Wenjian Luo

Zoe L. Jiang, Jiajing Gu, Hongxiao Wang et al.

With the development of machine learning, it is difficult for a single server to process all the data. So machine learning tasks need to be spread across multiple servers, turning the centralized machine learning into a distributed one. However, privacy remains an unsolved problem in distributed machine learning. Multi-key homomorphic encryption is one of the suitable candidates to solve the problem. However, the most recent result of the Multi-key homomorphic encryption scheme (MKTFHE) only supports the NAND gate. Although it is Turing complete, it requires efficient encapsulation of the NAND gate to further support mathematical calculation. This paper designs and implements a series of operations on positive and negative integers accurately. First, we design basic bootstrapped gates with the same efficiency as that of the NAND gate. Second, we construct practical $k$-bit complement mathematical operators based on our basic binary bootstrapped gates. The constructed created can perform addition, subtraction, multiplication, and division on both positive and negative integers. Finally, we demonstrated the generality of the designed operators by achieving a distributed privacy-preserving machine learning algorithm, i.e. linear regression with two different solutions. Experiments show that the operators we designed are practical and efficient.

Kesheng Chen, Wenjian Luo, Zhenqian Zhu et al.

Constructing a Pareto set is pivotal for navigating the capability-efficiency trade-offs in Large Language Models (LLMs); however, existing merging techniques remain inadequate for this task. Coarse-grained, model-level methods yield only a sparse set of suboptimal solutions, while fine-grained, layer-wise approaches suffer from the "curse of dimensionality," rendering the search space computationally intractable. To resolve this dichotomy, we propose BAMBO (Bayesian Adaptive Multi-objective Block-wise Optimization), a novel framework that automatically constructs the LLM Pareto set. BAMBO renders the search tractable by introducing a Hybrid Optimal Block Partitioning strategy. Formulated as a 1D clustering problem, this strategy leverages a dynamic programming approach to optimally balance intra-block homogeneity and inter-block information distribution, thereby dramatically reducing dimensionality without sacrificing critical granularity. The entire process is automated within an evolutionary loop driven by the q-Expected Hypervolume Improvement (qEHVI) acquisition function. Experiments demonstrate that BAMBO discovers a superior and more comprehensive Pareto frontier than baselines, enabling agile model selection tailored to diverse operational constraints. Code is available at: https://github.com/xin8coder/BAMBO.

Wenjian Luo, Hongwei Zhang, Linghao Kong et al.

The security issues in DNNs, such as adversarial examples, have attracted much attention. Adversarial examples refer to the examples which are capable to induce the DNNs return completely predictions by introducing carefully designed perturbations. Obviously, adversarial examples bring great security risks to the development of deep learning. Recently, Some defense approaches against adversarial examples have been proposed, however, in our opinion, the performance of these approaches are still limited. In this paper, we propose a new ensemble defense approach named the Negative Correlation Ensemble (NCEn), which achieves compelling results by introducing gradient directions and gradient magnitudes of each member in the ensemble negatively correlated and at the same time, reducing the transferability of adversarial examples among them. Extensive experiments have been conducted, and the results demonstrate that NCEn can improve the adversarial robustness of ensembles effectively.

Kesheng Chen, Wenjian Luo, Xin Lin et al.

Unmanned aerial vehicles (UAVs) have been widely used in urban missions, and proper planning of UAV paths can improve mission efficiency while reducing the risk of potential third-party impact. Existing work has considered all efficiency and safety objectives for a single decision-maker (DM) and regarded this as a multiobjective optimization problem (MOP). However, there is usually not a single DM but two DMs, i.e., an efficiency DM and a safety DM, and the DMs are only concerned with their respective objectives. The final decision is made based on the solutions of both DMs. In this paper, for the first time, biparty multiobjective UAV path planning (BPMO-UAVPP) problems involving both efficiency and safety departments are modeled. The existing multiobjective immune algorithm with nondominated neighbor-based selection (NNIA), the hybrid evolutionary framework for the multiobjective immune algorithm (HEIA), and the adaptive immune-inspired multiobjective algorithm (AIMA) are modified for solving the BPMO-UAVPP problem, and then biparty multiobjective optimization algorithms, including the BPNNIA, BPHEIA, and BPAIMA, are proposed and comprehensively compared with traditional multiobjective evolutionary algorithms and typical multiparty multiobjective evolutionary algorithms (i.e., OptMPNDS and OptMPNDS2). The experimental results show that BPAIMA performs better than ordinary multiobjective evolutionary algorithms such as NSGA-II and multiparty multiobjective evolutionary algorithms such as OptMPNDS, OptMPNDS2, BPNNIA and BPHEIA.

