Varun Ojha

Varun Ojha, Jon Timmis, Giuseppe Nicosia

We present a comprehensive global sensitivity analysis of two single-objective and two multi-objective state-of-the-art global optimization evolutionary algorithms as an algorithm configuration problem. That is, we investigate the quality of influence hyperparameters have on the performance of algorithms in terms of their direct effect and interaction effect with other hyperparameters. Using three sensitivity analysis methods, Morris LHS, Morris, and Sobol, to systematically analyze tunable hyperparameters of covariance matrix adaptation evolutionary strategy, differential evolution, non-dominated sorting genetic algorithm III, and multi-objective evolutionary algorithm based on decomposition, the framework reveals the behaviors of hyperparameters to sampling methods and performance metrics. That is, it answers questions like what hyperparameters influence patterns, how they interact, how much they interact, and how much their direct influence is. Consequently, the ranking of hyperparameters suggests their order of tuning, and the pattern of influence reveals the stability of the algorithms.

Varun Ojha, Bartolomeo Panto, Giuseppe Nicosia

The paper proposes a novel adaptive search space decomposition method and a novel gradient-free optimization-based formulation for the pre- and post-buckling analyses of space truss structures. Space trusses are often employed in structural engineering to build large steel constructions, such as bridges and domes, whose structural response is characterized by large displacements. Therefore, these structures are vulnerable to progressive collapses due to local or global buckling effects, leading to sudden failures. The method proposed in this paper allows the analysis of the load-equilibrium path of truss structures to permanent and variable loading, including stable and unstable equilibrium stages and explicitly considering geometric nonlinearities. The goal of this work is to determine these equilibrium stages via optimization of the Lagrangian kinematic parameters of the system, determining the global equilibrium. However, this optimization problem is non-trivial due to the undefined parameter domain and the sensitivity and interaction among the Lagrangian parameters. Therefore, we propose formulating this problem as a nonlinear, multimodal, unconstrained, continuous optimization problem and develop a novel adaptive search space decomposition method, which progressively and adaptively re-defines the search domain (hypersphere) to evaluate the equilibrium of the system using a gradient-free optimization algorithm. We tackle three benchmark problems and evaluate a medium-sized test representing a real structural problem in this paper. The results are compared to those available in the literature regarding displacement-load curves and deformed configurations. The accuracy and robustness of the adopted methodology show a high potential of gradient-free algorithms in analyzing space truss structures.

Zhenyu Liu, Haoran Duan, Huizhi Liang et al.

Adversarial training is one of the most effective methods for enhancing model robustness. Recent approaches incorporate adversarial distillation in adversarial training architectures. However, we notice two scenarios of defense methods that limit their performance: (1) Previous methods primarily use static ground truth for adversarial training, but this often causes robust overfitting; (2) The loss functions are either Mean Squared Error or KL-divergence leading to a sub-optimal performance on clean accuracy. To solve those problems, we propose a dynamic label adversarial training (DYNAT) algorithm that enables the target model to gradually and dynamically gain robustness from the guide model's decisions. Additionally, we found that a budgeted dimension of inner optimization for the target model may contribute to the trade-off between clean accuracy and robust accuracy. Therefore, we propose a novel inner optimization method to be incorporated into the adversarial training. This will enable the target model to adaptively search for adversarial examples based on dynamic labels from the guiding model, contributing to the robustness of the target model. Extensive experiments validate the superior performance of our approach.

Punitha Jaikumar, Remy Vandaele, Varun Ojha

This paper proposes a methodological approach with a transfer learning scheme for plastic waste bottle detection and instance segmentation using the \textit{mask region proposal convolutional neural network} (Mask R-CNN). Plastic bottles constitute one of the major pollutants posing a serious threat to the environment both in oceans and on land. The automated identification and segregation of bottles can facilitate plastic waste recycling. We prepare a custom-made dataset of 192 bottle images with pixel-by pixel-polygon annotation for the automatic segmentation task. The proposed transfer learning scheme makes use of a Mask R-CNN model pre-trained on the Microsoft COCO dataset. We present a comprehensive scheme for fine-tuning the base pre-trained Mask-RCNN model on our custom dataset. Our final fine-tuned model has achieved 59.4 \textit{mean average precision} (mAP), which corresponds to the MS COCO metric. The results indicate a promising application of deep learning for detecting waste bottles.

