Quality-diversity (QD) optimization, as a paradigm of evolutionary algorithms, aims to generate diverse and high-performing solutions. However, existing QD algorithms fail to leverage historical and domain sequential scheduling knowledge effectively, making it challenging for them to handle large-scale discrete problems with conflicting objectives. This article proposes an extension of QD optimization algorithms, called the Deep Reinforcement Learning Enhanced Multi-Objective MAP-Elites (DMOME) algorithm, to solve a real-world combinatorial optimization problem. The DMOME algorithm seamlessly combines the feature diversity of solutions, domain knowledge heuristics and deep reinforcement learning techniques by adding Pareto fronts to different cells. The results on real-world mechanical processing factory instances demonstrate that the DMOME algorithm outperforms state-of-the-art algorithms, such as the enhanced genetic algorithm, achieving improvements of 25.6% to 59.4% in performance metrics.

Dynamic multi-objective optimization problems (DMOPs) are difficult because the Pareto set (PS) and Pareto front (PF) change over time, requiring algorithms to respond quickly while maintaining convergence and diversity. Existing prediction-based dynamic multi-objective evolutionary algorithms (DMOEAs) often rely on linear assumptions or individual-level modeling, which may limit their ability to respond to non-affine or structurally changing PS trajectories. To address this issue, this paper proposes a dynamic multi-objective evolutionary algorithm based on population partition and prediction strategy, termed PPDMOEA. It employs a cooperative response mechanism in which elite solutions mainly support convergence recovery and regular solutions preserve diversity. First, a two-dimensional evaluation strategy is used to select representative elite solutions for prediction by considering both convergence and distribution. Then, an order-insensitive set-encoded LSTM model is used to describe the temporal evolution of elite solution sets without relying on fixed element positions. Finally, a dynamic solution redistribution strategy is introduced to improve diversity and adaptability in new environments. Experiments on the CEC2018 dynamic multi-objective benchmark against seven representative DMOEAs show that the proposed algorithm achieves competitive MIGD and MHV performance on this benchmark, while its advantages are not uniform across all problem instances.

Pairwise testing is the most commonly used combinatorial interaction testing (CIT) technique to verify highly configurable systems, aiming to select the minimum number of testing configurations to cover all valid pairwise combinations of option values. The core problem of pairwise testing is the pairwise covering array generation (PCAG) problem. Existing PCAG methods typically struggle to generate small-scale pairwise covering arrays (PCA) for instances with complex constraints, or they require excessive computational time. To address these limitations, we propose DivSampCA, which employs a tuple-oriented adaptive sampling technique to enhance the diversity of the sampled configurations. Moreover, DivSampCA employs a novel full coverage strategy to ensure that the remaining uncovered pairwise tuples are covered with as few configurations as possible. We validate our method on 121 publicly available configurable system instances, and the experimental results show that DivSampCA achieves the smallest covering array in 71% of the instances, which is on average 15.54% smaller than that of other algorithms. Moreover, it is the fastest in 65% of the instances, reducing the average time by 42.36%. These results indicate that DivSampCA can generate smaller covering arrays in a shorter time and represents a significant advancement in solving the PCAG problem.

Distributed Flexible Job Shop Scheduling with Transportation Constraints (DFJSP-T) is widely used in manufacturing workshops across various industries, as it more accurately represents real-world production scenarios. However, many existing studies do not fully leverage critical problem features or domain knowledge, limiting the ability of current algorithms to find high-quality solutions for complex large-scale problems. To address these challenges, this paper proposes a Self-Adaptive Differential Evolution Enhanced Quality-Diversity Optimization (SADE-QD). The SADE-QD incorporates domain knowledge in three main ways: (1) it models the problem using machine idle and job transportation features, allowing the algorithm to retain solutions with diverse behaviors; (2) it introduces a knowledge-guided heuristic search strategy based on critical path to discover more high-quality solutions; and (3) it applies an self-adaptive differential evolution search method that leverages machine idle and transportation features to explore a broader range of solutions. This helps valuable information from the feature space contribute directly to the search process. Experiments on small, medium, and large scale benchmarks show that SADE-QD achieves an average makespan reduction of 12% compared to several recent state-of-the-art algorithms.