Zeneng She, Wenjian Luo, Xin Lin et al.

In the field of evolutionary multiobjective optimization, the decision maker (DM) concerns conflicting objectives. In the real-world applications, there usually exist more than one DM and each DM concerns parts of these objectives. Multiparty multiobjective optimization problems (MPMOPs) are proposed to depict the MOP with multiple decision makers involved, where each party concerns about certain some objectives of all. However, in the evolutionary computation field, there is not much attention paid on MPMOPs. This paper constructs a series of MPMOPs based on distance minimization problems (DMPs), whose Pareto optimal solutions can be vividly visualized. To address MPMOPs, the new proposed algorithm OptMPNDS3 uses the multiparty initializing method to initialize the population and takes JADE2 operator to generate the offsprings. OptMPNDS3 is compared with OptAll, OptMPNDS and OptMPNDS2 on the problem suite. The result shows that OptMPNDS3 is strongly comparable to other algorithms

Xiaolei Fang, Peilan Xu, Wenjian Luo

Multi-party multi-objective optimization problems (MPMOPs) require consensus among autonomous decision makers and therefore differ from flattened many-objective formulations. Existing runtime theory for multi-objective evolutionary algorithms is largely tailored to single-party Pareto-front approximation and does not directly explain common-solution search in MPMOPs. We investigate cross-party recombination in two representative settings. On MP-JCG, a pseudo-Boolean benchmark with an explicit gap region, we prove that a payoff-guided mutation baseline faces a gap-crossing bottleneck requiring \(Θ(n^2)\) expected fitness evaluations. In contrast, an analytical CPR-NSGA-II variant discovers both common Pareto-optimal solutions in \(O(n\log n)\) expected evaluations by directly assembling complementary prefix and suffix templates distributed across party populations. Comparing this with the flattened four-objective formulation F-JCG, our full-front coverage analysis illustrates the additional coverage burden introduced by flattening. For BPBOMST, the bi-party, two-objective-per-party specialization of the multi-party multi-objective minimum spanning tree problem, we develop a layered support-cover analysis. For each common Pareto objective vector, the symmetric average projection induces an auxiliary bi-objective MST instance, and suitable support representatives yield a \(2λ\)-common approximation cover with \(λ\in[1,2]\). We further derive an instance-parameterized expected runtime bound for a representative-pool CPR-NSGA-II variant using edge-union recombination and uniform repair. This bound separates the effects of local auxiliary-front filling, cross-party recombination shortcuts, and edge-union repair ambiguity.

Kesheng Chen, Wenjian Luo, Qi Zhou et al.

Traditional multiobjective optimization problems (MOPs) are insufficiently equipped for scenarios involving multiple decision makers (DMs), which are prevalent in many practical applications. These scenarios are categorized as multiparty multiobjective optimization problems (MPMOPs). For MPMOPs, the goal is to find a solution set that is as close to the Pareto front of each DM as much as possible. This poses challenges for evolutionary algorithms in terms of searching and selecting. To better solve MPMOPs, this paper proposes a novel approach called the multiparty immune algorithm (MPIA). The MPIA incorporates an inter-party guided crossover strategy based on the individual's non-dominated sorting ranks from different DM perspectives and an adaptive activation strategy based on the proposed multiparty cover metric (MCM). These strategies enable MPIA to activate suitable individuals for the next operations, maintain population diversity from different DM perspectives, and enhance the algorithm's search capability. To evaluate the performance of MPIA, we compare it with ordinary multiobjective evolutionary algorithms (MOEAs) and state-of-the-art multiparty multiobjective optimization evolutionary algorithms (MPMOEAs) by solving synthetic multiparty multiobjective problems and real-world biparty multiobjective unmanned aerial vehicle path planning (BPUAV-PP) problems involving multiple DMs. Experimental results demonstrate that MPIA outperforms other algorithms.

Qi Zhou, Zipeng Ye, Yubo Tang et al.