Ruikai Li, Xinrun Li, Mengwei Xie et al.

Online High-Definition (HD) map construction is pivotal for autonomous driving. While recent approaches leverage historical temporal fusion to improve performance, we identify a critical safety flaw in this paradigm: it is inherently ``spatially backward-looking." These methods predominantly enhance map reconstruction in traversed areas, offering minimal improvement for the unseen road ahead. Crucially, our analysis of downstream planning tasks reveals a severe asymmetry: while rearward perception errors are often tolerable, inaccuracies in the forward region directly precipitate hazardous driving maneuvers. To bridge this safety gap, we propose AMap, a novel framework for Ahead-aware online HD Mapping. We pioneer a ``distill-from-future" paradigm, where a teacher model with privileged access to future temporal contexts guides a lightweight student model restricted to the current frame. This process implicitly compresses prospective knowledge into the student model, endowing it with ``look-ahead" capabilities at zero inference-time cost. Technically, we introduce a Multi-Level BEV Distillation strategy with spatial masking and an Asymmetric Query Adaptation module to effectively transfer future-aware representations to the student's static queries. Extensive experiments on the nuScenes and Argoverse 2 benchmark demonstrate that AMap significantly enhances current-frame perception. Most notably, it outperforms state-of-the-art temporal models in critical forward regions while maintaining the efficiency of single current frame inference.

Ziwei Zheng, Huizhi Liang, Vaclav Snasel et al.

We scrutinize the structural and operational aspects of deep learning models, particularly focusing on the nuances of learnable parameters (weight) statistics, distribution, node interaction, and visualization. By establishing correlations between variance in weight patterns and overall network performance, we investigate the varying (optimal and suboptimal) performances of various deep-learning models. Our empirical analysis extends across widely recognized datasets such as MNIST, Fashion-MNIST, and CIFAR-10, and various deep learning models such as deep neural networks (DNNs), convolutional neural networks (CNNs), and vision transformer (ViT), enabling us to pinpoint characteristics of learnable parameters that correlate with successful networks. Through extensive experiments on the diverse architectures of deep learning models, we shed light on the critical factors that influence the functionality and efficiency of DNNs. Our findings reveal that successful networks, irrespective of datasets or models, are invariably similar to other successful networks in their converged weights statistics and distribution, while poor-performing networks vary in their weights. In addition, our research shows that the learnable parameters of widely varied deep learning models such as DNN, CNN, and ViT exhibit similar learning characteristics.

Xingyu Miao, Haoran Duan, Varun Ojha et al.

In this work, we propose a novel Trajectory Score Matching (TSM) method that aims to solve the pseudo ground truth inconsistency problem caused by the accumulated error in Interval Score Matching (ISM) when using the Denoising Diffusion Implicit Models (DDIM) inversion process. Unlike ISM which adopts the inversion process of DDIM to calculate on a single path, our TSM method leverages the inversion process of DDIM to generate two paths from the same starting point for calculation. Since both paths start from the same starting point, TSM can reduce the accumulated error compared to ISM, thus alleviating the problem of pseudo ground truth inconsistency. TSM enhances the stability and consistency of the model's generated paths during the distillation process. We demonstrate this experimentally and further show that ISM is a special case of TSM. Furthermore, to optimize the current multi-stage optimization process from high-resolution text to 3D generation, we adopt Stable Diffusion XL for guidance. In response to the issues of abnormal replication and splitting caused by unstable gradients during the 3D Gaussian splatting process when using Stable Diffusion XL, we propose a pixel-by-pixel gradient clipping method. Extensive experiments show that our model significantly surpasses the state-of-the-art models in terms of visual quality and performance. Code: \url{https://github.com/xingy038/Dreamer-XL}.

Feng Xiong, Thanet Markchom, Ziwei Zheng et al.

SemEval-2024 Task 8 introduces the challenge of identifying machine-generated texts from diverse Large Language Models (LLMs) in various languages and domains. The task comprises three subtasks: binary classification in monolingual and multilingual (Subtask A), multi-class classification (Subtask B), and mixed text detection (Subtask C). This paper focuses on Subtask A & B. Each subtask is supported by three datasets for training, development, and testing. To tackle this task, two methods: 1) using traditional machine learning (ML) with natural language preprocessing (NLP) for feature extraction, and 2) fine-tuning LLMs for text classification. The results show that transformer models, particularly LoRA-RoBERTa, exceed traditional ML methods in effectiveness, with majority voting being particularly effective in multilingual contexts for identifying machine-generated texts.