Unmanned aerial vehicles (UAVs) are increasingly deployed in complex autonomous missions, making systematic safety testing essential for reliable operation. Simulation-based testing provides a practical and risk-free way to assess UAV behavior, but its effectiveness critically depends on generating diverse, failure-revealing scenarios under tight computational budgets. Existing automated test generation approaches struggle to meet these requirements: objective-driven methods typically optimize a single aggregated risk score and tend to produce clustered, redundant test cases, whereas structure-based heuristics encourage diversity but lack principled guidance and computational efficiency. To better address these challenges, we frame UAV test case generation as a quality–diversity (QD) optimization problem that balances behavioral coverage and failure potential under a fixed evaluation budget. Building on this formulation, we propose TLQD, a behavior-guided two-level QD framework for UAV test case generation. The first level explores a compact two-dimensional behavior space, parameterized by the obstacle–obstacle angle and the obstacle–environment cross-sectional ratio, to obtain broad behavioral coverage at low computational cost without invoking the simulator. The second level then concentrates the remaining evaluation budget on behaviorally promising regions, using a behavior-based perturbation operator together with a repulsion-based repair operator to intensify failure discovery, maintain behavioral diversity, and enforce structurally feasible obstacle layouts. Extensive experiments on two UAV testing benchmarks, SBFT 2024 and ICST 2025, show that TLQD consistently outperforms state-of-the-art baselines in both scenario diversity and fault-triggering effectiveness, demonstrating the benefits of behavior-guided two-level QD optimization for efficient and reliable UAV test generation.

Since software product lines (SPLs) are widely used to analyze the commonality and variability of domain requirements for core asset reuse, automatically modeling SPLs using feature models is conducive to improving requirements analysis efficiency and reducing development costs. Existing methods extract feature model components from unstructured natural language requirements through manually designed heuristics or machine learning methods. The methods based on large language model (LLM) hold an advantage over others due to their robust language comprehension and inference capabilities. Although LLM-based methods effectively capture the superficial hierarchical constraints of the feature model from the semantics of requirements, they struggle to infer implicit associations and complicated crossed constraints between features. UML use case diagrams reveal the structure and behavior of a system from an object-oriented perspective, with overlapping characteristics compared to feature models. Therefore, we propose LLM4FM, an automatic method to generate SPL feature models via an LLM augmented with use case relationships. By incorporating use case relationships into model fine-tuning, this method enhances an LLM in acquiring features and constraints. It compensates for the deficiencies of current methods in reasoning, as well as the difficulty of accurately representing features and their complex interactions. Extensive evaluation on public data and real-world cases demonstrates that LLM4FM delivers superior performance over state-of-the-art methods in terms of \textit{Precision}, \textit{Recall} and \textit{F1-score} of auto-generated feature models.

Fault localization is a critical task in software debugging and maintenance. In software product lines (SPLs), variability complicates this task because faults may manifest only under specific feature combinations. Existing approaches rely on spectrum-based correlations or causal models with uniform priors, which struggle to distinguish true causal relationships from spurious associations, particularly when observable evidence is limited. To address this limitation, we reformulate SPL fault localization as a structured probabilistic causal inference problem. The proposed approach models features, statements, and execution outcomes within a factor graph that captures structural and dynamic dependencies across product configurations. Instead of relying solely on statistical correlations, we derive heterogeneous prior probabilities from two complementary sources of evidence: feature-outcome associations quantified by symmetric uncertainty, and statement-level spectrum metrics. These priors are then incorporated into Bayesian inference to guide posterior estimation. This integration mitigates variability-induced confounding and enables fault probabilities to be inferred without the need for additional test executions. We evaluate the proposed approach on eight publicly available SPL systems and compare it with five state-of-the-art SPL fault localization techniques. Notably, all experiments are conducted without incurring additional testing overhead, reflecting realistic scenarios characterized by inherently limited observable evidence. The results show that our approach ranks the faulty statement at the top position in 48.23% of single-fault cases and achieves 0.1%–16% improvements in multi-fault scenarios. In addition, relative to the statement-isolation-based approach, our approach improves localization efficiency by approximately 1.29–663.12 times on most subject systems.

