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This paper presents an approach to synthesizing optimization test functions that couples generative adversarial networks and adaptive neuro-fuzzy systems. A generative adversarial network produces optimization landscapes from a database of known optimization test functions, and an adaptive neuro-fuzzy system performs regression on the generated landscapes to provide closed-form expressions. These expressions can be implemented as fuzzy basis function expansions. Eight databases of two-dimensional optimization landscapes reported in the literature are used to train the generative network. Exploratory landscape analysis over the generated samples reveals that the network can lead to new optimization landscapes with features of interest. In addition, fuzzy basis function expansions provide the best approximation results when compared against two symbolic regression frameworks over several selected landscapes. Examples are used to illustrate the ability of these functions to model complex surface artifacts such as plateaus. The proposed approach can be used as a mathematical collaboration tool that couples generative artificial and computational intelligence techniques to formulate high-dimensional optimization test problems from two-dimensional synthesized functions.

In recent decades, there has been an increasing demand for effectively handling high-dimensional multi-channel tensor data. Due to the inability to utilize internal structural information, Support Vector Machine (SVM) and its variations struggle to classify flattened tensor data, consequently resulting in the ‘curse of dimensionality’ issue. Furthermore, most of these methods can not directly apply to multiclass datasets. To overcome these challenges, we have developed a novel classification method called Multiclass Low-Rank Support Tensor Machine (MLRSTM). Our method is inspired by the well-established low-rank tensor hypothesis, which suggests a correlation between each channel of the feature tensor. Specifically, MLRSTM adopts the hinge loss function and introduces a convex approximation of tensor rank, the order-d Tensor Nuclear Norm (order-d TNN), in the regularization term. By leveraging the order-d TNN, MLRSTM effectively exploits the inherent structural information in tensor data to enhance generalization performance and avoid the curse of dimensionality. Moreover, we develop the Alternating Direction Method of Multipliers (ADMM) algorithm to optimize the convex problem inherent in training MLRSTM. Finally, comprehensive experiments validate the excellent performance of MLRSTM in tensor multi-classification tasks, showcasing its potential and efficacy in handling high-dimensional multi-channel tensor data.

The Differential Evolution (DE) algorithm is one of the most efficient algorithms for complex numerical optimization. However, the nature of differential mutation and crossover hinders the individuals from a major change and always guides them toward their superior neighbors. There's a lack of useful directional information to help the population escape from early convergence. To solve the above problem, this paper proposes a novel Triple-population-based Adaptive Differential Evolution (TPADE) to enhance the evolutionary efficiency in solving various complex numerical optimization problems. First, a population division method with symmetrical linear reduction is designed to divide the parent population of each iteration into three sub-populations of different sizes, i.e., superior sub-population, medium sub-population, and inferior sub-population. Each sub-population adopts distinct differential mutation and crossover operators to maintain balanced search directions. Second, a superior-trial-preserved selection mechanism is proposed to screen useful directional information to guide the next iteration of evolution. Third, an effective parameter adaptation strategy is designed with the linear population size reduction strategy to avoid redundant search. Experiments are then conducted to show that the TPADE exhibits well performance compared with eleven state-of-the-art DE variants, CEC winners, and their variants on the CEC'2014, CEC'2017, and CEC'2022 benchmark suites. The C++ source code of TPADE can be downloaded from https://github.com/DoubleGong/TPADE.

This paper addresses the path detectability verification problem for time-dependent systems modeled by time labeled Petri nets (TLPNs). To capture the information precisely, it may not be sufficient to estimate the current state by resorting to the partial system observation, and it is usually crucial to decide the path of a system to reach the current state. Path detectability characterizes a time-dependent system whose current state and the corresponding path can be uniquely determined after a real-time observation (RTO). Revised state class graphs (RSCGs) are proposed to capture the time information for the evolution of the RTO in a TLPN system. We demonstrate the time information overlap problem in the RSCG, i.e., several paths are associated with the same observable events and the same time instants, which leads to such paths that cannot be distinguished. The nodes required to be computed in the proposed RSCGs are always less or equal to those of the modified state class graphs reported in the literature, since the enumeration of all the states is avoided. Based on the RSCG, an RSCG observer is formulated to address the time information overlap problem and capture the number of such paths in the TLPN system. The efficiency analysis of this verification method is provided. In this paper, the results are applied to a real production system, exposing the practical value of the reported method.

In multi-view multi-label (MVML) learning, each sample is represented by several heterogeneous distinct feature representations while associated with a set of class labels simultaneously. To achieve MVML learning, most of the existing methods contribute to the recovery of a consistent subspace, i.e., a shared feature representation, among multiple views. Nevertheless, each view has its inherent specific properties used in the discrimination process of labels. These methods lose sight in the specific information exploitation, and therefore are easily trapped in a sub-optimal result. In this study, we present an optimization framework CSVL to solve the learning problem. The main technical contribution in CSVL is a formulation for MVML learning while consistent subspace across views, specific subspace for each view, and the correlations among labels are taken into account. Specifically, consistent subspace is recovered by imposing a low-rank constraint among multiple views, and specific subspace of each view is extra generated with $Frobenius$ norm. To further improve model generalization capability, we preserve both feature manifolds from multiple views and label correlations from multiple labels. Extensive experiments on 7 benchmark datasets show that our proposal CSVL has the advantages in MVML learning.