Deep Neural Networks (DNNs) have been widely used in many areas such as autonomous driving and face recognition. However, DNN model is fragile to backdoor attack. A backdoor in the DNN model can be activated by a poisoned input with trigger and leads to wrong prediction, which causes serious security issues in applications. It is challenging for current defenses to eliminate the backdoor effectively with limited computing resources, especially when the sizes and numbers of the triggers are variable as in the physical world. We propose an efficient backdoor defense based on evolutionary trigger detection and lightweight model repair. In the first phase of our method, CAM-focus Evolutionary Trigger Filter (CETF) is proposed for trigger detection. CETF is an effective sample-preprocessing based method with the evolutionary algorithm, and our experimental results show that CETF not only distinguishes the images with triggers accurately from the clean images, but also can be widely used in practice for its simplicity and stability in different backdoor attack situations. In the second phase of our method, we leverage several lightweight unlearning methods with the trigger detected by CETF for model repair, which also constructively demonstrate the underlying correlation of the backdoor with Batch Normalization layers. Source code will be published after accepted.

Kesheng Chen, Yamin Hu, Qi Zhou et al.

Vision-language models (VLMs) achieve strong performance on many benchmarks, yet a basic reliability question remains underexplored: when visual evidence conflicts with commonsense, do models follow what is shown or what commonsense suggests? A characteristic failure in this setting is that the model overrides visual evidence and outputs the commonsense alternative. We term this phenomenon \textbf{commonsense-driven hallucination} (CDH). To evaluate it, we introduce \textbf{CDH-Bench}, a benchmark designed to create explicit \textbf{visual evidence--commonsense conflicts}. CDH-Bench covers three dimensions: \textit{counting anomalies}, \textit{relational anomalies}, and \textit{attribute anomalies}. We evaluate frontier VLMs under \textit{binary Question Answering (QA)} and \textit{multiple-choice QA}, and report metrics including \textit{Counterfactual Accuracy} (CF-Acc), \textit{Commonsense Accuracy} (CS-Acc), \textit{Counterfactual Accuracy Drop} (CFAD), \textit{Commonsense Collapse Rate} (CCR), and \textit{Relative Prior Dependency} (RPD). Results show that even strong models remain vulnerable to prior-driven normalization under visual evidence--commonsense conflict. CDH-Bench provides a controlled diagnostic of visual fidelity under visual evidence--commonsense conflict.

Yujiang Liu, Wenjian Luo, Zhijian Chen et al.

With the rapid development of Deep Neural Networks (DNNs), they have been applied in numerous fields. However, research indicates that DNNs are susceptible to adversarial examples, and this is equally true in the multi-label domain. To further investigate multi-label adversarial examples, we introduce a novel type of attacks, termed "Showing Many Labels". The objective of this attack is to maximize the number of labels included in the classifier's prediction results. In our experiments, we select nine attack algorithms and evaluate their performance under "Showing Many Labels". Eight of the attack algorithms were adapted from the multi-class environment to the multi-label environment, while the remaining one was specifically designed for the multi-label environment. We choose ML-LIW and ML-GCN as target models and train them on four popular multi-label datasets: VOC2007, VOC2012, NUS-WIDE, and COCO. We record the success rate of each algorithm when it shows the expected number of labels in eight different scenarios. Experimental results indicate that under the "Showing Many Labels", iterative attacks perform significantly better than one-step attacks. Moreover, it is possible to show all labels in the dataset.

Tianqiang Yan, Sihan Shang, Yuheng Li et al.

While self-reflection can enhance language model reliability, its underlying mechanisms remain opaque, with existing analyses often yielding correlation-based insights that fail to generalize. To address this, we introduce \textbf{\texttt{ReBeCA}} (self-\textbf{\texttt{Re}}flection \textbf{\texttt{Be}}havior explained through \textbf{\texttt{C}}ausal \textbf{\texttt{A}}nalysis), a framework that unveils the interpretable behavioral hierarchy governing the self-reflection outcome. By modeling self-reflection trajectories as causal graphs, ReBeCA isolates genuine determinants of performance through a three-stage Invariant Causal Prediction (ICP) pipeline. We establish three critical findings: (1) \textbf{Behavioral hierarchy:} Semantic behaviors of the model influence final self-reflection results hierarchically: directly or indirectly; (2) \textbf{Causation matters:} Generalizability in self-reflection effects is limited to just a few semantic behaviors; (3) \textbf{More $\mathbf{\neq}$ better:} The confluence of seemingly positive semantic behaviors, even among direct causal factors, can impair the efficacy of self-reflection. ICP-based verification identifies sparse causal parents achieving up to $49.6\%$ structural likelihood gains, stable across tasks where correlation-based patterns fail. Intervention studies on novel datasets confirm these causal relationships hold out-of-distribution ($p = .013, η^2_\mathrm{p} = .071$). ReBeCA thus provides a rigorous methodology for disentangling genuine causal mechanisms from spurious associations in self-reflection dynamics.