Standard unsupervised multi-view feature selection (UMFS) methods for large datasets exhibit limitations in modeling the competition between cross-view alignment and intra-view diversity, resulting in suboptimal solutions and expensive computational costs. This challenge is exacerbated by the diverse signals inherent in complex samples, which tend to mask shared patterns, thus complicating the pursuit of an optimal trade-off. In this work, we propose a Progressive Adversarial Feature Selection (ProAd-FS) framework for large-scale multi-view learning, which formulates this static trade-off objective as a dynamic competitive process. To be specific, ProAd-FS develops an adversarial decoupled architecture that assigns these competing objectives to distinct inter-view and intra-view games, guided by a robust gated curriculum to prioritize the learning of underlying structures. The entire framework exhibits linear computational complexity in both sample size and feature dimension, and embeds structural sparse regularization for end-to-end optimization. Extensive experimental results show that ProAd-FS achieves state-of-the-art performance while being highly scalable as well, providing an effective solution for large-scale UMFS tasks.

Unsupervised domain adaptation (UDA) has been widely concerned in the fields of machine learning, pattern recognition, and computer vision. Traditional UDA learning usually assumes that the label spaces of the source and target domains are exactly the same and only needs to solve the problem of sample distribution drift existing between two domains. However, in real world applications, the label spaces between two domains may be different. In this case, there are both sample distribution drift and class spatial difference between domains, namely Universal Domain Adaptation (UniDA) learning scenario. At present, existing works rarely offer theoretical analysis for universal domain adaptation. In this paper, we provide an upper bound of the generalization error for universal domain adaptation. According to the proposed generalization error bound, we propose a novel UniDA algorithm called Joint Distribution Alignment for Universal Domain Adaptation (JAUA), which aligns the joint distributions by minimizing the distribution discrepancy calculated by Chi-Square divergence. Furthermore, we propose a progressive pseudo-labeling method to assign the pseudo labels to unlabeled target samples. The experiment results on six public image datasets demonstrate the superiority of JAUA in handling the UniDA problem.

The Flexible Job Shop Scheduling problem with Automated Guided Vehicles (FJSP-AGVs) is commonly encountered in modern manufacturing systems, with complexity increasing exponentially as the problem scales, making traditional methods inadequate. So far, a limitation of meta-heuristic algorithms incorporating machine learning for solving FJSP-AGVs is that machine learning is primarily used for heuristic selection (e.g., dispatching rules or local search operators) rather than actively guiding solution evolution based on the diverse features of solutions, leading to incomplete exploration and premature convergence. To tackle these issues, this paper first presents a Q-Learning Region Selection Enhanced Quality-Diversity (Q-QD) algorithm, which integrates a pairwise selection scheme to identify potential collaborative solutions within the feature space for two practical Chinese manufacturing scenarios: a coal machinery structural parts production workshop and a machining workshop in Nanjing. Unlike traditional approaches that focus solely on optimizing the objective, Q-QD leverages the customized feature space incorporating behaviors such as job transportation times and machine idle times. By combining Q-learning-based region selection with heuristic rule-based local search for AGV transportation, the proposed method effectively discovers high-performing and diverse solutions. The results obtained from two real-world cases and 21 benchmark instances indicate that the proposed Q-QD algorithm surpasses five advanced counterparts, achieving a makespan reduction of 12.2-30.8% relative to the strongest baseline. These substantial performance gains highlight the robustness and efficiency of QD-based optimization for solving FJSP-AGVs and suggest a valuable avenue for future research in intelligent job shop scheduling.

TLQD is an unmanned aerial vehicle (UAV) test case generation tool based on quality–diversity algorithms. It employs a two-level structural strategy with behavior-guided search, exploring test cases at different granularities in both global and local regions of the search space. In addition, TLQD includes a feasibility repair operator to handle constraint-violating test cases. This short paper reports the implementation of TLQD in the UAV Testing Tool Competition at ICST 2026.

Dynamic constrained multi-objective optimization problems involve time-varying objective functions and constraints and arise in many real-world engineering applications. However, existing algorithms often cannot rapidly identify the Pareto-optimal set and may converge slowly when the environment changes frequently. To address these challenges, this paper proposes a temporal graph attention network-assisted evolutionary algorithm, termed T-DCMOEA. T-DCMOEA constructs a temporal graph to represent the evolution of solution populations and uses an attention mechanism to capture temporal dependencies among solutions, thereby establishing an offline model for predicting solution quality. A Rényi divergence-based update-trigger indicator then determines whether the prediction model should be updated online. Finally, the resulting model guides the selection of promising solutions during environmental response, while an elite-preservation strategy generates additional candidates. Experimental results show that T-DCMOEA outperforms state-of-the-art algorithms across multiple performance metrics and produces solution sets with good convergence and diversity in dynamic environments.