Complementary Label Learning (CLL) is a typical weakly supervised learning protocol, where each instance is associated with one complementary label to specify a class that the instance does not belong to. Current CLL approaches assume that complementary labels are uniformly sampled from all non-ground-truth labels, so as to implicitly and locally share complementary labels by solely reducing the logit of complementary label in one way or another. In this paper, we point out that, when the uniform assumption does not hold, existing CLL methods are weakened their ability to share complementary labels and fail in creating classifiers with large logit margin (LM), resulting in a significant performance drop. To address these issues, we instead present complementary logit margin (CLM) and empirically prove that increasing CLM contributes to the share of complementary labels under the biased CLL setting. Accordingly, we propose a surrogate complementary one-versus-rest loss (COVR) and demonstrate that optimization on COVR can effectively increase CLM with both theoretical and empirical evidences. Extensive experiments verify that the proposed COVR exhibits substantial improvement for both the biased CLL and even a more practical CLL setting: instance-dependent complementary label learning.

Multi-view clustering aims to group objects with high similarity into one group according to the heterogeneous features of different views. The graph-based clustering methods have obtained excellent results. However, there remain a few common drawbacks. For example, some methods do not consider graphs' high-order structure information. Thus, fuller data information cannot be obtained. In addition, some methods remove noise, outliers, and redundant information in the graph learning phase, resulting in the loss of graph information. Furthermore, using predefined graphs cannot exploit complementary information between views. A triple strategy-based multi-view clustering method is presented to solve the above issues. First, Laplacian graphs are used for fusion learning, and the underlying first-order and second-order structure information among views are explored simultaneously. Then, a label fusion scheme is designed to eliminate noise, outliers, and redundant information and to mine the intrinsic characteristics of data labels. Besides, the consistent label matrix in adaptive regression learning is used to explore complementary information between views in a mutually guided learning way. Finally, the objective function is solved by using an efficient iterative method. Six types of experiments are conducted on eleven real-world multi-view datasets, and the conclusions that can be drawn are: (1) the proposed algorithm achieves the best results in terms of clustering accuracy on ten datasets with an average accuracy improvement of 5.11% compared to other algorithms. Specifically, the accuracy improved by 9.05% on dataset HW and 10.95% on dataset Reuters compared to the second results; (2) The ablation experiments confirm that the different learning strategies included in the proposed algorithm allow it to achieve better clustering performance.

An accurate and efficient fault diagnosis method for battery systems is crucial to ensuring the safety of battery packs. Addressing the issue of insufficient actual fault data in battery operations, this paper proposes an intelligent fault diagnosis method based on feature-enhanced stochastic configuration networks and adversarial domain expansion of imbalanced battery fault data (AFDEM-FESCN). Firstly, we designed an adversarial fault domain data expansion method (AFDEM). By learning the distribution of fault data through adversarial training, the distribution of sample domains is balanced, thereby reducing model bias. Subsequently, we adjusted the distribution of SCN iterative parameters and added a linear feature layer. This enhances the feature extraction capability of the network through distribution overlay, enabling fault diagnosis. Finally, the effectiveness and feasibility of the proposed method were validated through a practical battery system fault diagnosis case, achieving a diagnostic accuracy of 92.1%. Experimental results demonstrate that the AFDEM-FESCN method exhibits good accuracy in battery system fault diagnosis, providing an effective solution to the challenge of imbalanced data in intelligent fault diagnosis.

Recently, Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been widely employed in solving Expensive Optimization Problems (EOPs) due to their efficiency in obtaining satisfactory solutions with limited resources. By leveraging historical data to construct surrogate models for approximation, SAEAs can significantly reduce the number of expensive fitness evaluations for EOPs. A hierarchical SAEA optimization framework based on evolutionary sampling methods has achieved remarkable success in High-dimensional EOPs (HEOPs), which can effectively balance the exploration and exploitation capabilities. However, the majority of existing hierarchical SAEAs focus on either switching between different sampling strategies or enhancing a single sampling strategy, potentially overlooking the potential to improve multiple sampling strategies simultaneously. In this paper, we propose a Surrogate-Assisted Differential Evolution with Multiple Sampling Mechanisms (SADE-MSM) to tackle HEOPs, incorporating three sampling strategies with different mechanisms. The contributions of SADE-MSM are summarized as follows: 1) A centroid sampling method is applied before iterative optimization to enhance the early exploration ability; 2) An improved global prescreening sampling strategy is introduced to balance the exploration and exploitation capabilities; 3) A local search sampling with the adaptive optimal region strategy is proposed, significantly improving the exploitation ability. To validate the performance of SADE-MSM, we compared it with the state-of-the-art SAEAs on benchmark problems with dimensions ranging from 30 to 500. Experimental results demonstrate that SADE-MSM has a significant performance superiority.

Group decision-making (GDM) characterized by complexity and uncertainty is an essential part of various life scenarios. Most existing researches lack tools to fuse information quickly and interpret decision results for partially formed decisions. This limitation is particularly noticeable when there is a need to improve the efficiency of GDM. To address this issue, a novel multi-level sequential three-way decision for group decision-making (S3W-GDM) method is constructed from the perspective of granular computing. This method simultaneously considers the vagueness, hesitation, and variation of GDM problems under double hierarchy hesitant fuzzy linguistic term sets (DHHFLTS) environment. First, for fusing information efficiently, a novel multi-level expert information fusion method is proposed, and the concepts of expert decision table and the extraction/aggregation of decision-leveled information based on the multi-level granularity are defined. Second, the neighborhood theory, outranking relation and regret theory (RT) are utilized to redesign the calculations of conditional probability and relative loss function. Then, the granular structure of DHHFLTS based on the sequential three-way decision (S3WD) is defined to improve the decision-making efficiency, and the decision-making strategy and interpretation of each decision-level are proposed. Furthermore, the algorithm of S3W-GDM is given. Finally, an illustrative example of diagnosis is presented, and the comparative and sensitivity analysis with other methods are performed to verify the efficiency and rationality of the proposed method.