Jiahao Huang, Peilan Xu, Xiaoya Nan et al.

Automating operations research (OR) with large language models (LLMs) remains limited by hand-crafted reasoning--execution workflows. Complex OR tasks require adaptive coordination among problem interpretation, mathematical formulation, solver selection, code generation, and iterative debugging. To address this limitation, we propose EvoOR-Agent, a co-evolutionary framework for automated optimization. The framework represents agent workflows as activity-on-edge (AOE)-style networks, making workflow topology, execution dependencies, and alternative reasoning paths explicit. On this representation, the framework maintains an architecture graph and evolves a population of reasoning individuals through graph-mediated path-conditioned recombination, multi-granularity semantic mutation, and elitist population update. A knowledge-base-assisted experience-acquisition module further injects reusable OR practices into initialization and semantic variation. Empirical results on heterogeneous OR benchmarks show that the proposed framework consistently improves over zero-shot LLMs, fixed-pipeline OR agents, and representative evolutionary agent frameworks. Case studies and ablation analyses further indicate that explicit architecture evolution and graph-supported reasoning-trajectory search contribute to both performance improvement and structural interpretability. These results suggest that treating agent architectures and reasoning trajectories as evolvable objects provides an effective route toward adaptive and interpretable automated optimization.

Wenjian Luo, Peilan Xu, Shengxiang Yang et al.

The competition focuses on Multiparty Multiobjective Optimization Problems (MPMOPs), where multiple decision makers have conflicting objectives, as seen in applications like UAV path planning. Despite their importance, MPMOPs remain understudied in comparison to conventional multiobjective optimization. The competition aims to address this gap by encouraging researchers to explore tailored modeling approaches. The test suite comprises two parts: problems with common Pareto optimal solutions and Biparty Multiobjective UAV Path Planning (BPMO-UAVPP) problems with unknown solutions. Optimization algorithms for the first part are evaluated using Multiparty Inverted Generational Distance (MPIGD), and the second part is evaluated using Multiparty Hypervolume (MPHV) metrics. The average algorithm ranking across all problems serves as a performance benchmark.

Kesheng Chen, Wenjian Luo, Bang Zhang et al.

Episodic rewards present a significant challenge in reinforcement learning. While intrinsic reward methods have demonstrated effectiveness in single-agent rein-forcement learning scenarios, their application to multi-agent reinforcement learn-ing (MARL) remains problematic. The primary difficulties stem from two fac-tors: (1) the exponential sparsity of joint action trajectories that lead to rewards as the exploration space expands, and (2) existing methods often fail to account for joint actions that can influence team states. To address these challenges, this paper introduces Mutual Intrinsic Reward (MIR), a simple yet effective enhancement strategy for MARL with extremely sparse rewards like episodic rewards. MIR incentivizes individual agents to explore actions that affect their teammates, and when combined with original strategies, effectively stimulates team exploration and improves algorithm performance. For comprehensive experimental valida-tion, we extend the representative single-agent MiniGrid environment to create MiniGrid-MA, a series of MARL environments with sparse rewards. Our evalu-ation compares the proposed method against state-of-the-art approaches in the MiniGrid-MA setting, with experimental results demonstrating superior perfor-mance.

Yiya Diao, Changhe Li, Sanyou Zeng et al.

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of the method to combinatorial optimization problems is challenging but very important for analyzing the algorithm's behavior. This paper provides a straightforward theoretical derivation showing that the NBN network essentially functions as the maximum probability transition network for algorithms. This paper also presents an efficient NBN computation method with logarithmic linear time complexity to address the time-consuming issue. By applying this efficient NBN algorithm to the OneMax problem and the Traveling Salesman Problem (TSP), we have made several remarkable discoveries for the first time: The fitness landscape of OneMax exhibits neutrality, ruggedness, and modality features. The primary challenges of TSP problems are ruggedness, modality, and deception. Two state-of-the-art TSP algorithms (i.e., EAX and LKH) have limitations when addressing challenges related to modality and deception, respectively. LKH, based on local search operators, fails when there are deceptive solutions near global optima. EAX, which is based on a single population, can efficiently maintain diversity. However, when multiple attraction basins exist, EAX retains individuals within multiple basins simultaneously, reducing inter-basin interaction efficiency and leading to algorithm's stagnation.

Li Ni, Hengkai Xu, Lin Mu et al.

Real-world networks often involve both keywords and locations, along with travel time variations between locations due to traffic conditions. However, most existing cohesive subgraph-based community search studies utilize a single attribute, either keywords or locations, to identify communities. They do not simultaneously consider both keywords and locations, which results in low semantic or spatial cohesiveness of the detected communities, and they fail to account for variations in travel time. Additionally, these studies traverse the entire network to build efficient indexes, but the detected community only involves nodes around the query node, leading to the traversal of nodes that are not relevant to the community. Therefore, we propose the problem of discovering semantic-spatial aware k-core, which refers to a k-core with high semantic and time-dependent spatial cohesiveness containing the query node. To address this problem, we propose an exact and a greedy algorithm, both of which gradually expand outward from the query node. They are local methods that only access the local part of the attributed network near the query node rather than the entire network. Moreover, we design a method to calculate the semantic similarity between two keywords using large language models. This method alleviates the disadvantages of keyword-matching methods used in existing community search studies, such as mismatches caused by differently expressed synonyms and the presence of irrelevant words. Experimental results show that the greedy algorithm outperforms baselines in terms of structural, semantic, and time-dependent spatial cohesiveness.

Li Ni, Hengkai Xu, Lin Mu et al.

Semi-supervised local community detection aims to leverage known communities to detect the community containing a given node. Although existing semi-supervised local community detection studies yield promising results, they suffer from time-consuming issues, highlighting the need for more efficient algorithms. Therefore, we apply the "pre-train, prompt" paradigm to semi-supervised local community detection and propose the Pre-trained Prompt-driven Semi-supervised Local community detection method (PPSL). PPSL consists of three main components: node encoding, sample generation, and prompt-driven fine-tuning. Specifically, the node encoding component employs graph neural networks to learn the representations of nodes and communities. Based on representations of nodes and communities, the sample generation component selects known communities that are structurally similar to the local structure of the given node as training samples. Finally, the prompt-driven fine-tuning component leverages these training samples as prompts to guide the final community prediction. Experimental results on five real-world datasets demonstrate that PPSL outperforms baselines in both community quality and efficiency.

Li Ni, Ziqi Deng, Lin Mu et al.

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding relationship between genes and their protein products, drive the establishment of interconnections between multiple hypergraphs. Here, we demonstrate how to utilize those interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems, thereby enhancing understanding of underlying structures. We propose a model based on the stochastic block model, which integrates information from multiple hypergraphs to reveal latent high-order structures. Real-world hyperedges exhibit preferential attachment, where certain nodes dominate hyperedge formation. To characterize this phenomenon, our model introduces hyperedge internal degree to quantify nodes' contributions to hyperedge formation. This model is capable of mining communities, predicting missing hyperedges of arbitrary sizes within hypergraphs, and inferring inter-hypergraph edges between hypergraphs. We apply our model to high-order datasets to evaluate its performance. Experimental results demonstrate strong performance of our model in community detection, hyperedge prediction, and inter-hypergraph edge prediction tasks. Moreover, we show that our model enables analysis of multiple hypergraphs of different types and supports the analysis of a single hypergraph in the absence of inter-hypergraph edges. Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.

Yuetong Sun, Peilan Xu, Wenjian Luo

In scenarios where multiple decision-makers operate within a common decision space, each focusing on their own multi-objective optimization problem (e.g., bargaining games), the problem can be modeled as a multi-party multi-objective optimization problem (MPMOP). While numerous evolutionary algorithms have been proposed to solve MPMOPs, most results remain empirical. This paper presents the first theoretical analysis of the expected runtime of evolutionary algorithms on bi-party multi-objective optimization problems (BPMOPs). Our findings demonstrate that employing traditional multi-objective optimization algorithms to solve MPMOPs is both time-consuming and inefficient, as the resulting population contains many solutions that fail to achieve consensus among decision-makers. An alternative approach involves decision-makers individually solving their respective optimization problems and seeking consensus only in the final stage. While feasible for pseudo-Boolean optimization problems, this method may fail to guarantee approximate performance for one party in NP-hard problems. Finally, we propose evolutionary multi-party multi-objective optimizers (EMPMO) for pseudo-Boolean optimization and shortest path problems within a multi-party multi-objective context, maintain a common solution set among all parties. Theoretical and experimental results demonstrate that the proposed \( \text{EMPMO}_{\text{random}} \) outperforms previous algorithms in terms of the lower bound on the expected runtime for pseudo-Boolean optimization problems. Additionally, the consensus-based evolutionary multi-party multi-objective optimizer( \( \text{EMPMO}_{\text{cons}}^{\text{SP}} \) ) achieves better efficiency and precision in solving shortest path problems compared to existing algorithms.