Objective The task of code generation aims to transform natural language descriptions into corresponding target code. Among the various approaches, syntax-aware code generation has emerged as a significant approach that strives to generate code by directly modeling the underlying syntactic rules. However, existing works typically adopt an autoregressive approach to sequentially generate each abstract syntax rule, which inevitably neglects the rich structural semantic information inherent within the syntax rules. To address this issue, we propose an enhanced architecture of structure semantics based on Graph Neural Network for code generation.Methods Our approach explicitly models the internal structure of syntactic rules by treating them as graph data, thereby enabling the extraction of deeper structural semantics. Furthermore, we jointly model both the sequential semantics and structural semantics of syntactic rules, effectively addressing the limitations of solely sequence-based approaches in capturing the inherent structural semantics of code.Results Experimental results on two widely used code generation datasets demonstrate that the proposed model consistently outperforms strong baselines, with gains of up to 2.14 BLEU points and 2.02 CodeBLEU points, highlighting the effectiveness of our structural-semantic modeling approach for code generation.

Quality-Diversity (QD) optimization is a paradigm of evolutionary computation (EC) that extends the classic approaches, aiming to generate a collection of solutions that are both diverse and high-performing. Unlike traditional evolutionary algorithms (EAs), QD methods emphasize the illumination (or coverage) of a user-defined feature space, while simultaneously aiming for local optimization within each discovered region of the feature space. Over the past decade, QD has rapidly developed and proven effective in areas such as evolutionary robotics and video games. However, a systematic review of this growing field remains lacking. To date, the most recent review article on QD was published in 2021. Therefore, to offer a more comprehensive overview of the latest QD research, this paper provides a thorough survey of QD optimization, covering its foundational principles and representative algorithmic frameworks such as Novelty Search with Local Competition (NSLC), MAP-Elites, the unified modular QD framework, and RIBS. In addition, we divide the algorithm improvement part into three modules for discussion: containers, selection, and mutation. Then, the evaluation metrics widely used in QD optimization are listed for researchers. We further explore its diverse applications across domains such as evolutionary robotics, video games, scheduling, software testing, and engineering design. Finally, we discuss the current challenges in the field and outline promising directions for future research.

Constrained optimization problems constitute a class of optimization tasks that aim to maximize or minimize an objective function subject to intricate constraints. Evolutionary algorithms are extensively employed to tackle these problems, but the inherent nonlinearity, discontinuity, and restricted feasible regions of constrained optimization problems present significant challenges, and existing approaches often rely on predefined rules or empirical thresholds, which limit their adaptability and hinder causal interpretability. To overcome this limitation, this study proposes an evolutionary constrained optimization algorithm based on causal random forest that leverages causal random forest to quantify the causal strength between objective optimization and constraint satisfaction, thereby guiding the evolutionary search in a principled and informed manner. Furthermore, a dynamic adaptive strategy-switching mechanism is incorporated into the algorithm to reduce the reliance on empirical thresholds and fixed rules, which enhances the self-adaptive capability of the algorithm under complex and sophisticated constraints. Extensive experimental results on the CEC2006, CEC2010, and CEC2017 benchmark suites demonstrate that the proposed method consistently outperforms existing methods, underscoring its effectiveness and robustness in handling constrained optimization problems.

In Software Product Lines (SPLs), localizing buggy feature interactions helps developers identify the root cause of test failures, thereby reducing their workload. This task is challenging because the number of potential interactions grows exponentially with the number of features, resulting in a vast search space, especially for large SPLs. Previous approaches have partially addressed this issue by constructing and examining potential feature interactions based on suspicious feature selections (e.g., those present in failed configurations but not in passed ones). However, these approaches often overlook the causal relationship between buggy feature interaction and test failures, resulting in an excessive search space and high-cost fault localization. To address this, we propose a low-cost Counterfactual Reasoning-Based Fault Localization (CRFL) approach for SPLs, which enhances fault localization efficiency by reducing both the search space and redundant computations. Specifically, CRFL employs counterfactual reasoning to infer suspicious feature selections and utilizes symmetric uncertainty to filter out irrelevant feature interactions. Additionally, CRFL incorporates two findings to prevent the repeated generation and examination of the same feature interactions. We evaluate the performance of our approach using eight publicly available SPL systems. To enable comparisons on larger real-world SPLs, we generate multiple buggy mutants for both BerkeleyDB and TankWar. Experimental results show that our approach reduces the search space by 51%∼73% for small SPLs (with 6∼9 features) and by 71%∼88% for larger SPLs (with 13∼99 features). The average runtime of our approach is approximately 15.6 times faster than that of a state-of-the-art method. Furthermore, when combined with statement-level localization techniques, CRFL can efficiently localize buggy statements, demonstrating its ability to accurately identify buggy feature interactions.