Haoran Duan, Shidong Wang, Varun Ojha et al.

While traditional feature engineering for Human Activity Recognition (HAR) involves a trial-anderror process, deep learning has emerged as a preferred method for high-level representations of sensor-based human activities. However, most deep learning-based HAR requires a large amount of labelled data and extracting HAR features from unlabelled data for effective deep learning training remains challenging. We, therefore, introduce a deep semi-supervised HAR approach, MixHAR, which concurrently uses labelled and unlabelled activities. Our MixHAR employs a linear interpolation mechanism to blend labelled and unlabelled activities while addressing both inter- and intra-activity variability. A unique challenge identified is the activityintrusion problem during mixing, for which we propose a mixing calibration mechanism to mitigate it in the feature embedding space. Additionally, we rigorously explored and evaluated the five conventional/popular deep semi-supervised technologies on HAR, acting as the benchmark of deep semi-supervised HAR. Our results demonstrate that MixHAR significantly improves performance, underscoring the potential of deep semi-supervised techniques in HAR.

Chandresh Pravin, Ivan Martino, Giuseppe Nicosia et al.

We propose a systematic analysis of deep neural networks (DNNs) based on a signal processing technique for network parameter removal, in the form of synaptic filters that identifies the fragility, robustness and antifragility characteristics of DNN parameters. Our proposed analysis investigates if the DNN performance is impacted negatively, invariantly, or positively on both clean and adversarially perturbed test datasets when the DNN undergoes synaptic filtering. We define three \textit{filtering scores} for quantifying the fragility, robustness and antifragility characteristics of DNN parameters based on the performances for (i) clean dataset, (ii) adversarial dataset, and (iii) the difference in performances of clean and adversarial datasets. We validate the proposed systematic analysis on ResNet-18, ResNet-50, SqueezeNet-v1.1 and ShuffleNet V2 x1.0 network architectures for MNIST, CIFAR10 and Tiny ImageNet datasets. The filtering scores, for a given network architecture, identify network parameters that are invariant in characteristics across different datasets over learning epochs. Vice-versa, for a given dataset, the filtering scores identify the parameters that are invariant in characteristics across different network architectures. We show that our synaptic filtering method improves the test accuracy of ResNet and ShuffleNet models on adversarial datasets when only the robust and antifragile parameters are selectively retrained at any given epoch, thus demonstrating applications of the proposed strategy in improving model robustness.

Pengru Deng, Jiapeng Yao, Chun Li et al.

Visual-Spatial Systems has become increasingly essential in concrete crack inspection. However, existing methods often lacks adaptability to diverse scenarios, exhibits limited robustness in image-based approaches, and struggles with curved or complex geometries. To address these limitations, an innovative framework for two-dimensional (2D) crack detection, three-dimensional (3D) reconstruction, and 3D automatic crack measurement was proposed by integrating computer vision technologies and multi-modal Simultaneous localization and mapping (SLAM) in this study. Firstly, building on a base DeepLabv3+ segmentation model, and incorporating specific refinements utilizing foundation model Segment Anything Model (SAM), we developed a crack segmentation method with strong generalization across unfamiliar scenarios, enabling the generation of precise 2D crack masks. To enhance the accuracy and robustness of 3D reconstruction, Light Detection and Ranging (LiDAR) point clouds were utilized together with image data and segmentation masks. By leveraging both image- and LiDAR-SLAM, we developed a multi-frame and multi-modal fusion framework that produces dense, colorized point clouds, effectively capturing crack semantics at a 3D real-world scale. Furthermore, the crack geometric attributions were measured automatically and directly within 3D dense point cloud space, surpassing the limitations of conventional 2D image-based measurements. This advancement makes the method suitable for structural components with curved and complex 3D geometries. Experimental results across various concrete structures highlight the significant improvements and unique advantages of the proposed method, demonstrating its effectiveness, accuracy, and robustness in real-world applications.

Rui Sun, Haoran Duan, Jiahua Dong et al.