Wenjian Luo, Xin Lin, Changhe Li et al.

Dynamic and multimodal features are two important properties and widely existed in many real-world optimization problems. The former illustrates that the objectives and/or constraints of the problems change over time, while the latter means there is more than one optimal solution (sometimes including the accepted local solutions) in each environment. The dynamic multimodal optimization problems (DMMOPs) have both of these characteristics, which have been studied in the field of evolutionary computation and swarm intelligence for years, and attract more and more attention. Solving such problems requires optimization algorithms to simultaneously track multiple optima in the changing environments. So that the decision makers can pick out one optimal solution in each environment according to their experiences and preferences, or quickly turn to other solutions when the current one cannot work well. This is very helpful for the decision makers, especially when facing changing environments. In this competition, a test suit about DMMOPs is given, which models the real-world applications. Specifically, this test suit adopts 8 multimodal functions and 8 change modes to construct 24 typical dynamic multimodal optimization problems. Meanwhile, the metric is also given to measure the algorithm performance, which considers the average number of optimal solutions found in all environments. This competition will be very helpful to promote the development of dynamic multimodal optimization algorithms.

Danial Yazdani, Michalis Mavrovouniotis, Changhe Li et al.

The Generalized Moving Peaks Benchmark (GMPB) is a tool for generating continuous dynamic optimization problem instances with controllable dynamic and morphological characteristics. GMPB has been used in recent Competitions on Dynamic Optimization at prestigious conferences, such as the IEEE Congress on Evolutionary Computation (CEC). This dynamic benchmark generator can create a wide variety of landscapes, ranging from simple unimodal to highly complex multimodal configurations and from symmetric to asymmetric forms. It also supports diverse surface textures, from smooth to highly irregular, and can generate varying levels of variable interaction and conditioning. This document provides an overview of GMPB, emphasizing how its parameters can be adjusted to produce landscapes with customizable characteristics. The MATLAB implementation of GMPB is available on the EDOLAB Platform.

Wenjian Luo, Chenwang Wu, Nan Zhou et al.

Deep neural networks (DNNs) have been widely used in many fields such as images processing, speech recognition; however, they are vulnerable to adversarial examples, and this is a security issue worthy of attention. Because the training process of DNNs converge the loss by updating the weights along the gradient descent direction, many gradient-based methods attempt to destroy the DNN model by adding perturbations in the gradient direction. Unfortunately, as the model is nonlinear in most cases, the addition of perturbations in the gradient direction does not necessarily increase loss. Thus, we propose a random directed attack (RDA) for generating adversarial examples in this paper. Rather than limiting the gradient direction to generate an attack, RDA searches the attack direction based on hill climbing and uses multiple strategies to avoid local optima that cause attack failure. Compared with state-of-the-art gradient-based methods, the attack performance of RDA is very competitive. Moreover, RDA can attack without any internal knowledge of the model, and its performance under black-box attack is similar to that of the white-box attack in most cases, which is difficult to achieve using existing gradient-based attack methods.

Yamin Hu, Wenjian Luo, Junteng Wang

It is crucial to generate crafted SAT formulas with predefined solutions for the testing and development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some generating algorithms have been proposed to generate SAT formulas with predefined solutions, community structures of SAT formulas are not considered. We propose a 3-SAT formula generating algorithm that not only guarantees the existence of a predefined solution, but also simultaneously considers community structures and clause distributions. The proposed 3-SAT formula generating algorithm controls the quality of community structures through controlling (1) the number of clauses whose variables have a common community, which we call intra-community clauses, and (2) the number of variables that only belong to one community, which we call intra-community variables. To study the combined effect of community structures and clause distributions on the hardness of SAT formulas, we measure solving runtimes of two solvers, gluHack (a leading CDCL solver) and CPSparrow (a leading SLS solver), on the generated SAT formulas under different groups of parameter settings. Through extensive experiments, we obtain some noteworthy observations on the SAT formulas generated by the proposed algorithm: (1) The community structure has little or no effects on the hardness of SAT formulas with regard to CPSparrow but a strong effect with regard to gluHack. (2) Only when the proportion of true literals in a SAT formula in terms of the predefined solution is 0.5, SAT formulas are hard-to-solve with regard to gluHack; when this proportion is below 0.5, SAT formulas are hard-to-solve with regard to CPSparrow. (3) When the ratio of the number of clauses to that of variables is around 4.25, the SAT formulas are hard-to-solve with regard to both gluHack and CPSparrow.