Automated test case generation for path coverage (ATCG-PC) is a major challenge in search-based software engineering due to its complexity as a large-scale black-box optimization problem. However, existing search-based approaches often fail to achieve high path coverage in large-scale unit programs. This is due to their expansive decision space and the presence of hundreds of feasible paths. In this paper, we present a microscale (small-size subsets of the decomposed decision set) search-based algorithm with time-space transfer (MISA-TST). This algorithm aims to identify more accurate subspaces consisting of optimal solutions based on two strategies. The dimension partition strategy employs a relationship matrix to track subspaces corresponding to the target paths. Additionally, the specific value strategy allows MISA-TST to focus the search on the neighborhood of specific dimension values rather than the entire dimension space. Experiments conducted on nine normal-scale and six large-scale benchmarks demonstrate the effectiveness of MISA-TST. The large-scale unit programs encompass hundreds of feasible paths or more than 1.00E+50 test cases. The results show that MISA-TST achieves significantly higher path coverage than other state-of-the-art algorithms in most benchmarks. Furthermore, the combination of the two time-space transfer strategies significantly enhances the performance of search-based algorithms like MISA, especially in large-scale unit programs.

The ℓ2,0-norm is playing an increasingly important role in unsupervised feature selection. However, existing algorithm for optimization problem with ℓ2,0-norm constraint has two problems: First, they cannot automatically determine the sparsity, also known as the number of key features. Second, they have the risk of converging towards local optima, therefore selecting trivial (less informative) features. To address these problems, this paper proposes an unsupervised feature selection method with evolutionary sparsity (EVSP), which integrates the feature selection process with a sparse projection matrix and population search mechanisms into a unified unsupervised feature selection framework. Specifically, the level of sparsity is encoded as population individuals, and subsequently, a multi-objective evolutionary algorithm based on binary encoding is introduced to recursively determine the optimal level of sparsity, thus unsupervisedly guiding the learning of an optimal row-sparse projection matrix. Moreover, by utilizing the feature weights learned through sparse projection, a two-stage strategy called the mutation-repair operator is designed to steer the evolution of the population, aiming to generate high-quality candidate solutions. Comprehensive experiments on eleven benchmark datasets, with a maximum dimensionality of 10304 features and a maximum size of 9298 samples, demonstrate that the proposed EVSP method can effectively determine the optimal sparsity level, significantly outperforming several state-of-the-art methods.

The Flexible Job Shop Scheduling Problem with transportation constraints (FJSP-T) widely exists in manufacturing industry. Despite its prevalence, relatively little research has been done on it. To address the FJSP-T, several meta-heuristic algorithms have been proposed, but they do not take into account the diversity of solution features, potentially leading the algorithm to get trapped in local optima. In addition, transportation constraints directly affect the final objective value, yet there are few efficient strategies specifically dedicated to this aspect of the issue. Moreover, when confronted with the challenge of selecting local search operators, the probabilistic randomization approach introduces considerable uncertainty. This method can engender a substantial volume of invalid searches, consequently degrading the efficiency of the algorithm. To address the above issues, we propose a reinforcement learning enhanced Quality-Diversity (QD) algorithm for FJSP-T. The QD framework, is employed to guarantee the diversity of solution features. This paper asserts that considering job transportation in local search operators can provide advantages in improving problem-solving abilities. Therefore, two local search operators based on job transportation are proposed. To make effective decisions between local search operators, a reinforcement learning method, named Q-learning, is applied. The results on 20 instances demonstrate that the superiority of the proposed algorithm, which has achieved an average reduction of 6% in the optimization objective, outperforming the best-performing algorithm. In summary, while exploiting characteristics of transportation constraints, enhancing QD with reinforcement learning provide a promising avenue to solve FJSP-T.