undesirable system behavior, that may eventually lead to safety violations, captured by Metamorphic Relations (MRs). When evaluated within the CARLA simulation environment on the Interfuser ADS, CoCoMEGA consistently outperforms baseline methods, demonstrating enhanced effectiveness and efficiency in generating severe, diverse MR violations and achieving broader exploration of the test space. These results underscore CoCoMEGA as a promising, more scalable solution to the inherent challenges in ADS testing with a simulator in the loop. Future research directions may include extending the approach to additional simulation platforms, applying it to other complex systems, and exploring methods for further improving testing efficiency such as surrogate modeling.