We introduce a rehearsal-free federated domain incremental learning framework, RefFiL, based on a global prompt-sharing paradigm to alleviate catastrophic forgetting challenges in federated domain-incremental learning, where unseen domains are continually learned. Typical methods for mitigating forgetting, such as the use of additional datasets and the retention of private data from earlier tasks, are not viable in federated learning (FL) due to devices' limited resources. Our method, RefFiL, addresses this by learning domain-invariant knowledge and incorporating various domain-specific prompts from the domains represented by different FL participants. A key feature of RefFiL is the generation of local fine-grained prompts by our domain adaptive prompt generator, which effectively learns from local domain knowledge while maintaining distinctive boundaries on a global scale. We also introduce a domain-specific prompt contrastive learning loss that differentiates between locally generated prompts and those from other domains, enhancing RefFiL's precision and effectiveness. Compared to existing methods, RefFiL significantly alleviates catastrophic forgetting without requiring extra memory space, making it ideal for privacy-sensitive and resource-constrained devices.

Zhenyu Liu, Huizhi Liang, Rajiv Ranjan et al.

The robustness of Deep Neural Network models is crucial for defending models against adversarial attacks. Recent defense methods have employed collaborative learning frameworks to enhance model robustness. Two key limitations of existing methods are (i) insufficient guidance of the target model via loss functions and (ii) non-collaborative adversarial generation. We, therefore, propose a dual regularization loss (D2R Loss) method and a collaborative adversarial generation (CAG) strategy for adversarial training. D2R loss includes two optimization steps. The adversarial distribution and clean distribution optimizations enhance the target model's robustness by leveraging the strengths of different loss functions obtained via a suitable function space exploration to focus more precisely on the target model's distribution. CAG generates adversarial samples using a gradient-based collaboration between guidance and target models. We conducted extensive experiments on three benchmark databases, including CIFAR-10, CIFAR-100, Tiny ImageNet, and two popular target models, WideResNet34-10 and PreActResNet18. Our results show that D2R loss with CAG produces highly robust models.

Ziwei Zheng, Huizhi Liang, Vaclav Snasel et al.

Deep learning networks excel at classification, yet identifying minimal architectures that reliably solve a task remains challenging. We present a computational methodology for systematically exploring and analyzing the relationships among convergence, pruning, and quantization. The workflow first performs a structured design sweep across a large set of architectures, then evaluates convergence behavior, pruning sensitivity, and quantization robustness on representative models. Focusing on well-known image classification of increasing complexity, and across Deep Neural Networks, Convolutional Neural Networks, and Vision Transformers, our initial results show that, despite architectural diversity, performance is largely invariant and learning dynamics consistently exhibit three regimes: unstable, learning, and overfitting. We further characterize the minimal learnable parameters required for stable learning, uncover distinct convergence and pruning phases, and quantify the effect of reduced numeric precision on trainable parameters. Aligning with intuition, the results confirm that deeper architectures are more resilient to pruning than shallower ones, with parameter redundancy as high as 60%, and quantization impacts models with fewer learnable parameters more severely and has a larger effect on harder image datasets. These findings provide actionable guidance for selecting compact, stable models under pruning and low-precision constraints in image classification.

Shoumeng Qiu, Xinrun Li, Yang Long et al.

The online construction of vectorized high-definition (HD) maps is a cornerstone of modern autonomous driving systems. State-of-the-art approaches, particularly those based on the DETR framework, formulate this as an instance detection problem. However, their reliance on independent, learnable object queries results in a predominantly local query perspective, neglecting the inherent global representation within HD maps. In this work, we propose \textbf{MapGR} (\textbf{G}lobal \textbf{R}epresentation learning for HD \textbf{Map} construction), an architecture designed to learn and utilize a global representations from queries. Our method introduces two synergistic modules: a Global Representation Learning (GRL) module, which encourages the distribution of all queries to better align with the global map through a carefully designed holistic segmentation task, and a Global Representation Guidance (GRG) module, which endows each individual query with explicit, global-level contextual information to facilitate its optimization. Evaluations on the nuScenes and Argoverse2 datasets validate the efficacy of our approach, demonstrating substantial improvements in mean Average Precision (mAP) compared to leading baselines.

Zhenyu Liu, Varun Ojha

Adversarial training is the most effective defense against adversarial attacks. The effectiveness of the adversarial attacks has been on the design of its loss function and regularization term. The most widely used loss function in adversarial training is cross-entropy and mean squared error (MSE) as its regularization objective. However, MSE enforces overly uniform optimization between two output distributions during training, which limits its robustness in adversarial training scenarios. To address this issue, we revisit the idea of mutual learning (originally designed for knowledge distillation) and propose two novel regularization strategies tailored for adversarial training: (i) weighted adversarial mutual regularization and (ii) adversarial generalization regularization. In the former, we formulate a decomposed adversarial mutual Kullback-Leibler divergence (KL-divergence) loss, which allows flexible control over the optimization process by assigning unequal weights to the main and auxiliary objectives. In the latter, we introduce an additional clean target distribution into the adversarial training objective, improving generalization and enhancing model robustness. Extensive experiments demonstrate that our proposed methods significantly improve adversarial robustness compared to existing regularization-based approaches.

Manish Bhardwaj, Huizhi Liang, Ashwin Sivaharan et al.

Sarcopenia is a progressive loss of muscle mass and function linked to poor surgical outcomes such as prolonged hospital stays, impaired mobility, and increased mortality. Although it can be assessed through cross-sectional imaging by measuring skeletal muscle area (SMA), the process is time-consuming and adds to clinical workloads, limiting timely detection and management; however, this process could become more efficient and scalable with the assistance of artificial intelligence applications. This paper presents high-quality three-dimensional cross-sectional computed tomography (CT) images of patients with sarcopenia collected at the Freeman Hospital, Newcastle upon Tyne Hospitals NHS Foundation Trust. Expert clinicians manually annotated the SMA at the third lumbar vertebra, generating precise segmentation masks. We develop deep-learning models to measure SMA in CT images and automate this task. Our methodology employed transfer learning and self-supervised learning approaches using labelled and unlabeled CT scan datasets. While we developed qualitative assessment models for detecting sarcopenia, we observed that the quantitative assessment of SMA is more precise and informative. This approach also mitigates the issue of class imbalance and limited data availability. Our model predicted the SMA, on average, with an error of +-3 percentage points against the manually measured SMA. The average dice similarity coefficient of the predicted masks was 93%. Our results, therefore, show a pathway to full automation of sarcopenia assessment and detection.

Zhenyu Liu, Huizhi Liang, Xinrun Li et al.

Adversarial distillation (AD) is a knowledge distillation technique that facilitates the transfer of robustness from teacher deep neural network (DNN) models to lightweight target (student) DNN models, enabling the target models to perform better than only training the student model independently. Some previous works focus on using a small, learnable teacher (guide) model to improve the robustness of a student model. Since a learnable guide model starts learning from scratch, maintaining its optimal state for effective knowledge transfer during co-training is challenging. Therefore, we propose a novel Adaptive Guidance Adversarial Training (AdaGAT) method. Our method, AdaGAT, dynamically adjusts the training state of the guide model to install robustness to the target model. Specifically, we develop two separate loss functions as part of the AdaGAT method, allowing the guide model to participate more actively in backpropagation to achieve its optimal state. We evaluated our approach via extensive experiments on three datasets: CIFAR-10, CIFAR-100, and TinyImageNet, using the WideResNet-34-10 model as the target model. Our observations reveal that appropriately adjusting the guide model within a certain accuracy range enhances the target model's robustness across various adversarial attacks compared to a variety of baseline models.

Rui Sun, Yumin Zhang, Varun Ojha et al.

We propose Exemplar-Condensed federated class-incremental learning (ECoral) to distil the training characteristics of real images from streaming data into informative rehearsal exemplars. The proposed method eliminates the limitations of exemplar selection in replay-based approaches for mitigating catastrophic forgetting in federated continual learning (FCL). The limitations particularly related to the heterogeneity of information density of each summarized data. Our approach maintains the consistency of training gradients and the relationship to past tasks for the summarized exemplars to represent the streaming data compared to the original images effectively. Additionally, our approach reduces the information-level heterogeneity of the summarized data by inter-client sharing of the disentanglement generative model. Extensive experiments show that our ECoral outperforms several state-of-the-art methods and can be seamlessly integrated with many existing approaches to enhance performance.

Varun Ojha, Giuseppe Nicosia

We propose a novel algorithm called Backpropagation Neural Tree (BNeuralT), which is a stochastic computational dendritic tree. BNeuralT takes random repeated inputs through its leaves and imposes dendritic nonlinearities through its internal connections like a biological dendritic tree would do. Considering the dendritic-tree like plausible biological properties, BNeuralT is a single neuron neural tree model with its internal sub-trees resembling dendritic nonlinearities. BNeuralT algorithm produces an ad hoc neural tree which is trained using a stochastic gradient descent optimizer like gradient descent (GD), momentum GD, Nesterov accelerated GD, Adagrad, RMSprop, or Adam. BNeuralT training has two phases, each computed in a depth-first search manner: the forward pass computes neural tree's output in a post-order traversal, while the error backpropagation during the backward pass is performed recursively in a pre-order traversal. A BNeuralT model can be considered a minimal subset of a neural network (NN), meaning it is a "thinned" NN whose complexity is lower than an ordinary NN. Our algorithm produces high-performing and parsimonious models balancing the complexity with descriptive ability on a wide variety of machine learning problems: classification, regression, and pattern recognition.

Chandresh Pravin, Ivan Martino, Giuseppe Nicosia et al.

We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks on the network. Adversarial robustness of neural networks has gained significant attention in recent times and highlights intrinsic weaknesses of deep learning networks against carefully constructed distortion applied to input images. In this paper, we evaluate the robustness of state-of-the-art image classification models trained on the MNIST and CIFAR10 datasets against the fast gradient sign method attack, a simple yet effective method of deceiving neural networks. Our method identifies the specific neurons of a network that are most affected by the adversarial attack being applied. We, therefore, propose to make fragile neurons more robust against these attacks by compressing features within robust neurons and amplifying the fragile neurons proportionally.

Haoran Duan, Fan Wan, Rui Sun et al.

Automatic Crowd behavior analysis can be applied to effectively help the daily transportation statistics and planning, which helps the smart city construction. As one of the most important keys, crowd counting has drawn increasing attention. Recent works achieved promising performance but relied on the supervised paradigm with expensive crowd annotations. To alleviate the annotation cost in real-world transportation scenarios, in this work we proposed a semi-supervised learning framework $S^{4}\textit{Crowd}$, which can leverage both unlabeled/labeled data for robust crowd counting. In the unsupervised pathway, two \textit{self-supervised losses} were proposed to simulate the crowd variations such as scale, illumination, based on which supervised information pseudo labels were generated and gradually refined. We also proposed a crowd-driven recurrent unit \textit{Gated-Crowd-Recurrent-Unit (GCRU)}, which can preserve discriminant crowd information by extracting second-order statistics, yielding pseudo labels with improved quality. A joint loss including both unsupervised/supervised information was proposed, and a dynamic weighting strategy was employed to balance the importance of the unsupervised loss and supervised loss at different training stages. We conducted extensive experiments on four popular crowd counting datasets in semi-supervised settings. Experimental results supported the effectiveness of each proposed component in our $S^{4}$Crowd framework. Our method achieved competitive performance in semi-supervised learning approaches on these crowd counting datasets.

Varun Ojha, Giuseppe Nicosia

We propose an algorithm and a new method to tackle the classification problems. We propose a multi-output neural tree (MONT) algorithm, which is an evolutionary learning algorithm trained by the non-dominated sorting genetic algorithm (NSGA)-III. Since evolutionary learning is stochastic, a hypothesis found in the form of MONT is unique for each run of evolutionary learning, i.e., each hypothesis (tree) generated bears distinct properties compared to any other hypothesis both in topological space and parameter-space. This leads to a challenging optimisation problem where the aim is to minimise the tree-size and maximise the classification accuracy. Therefore, the Pareto-optimality concerns were met by hypervolume indicator analysis. We used nine benchmark classification learning problems to evaluate the performance of the MONT. As a result of our experiments, we obtained MONTs which are able to tackle the classification problems with high accuracy. The performance of MONT emerged better over a set of problems tackled in this study compared with a set of well-known classifiers: multilayer perceptron, reduced-error pruning tree, naive Bayes classifier, decision tree, and support vector machine. Moreover, the performances of three versions of MONT's training using genetic programming, NSGA-II, and NSGA-III suggest that the NSGA-III gives the best Pareto-optimal solution.

Varun Ojha, Ajith Abraham, Vaclav Snasel

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi-Sugeno-Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems.