Shahryar Rahnamayan

Rasa Khosrowshahli, Stephen Asobiela, Beatrice Ombuki-Berman et al.

Machine unlearning aims to remove the influence of specific training samples while preserving the model's utility. Existing single-objective approaches, such as gradient ascent or random relabeling, often induce catastrophic forgetting due to conflicting optimization dynamics and unbounded forgetting objectives that cause the model to drift from its pre-trained knowledge. We propose Reference-Aligned UnLearning (RAUL), a multi-objective framework that jointly optimizes forgetting and retention by replacing unbounded loss maximization with a bounded KL alignment of predictions on forgotten samples toward a reference distribution representing unseen data, instantiated either as a uniform distribution or an empirical distribution from a held-out reference set, which constrains the forgetting objective and reduces gradient conflict with retention. The resulting multi-objective optimization (MOO) problem is solved via Jacobian descent, which aggregates multiple gradients into a direction that does not conflict. Our results demonstrate that RAUL achieves the closest gap compared to full retraining.

Amir H Gandomi, Kalyanmoy Deb, Ronald C Averill et al.

To solve complex real-world problems, heuristics and concept-based approaches can be used in order to incorporate information into the problem. In this study, a concept-based approach called variable functioning Fx is introduced to reduce the optimization variables and narrow down the search space. In this method, the relationships among one or more subset of variables are defined with functions using information prior to optimization; thus, instead of modifying the variables in the search process, the function variables are optimized. By using problem structure analysis technique and engineering expert knowledge, the $Fx$ method is used to enhance the steel frame design optimization process as a complex real-world problem. The proposed approach is coupled with particle swarm optimization and differential evolution algorithms and used for three case studies. The algorithms are applied to optimize the case studies by considering the relationships among column cross-section areas. The results show that $Fx$ can significantly improve both the convergence rate and the final design of a frame structure, even if it is only used for seeding.

Azam Asilian Bidgoli, Shahryar Rahnamayan, Taher Dehkharghanian et al.

One of the main obstacles of adopting digital pathology is the challenge of efficient processing of hyperdimensional digitized biopsy samples, called whole slide images (WSIs). Exploiting deep learning and introducing compact WSI representations are urgently needed to accelerate image analysis and facilitate the visualization and interpretability of pathology results in a postpandemic world. In this paper, we introduce a new evolutionary approach for WSI representation based on large-scale multi-objective optimization (LSMOP) of deep embeddings. We start with patch-based sampling to feed KimiaNet , a histopathology-specialized deep network, and to extract a multitude of feature vectors. Coarse multi-objective feature selection uses the reduced search space strategy guided by the classification accuracy and the number of features. In the second stage, the frequent features histogram (FFH), a novel WSI representation, is constructed by multiple runs of coarse LSMOP. Fine evolutionary feature selection is then applied to find a compact (short-length) feature vector based on the FFH and contributes to a more robust deep-learning approach to digital pathology supported by the stochastic power of evolutionary algorithms. We validate the proposed schemes using The Cancer Genome Atlas (TCGA) images in terms of WSI representation, classification accuracy, and feature quality. Furthermore, a novel decision space for multicriteria decision making in the LSMOP field is introduced. Finally, a patch-level visualization approach is proposed to increase the interpretability of deep features. The proposed evolutionary algorithm finds a very compact feature vector to represent a WSI (almost 14,000 times smaller than the original feature vectors) with 8% higher accuracy compared to the codes provided by the state-of-the-art methods.

Milad Sikaroudi, Shahryar Rahnamayan, H. R. Tizhoosh

Whole Slide Images (WSIs) in digital pathology are used to diagnose cancer subtypes. The difference in procedures to acquire WSIs at various trial sites gives rise to variability in the histopathology images, thus making consistent diagnosis challenging. These differences may stem from variability in image acquisition through multi-vendor scanners, variable acquisition parameters, and differences in staining procedure; as well, patient demographics may bias the glass slide batches before image acquisition. These variabilities are assumed to cause a domain shift in the images of different hospitals. It is crucial to overcome this domain shift because an ideal machine-learning model must be able to work on the diverse sources of images, independent of the acquisition center. A domain generalization technique is leveraged in this study to improve the generalization capability of a Deep Neural Network (DNN), to an unseen histopathology image set (i.e., from an unseen hospital/trial site) in the presence of domain shift. According to experimental results, the conventional supervised-learning regime generalizes poorly to data collected from different hospitals. However, the proposed hospital-agnostic learning can improve the generalization considering the low-dimensional latent space representation visualization, and classification accuracy results.

Pooria Mazaheri, Azam Asilian Bidgoli, Shahryar Rahnamayan et al.

Recently, deep learning has started to play an essential role in healthcare applications, including image search in digital pathology. Despite the recent progress in computer vision, significant issues remain for image searching in histopathology archives. A well-known problem is AI bias and lack of generalization. A more particular shortcoming of deep models is the ignorance toward search functionality. The former affects every model, the latter only search and matching. Due to the lack of ranking-based learning, researchers must train models based on the classification error and then use the resultant embedding for image search purposes. Moreover, deep models appear to be prone to internal bias even if using a large image repository of various hospitals. This paper proposes two novel ideas to improve image search performance. First, we use a ranking loss function to guide feature extraction toward the matching-oriented nature of the search. By forcing the model to learn the ranking of matched outputs, the representation learning is customized toward image search instead of learning a class label. Second, we introduce the concept of sequestering learning to enhance the generalization of feature extraction. By excluding the images of the input hospital from the matched outputs, i.e., sequestering the input domain, the institutional bias is reduced. The proposed ideas are implemented and validated through the largest public dataset of whole slide images. The experiments demonstrate superior results compare to the-state-of-art.

Milad Sikaroudi, Maryam Hosseini, Shahryar Rahnamayan et al.

We propose an exhaustive methodology that leverages all levels of feature abstraction, targeting an enhancement in the generalizability of image classification to unobserved hospitals. Our approach incorporates augmentation-based self-supervision with common distribution shifts in histopathology scenarios serving as the pretext task. This enables us to derive invariant features from training images without relying on training labels, thereby covering different abstraction levels. Moving onto the subsequent abstraction level, we employ a domain alignment module to facilitate further extraction of invariant features across varying training hospitals. To represent the highly specific features of participating hospitals, an encoder is trained to classify hospital labels, independent of their diagnostic labels. The features from each of these encoders are subsequently disentangled to minimize redundancy and segregate the features. This representation, which spans a broad spectrum of semantic information, enables the development of a model demonstrating increased robustness to unseen images from disparate distributions. Experimental results from the PACS dataset (a domain generalization benchmark), a synthetic dataset created by applying histopathology-specific jitters to the MHIST dataset (defining different domains with varied distribution shifts), and a Renal Cell Carcinoma dataset derived from four image repositories from TCGA, collectively indicate that our proposed model is adept at managing varying levels of image granularity. Thus, it shows improved generalizability when faced with new, out-of-distribution hospital images.

Sevil Zanjani Miyandoab, Shahryar Rahnamayan, Azam Asilian Bidgoli et al.

Feature selection plays a pivotal role in the data preprocessing and model-building pipeline, significantly enhancing model performance, interpretability, and resource efficiency across diverse domains. In population-based optimization methods, the generation of diverse individuals holds utmost importance for adequately exploring the problem landscape, particularly in highly multi-modal multi-objective optimization problems. Our study reveals that, in line with findings from several prior research papers, commonly employed crossover and mutation operations lack the capability to generate high-quality diverse individuals and tend to become confined to limited areas around various local optima. This paper introduces an augmentation to the diversity of the population in the well-established multi-objective scheme of the genetic algorithm, NSGA-II. This enhancement is achieved through two key components: the genuine initialization method and the substitution of the worst individuals with new randomly generated individuals as a re-initialization approach in each generation. The proposed multi-objective feature selection method undergoes testing on twelve real-world classification problems, with the number of features ranging from 2,400 to nearly 50,000. The results demonstrate that replacing the last front of the population with an equivalent number of new random individuals generated using the genuine initialization method and featuring a limited number of features substantially improves the population's quality and, consequently, enhances the performance of the multi-objective algorithm.

Farnaz Kheiri, Shahryar Rahnamayan, Masoud Makrehchi

In histopathology, human experts primarily rely on color as a means of enhancing contrast to interpret tissue morphology, whereas machine vision models process color as raw statistical information. This distinction raises a fundamental question: to what extent can pixel intensity alone, independent of structural and morphological cues, support cancer classification? To address this question, we systematically evaluated the standalone discriminative power of global color features while deliberately excluding all morphological information. Specifically, we extracted statistical color moments and discretized RGB and HSV color histograms, and assessed their performance across ten diverse experimental settings using classical machine learning classifiers. Our results demonstrate that color features alone can achieve strong performance in binary diagnostic tasks (e.g., benign versus malignant), with classification accuracies reaching up to 89%. This performance is likely attributable to global chromatic shifts associated with malignancy. Importantly, these simple color-based representations consistently outperformed random baselines by a substantial margin, indicating that raw color distributions encode a non-random and diagnostically relevant signal for cancer detection. Consequently, this study suggests that simple, computationally efficient color features can serve as an effective pre-screening tool. By identifying samples with strong chromatic indicators of malignancy, these lightweight models could function as a first-pass triage system, reducing the computational burden on complex deep learning architectures.

Rasa Khosrowshahli, Shahryar Rahnamayan, Beatrice Ombuki-Berman

Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In this modern deep learning era, the state-of-the-art DNN models have millions and billions of parameters, including weights and biases, making them huge-scale optimization problems in terms of search space. Tuning a huge number of parameters is a challenging task that causes vanishing/exploding gradients and overfitting; likewise, utilized loss functions do not exactly represent our targeted performance metrics. A practical solution to exploring large and complex solution space is meta-heuristic algorithms. Since DNNs exceed thousands and millions of parameters, even robust meta-heuristic algorithms, such as Differential Evolution, struggle to efficiently explore and converge in such huge-dimensional search spaces, leading to very slow convergence and high memory demand. To tackle the mentioned curse of dimensionality, the concept of blocking was recently proposed as a technique that reduces the search space dimensions by grouping them into blocks. In this study, we aim to introduce Histogram-based Blocking Differential Evolution (HBDE), a novel approach that hybridizes gradient-based and gradient-free algorithms to optimize parameters. Experimental results demonstrated that the HBDE could reduce the parameters in the ResNet-18 model from 11M to 3K during the training/optimizing phase by metaheuristics, namely, the proposed HBDE, which outperforms baseline gradient-based and parent gradient-free DE algorithms evaluated on CIFAR-10 and CIFAR-100 datasets showcasing its effectiveness with reduced computational demands for the very first time.

Ehsan Rokhsatyazdi, Shahryar Rahnamayan, Sevil Zanjani Miyandoab et al.

Training Artificial Neural Networks poses a challenging and critical problem in machine learning. Despite the effectiveness of gradient-based learning methods, such as Stochastic Gradient Descent (SGD), in training neural networks, they do have several limitations. For instance, they require differentiable activation functions, and cannot optimize a model based on several independent non-differentiable loss functions simultaneously; for example, the F1-score, which is used during testing, can be used during training when a gradient-free optimization algorithm is utilized. Furthermore, the training in any DNN can be possible with a small size of the training dataset. To address these concerns, we propose an efficient version of the gradient-free Coordinate Search (CS) algorithm, an instance of General Pattern Search methods, for training neural networks. The proposed algorithm can be used with non-differentiable activation functions and tailored to multi-objective/multi-loss problems. Finding the optimal values for weights of ANNs is a large-scale optimization problem. Therefore instead of finding the optimal value for each variable, which is the common technique in classical CS, we accelerate optimization and convergence by bundling the weights. In fact, this strategy is a form of dimension reduction for optimization problems. Based on the experimental results, the proposed method, in some cases, outperforms the gradient-based approach, particularly, in situations with insufficient labeled training data. The performance plots demonstrate a high convergence rate, highlighting the capability of our suggested method to find a reasonable solution with fewer function calls. As of now, the only practical and efficient way of training ANNs with hundreds of thousands of weights is gradient-based algorithms such as SGD or Adam. In this paper we introduce an alternative method for training ANN.

Sevil Zanjani Miyandoab, Shahryar Rahnamayan, Azam Asilian Bidgoli

A supervised feature selection method selects an appropriate but concise set of features to differentiate classes, which is highly expensive for large-scale datasets. Therefore, feature selection should aim at both minimizing the number of selected features and maximizing the accuracy of classification, or any other task. However, this crucial task is computationally highly demanding on many real-world datasets and requires a very efficient algorithm to reach a set of optimal features with a limited number of fitness evaluations. For this purpose, we have proposed the binary multi-objective coordinate search (MOCS) algorithm to solve large-scale feature selection problems. To the best of our knowledge, the proposed algorithm in this paper is the first multi-objective coordinate search algorithm. In this method, we generate new individuals by flipping a variable of the candidate solutions on the Pareto front. This enables us to investigate the effectiveness of each feature in the corresponding subset. In fact, this strategy can play the role of crossover and mutation operators to generate distinct subsets of features. The reported results indicate the significant superiority of our method over NSGA-II, on five real-world large-scale datasets, particularly when the computing budget is limited. Moreover, this simple hyper-parameter-free algorithm can solve feature selection much faster and more efficiently than NSGA-II.

Rasa Khosrowshahli, Shahryar Rahnamayan, Beatrice Ombuki-Berman

Deep neural networks suffer from storing millions and billions of weights in memory post-training, making challenging memory-intensive models to deploy on embedded devices. The weight-sharing technique is one of the popular compression approaches that use fewer weight values and share across specific connections in the network. In this paper, we propose a multi-objective evolutionary algorithm (MOEA) based compression framework independent of neural network architecture, dimension, task, and dataset. We use uniformly sized bins to quantize network weights into a single codebook (lookup table) for efficient weight representation. Using MOEA, we search for Pareto optimal $k$ bins by optimizing two objectives. Then, we apply the iterative merge technique to non-dominated Pareto frontier solutions by combining neighboring bins without degrading performance to decrease the number of bins and increase the compression ratio. Our approach is model- and layer-independent, meaning the weights are mixed in the clusters from any layer, and the uniform quantization method used in this work has $O(N)$ complexity instead of non-uniform quantization methods such as k-means with $O(Nkt)$ complexity. In addition, we use the center of clusters as the shared weight values instead of retraining shared weights, which is computationally expensive. The advantage of using evolutionary multi-objective optimization is that it can obtain non-dominated Pareto frontier solutions with respect to performance and shared weights. The experimental results show that we can reduce the neural network memory by $13.72 \sim14.98 \times$ on CIFAR-10, $11.61 \sim 12.99\times$ on CIFAR-100, and $7.44 \sim 8.58\times$ on ImageNet showcasing the effectiveness of the proposed deep neural network compression framework.

Amin Ibrahim, Azam Asilian Bidgoli, Shahryar Rahnamayan et al.

As the interest in multi- and many-objective optimization algorithms grows, the performance comparison of these algorithms becomes increasingly important. A large number of performance indicators for multi-objective optimization algorithms have been introduced, each of which evaluates these algorithms based on a certain aspect. Therefore, assessing the quality of multi-objective results using multiple indicators is essential to guarantee that the evaluation considers all quality perspectives. This paper proposes a novel multi-metric comparison method to rank the performance of multi-/ many-objective optimization algorithms based on a set of performance indicators. We utilize the Pareto optimality concept (i.e., non-dominated sorting algorithm) to create the rank levels of algorithms by simultaneously considering multiple performance indicators as criteria/objectives. As a result, four different techniques are proposed to rank algorithms based on their contribution at each Pareto level. This method allows researchers to utilize a set of existing/newly developed performance metrics to adequately assess/rank multi-/many-objective algorithms. The proposed methods are scalable and can accommodate in its comprehensive scheme any newly introduced metric. The method was applied to rank 10 competing algorithms in the 2018 CEC competition solving 15 many-objective test problems. The Pareto-optimal ranking was conducted based on 10 well-known multi-objective performance indicators and the results were compared to the final ranks reported by the competition, which were based on the inverted generational distance (IGD) and hypervolume indicator (HV) measures. The techniques suggested in this paper have broad applications in science and engineering, particularly in areas where multiple metrics are used for comparisons. Examples include machine learning and data mining.

Sevil Zanjani Miyandoab, Shahryar Rahnamayan, Azam Asilian Bidgoli

Feature selection is an expensive challenging task in machine learning and data mining aimed at removing irrelevant and redundant features. This contributes to an improvement in classification accuracy, as well as the budget and memory requirements for classification, or any other post-processing task conducted after feature selection. In this regard, we define feature selection as a multi-objective binary optimization task with the objectives of maximizing classification accuracy and minimizing the number of selected features. In order to select optimal features, we have proposed a binary Compact NSGA-II (CNSGA-II) algorithm. Compactness represents the population as a probability distribution to enhance evolutionary algorithms not only to be more memory-efficient but also to reduce the number of fitness evaluations. Instead of holding two populations during the optimization process, our proposed method uses several Probability Vectors (PVs) to generate new individuals. Each PV efficiently explores a region of the search space to find non-dominated solutions instead of generating candidate solutions from a small population as is the common approach in most evolutionary algorithms. To the best of our knowledge, this is the first compact multi-objective algorithm proposed for feature selection. The reported results for expensive optimization cases with a limited budget on five datasets show that the CNSGA-II performs more efficiently than the well-known NSGA-II method in terms of the hypervolume (HV) performance metric requiring less memory. The proposed method and experimental results are explained and analyzed in detail.

Soumen Sinha, Shahryar Rahnamayan, Azam Asilian Bidgoli

Efficient text embedding is crucial for large-scale natural language processing (NLP) applications, where storage and computational efficiency are key concerns. In this paper, we explore how using binary representations (barcodes) instead of real-valued features can be used for NLP embeddings derived from machine learning models such as BERT. Thresholding is a common method for converting continuous embeddings into binary representations, often using a fixed threshold across all features. We propose a Coordinate Search-based optimization framework that instead identifies the optimal threshold for each feature, demonstrating that feature-specific thresholds lead to improved performance in binary encoding. This ensures that the binary representations are both accurate and efficient, enhancing performance across various features. Our optimal barcode representations have shown promising results in various NLP applications, demonstrating their potential to transform text representation. We conducted extensive experiments and statistical tests on different NLP tasks and datasets to evaluate our approach and compare it to other thresholding methods. Binary embeddings generated using using optimal thresholds found by our method outperform traditional binarization methods in accuracy. This technique for generating binary representations is versatile and can be applied to any features, not just limited to NLP embeddings, making it useful for a wide range of domains in machine learning applications.

Azam Asilian Bidgoli, Shahryar Rahnamayan

Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel large-scale multi-objective evolutionary algorithm based on the search space shrinking, termed LMSSS, to tackle the challenges of feature selection particularly as a sparse optimization problem. The method includes a shrinking scheme to reduce dimensionality of the search space by eliminating irrelevant features before the main evolutionary process. This is achieved through a ranking-based filtering method that evaluates features based on their correlation with class labels and frequency in an initial, cost-effective evolutionary process. Additionally, a smart crossover scheme based on voting between parent solutions is introduced, giving higher weight to the parent with better classification accuracy. An intelligent mutation process is also designed to target features prematurely excluded from the population, ensuring they are evaluated in combination with other features. These integrated techniques allow the evolutionary process to explore the search space more efficiently and effectively, addressing the sparse and high-dimensional nature of large-scale feature selection problems. The effectiveness of the proposed algorithm is demonstrated through comprehensive experiments on 15 large-scale datasets, showcasing its potential to identify more accurate feature subsets compared to state-of-the-art large-scale feature selection algorithms. These results highlight LMSSS's capability to improve model performance and computational efficiency, setting a new benchmark in the field.

Shivam Kalra, Mohammed Adnan, Sobhan Hemati et al.

Deep learning methods such as convolutional neural networks (CNNs) are difficult to directly utilize to analyze whole slide images (WSIs) due to the large image dimensions. We overcome this limitation by proposing a novel two-stage approach. First, we extract a set of representative patches (called mosaic) from a WSI. Each patch of a mosaic is encoded to a feature vector using a deep network. The feature extractor model is fine-tuned using hierarchical target labels of WSIs, i.e., anatomic site and primary diagnosis. In the second stage, a set of encoded patch-level features from a WSI is used to compute the primary diagnosis probability through the proposed Pay Attention with Focus scheme, an attention-weighted averaging of predicted probabilities for all patches of a mosaic modulated by a trainable focal factor. Experimental results show that the proposed model can be robust, and effective for the classification of WSIs.

Aditya Sriram, Shivam Kalra, Morteza Babaie et al.

In this paper, we propose a novel image descriptor called Forming Local Intersections of Projections (FLIP) and its multi-resolution version (mFLIP) for representing histopathology images. The descriptor is based on the Radon transform wherein we apply parallel projections in small local neighborhoods of gray-level images. Using equidistant projection directions in each window, we extract unique and invariant characteristics of the neighborhood by taking the intersection of adjacent projections. Thereafter, we construct a histogram for each image, which we call the FLIP histogram. Various resolutions provide different FLIP histograms which are then concatenated to form the mFLIP descriptor. Our experiments included training common networks from scratch and fine-tuning pre-trained networks to benchmark our proposed descriptor. Experiments are conducted on the publicly available dataset KIMIA Path24 and KIMIA Path960. For both of these datasets, FLIP and mFLIP descriptors show promising results in all experiments.Using KIMIA Path24 data, FLIP outperformed non-fine-tuned Inception-v3 and fine-tuned VGG16 and mFLIP outperformed fine-tuned Inception-v3 in feature extracting.

Kyle Robert Harrison, Azam Asilian Bidgoli, Shahryar Rahnamayan et al.

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global optimization problems as images is proposed. In the proposed framework, the pixels visualize decision variables while the entire image represents the overall solution quality. This framework affords a number of benefits over existing visualization techniques including enhanced scalability (in terms of the number of decision variables), facilitation of standard image processing techniques, providing nearly infinite benchmark cases, and explicit alignment with human perception. Furthermore, image-based visualization can be used to visualize the optimization process in real-time, thereby allowing the user to ascertain characteristics of the search process as it is progressing. To the best of the authors' knowledge, this is the first realization of a dimension-preserving, scalable visualization framework that embeds the inherent relationship between decision space and objective space. The proposed framework is utilized with 10 different mapping schemes on an image-reconstruction problem that encompass continuous, discrete, binary, combinatorial, constrained, dynamic, and multi-objective optimization. The proposed framework is then demonstrated on arbitrary benchmark problems with known optima. Experimental results elucidate the flexibility and demonstrate how valuable information about the search process can be gathered via the proposed visualization framework.

Mostapha Kalami Heris, Shahryar Rahnamayan

One of the widely used models for studying economics of climate change is the Dynamic Integrated model of Climate and Economy (DICE), which has been developed by Professor William Nordhaus, one of the laureates of the 2018 Nobel Memorial Prize in Economic Sciences. Originally a single-objective optimal control problem has been defined on DICE dynamics, which is aimed to maximize the social welfare. In this paper, a bi-objective optimal control problem defined on DICE model, objectives of which are maximizing social welfare and minimizing the temperature deviation of atmosphere. This multi-objective optimal control problem solved using Non-Dominated Sorting Genetic Algorithm II (NSGA-II) also it is compared to previous works on single-objective version of the problem. The resulting Pareto front rediscovers the previous results and generalizes to a wide range of non-dominant solutions to minimize the global temperature deviation while optimizing the economic welfare. The previously used single-objective approach is unable to create such a variety of possibilities, hence, its offered solution is limited in vision and reachable performance. Beside this, resulting Pareto-optimal set reveals the fact that temperature deviation cannot go below a certain lower limit, unless we have significant technology advancement or positive change in global conditions.

Shahryar Rahnamayan, Seyed Jalaleddin Mousavirad

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their convergence, which is not affordable for practical applications since the most of them are computationally expensive. In other words, these problems are not only large-scale but also computationally expensive, that makes them very difficult to solve. There is no efficient surrogate model to support large-scale expensive global optimization (LSEGO) problems. As a result, the algorithms should address LSEGO problems using a limited computational budget to be applicable in real-world applications. Coordinate Descent (CD) algorithm is an optimization strategy based on the decomposition of a n-dimensional problem into n one-dimensional problem. To the best our knowledge, there is no significant study to assess benchmark functions with various dimensions and landscape properties to investigate CD algorithm. In this paper, we propose a modified Coordinate Descent algorithm (MCD) to tackle LSEGO problems with a limited computational budget. Our proposed algorithm benefits from two leading steps, namely, finding the region of interest and then shrinkage of the search space by folding it into the half with exponential speed. One of the main advantages of the proposed algorithm is being free of any control parameters, which makes it far from the intricacies of the tuning process. The proposed algorithm is compared with cooperative co-evolution with delta grouping on 20 benchmark functions with dimension 1000. Also, we conducted some experiments on CEC-2017, D=10, 30, 50, and 100, to investigate the behavior of MCD algorithm in lower dimensions. The results show that MCD is beneficial not only in large-scale problems, but also in low-scale optimization problems.

Aditya Sriram, Shivam Kalra, H. R. Tizhoosh et al.

Autoencoders have been recently used for encoding medical images. In this study, we design and validate a new framework for retrieving medical images by classifying Radon projections, compressed in the deepest layer of an autoencoder. As the autoencoder reduces the dimensionality, a multilayer perceptron (MLP) can be employed to classify the images. The integration of MLP promotes a rather shallow learning architecture which makes the training faster. We conducted a comparative study to examine the capabilities of autoencoders for different inputs such as raw images, Histogram of Oriented Gradients (HOG) and normalized Radon projections. Our framework is benchmarked on IRMA dataset containing $14,410$ x-ray images distributed across $57$ different classes. Experiments show an IRMA error of $313$ (equivalent to $\approx 82\%$ accuracy) outperforming state-of-the-art works on retrieval from IRMA dataset using autoencoders.

Hojjat Salehinejad, Shahryar Rahnamayan, Hamid R. Tizhoosh

Differential evolution (DE) algorithm with a small population size is called Micro-DE (MDE). A small population size decreases the computational complexity but also reduces the exploration ability of DE by limiting the population diversity. In this paper, we propose the idea of combining ensemble mutation scheme selection and opposition-based learning concepts to enhance the diversity of population in MDE at mutation and selection stages. The proposed algorithm enhances the diversity of population by generating a random mutation scale factor per individual and per dimension, randomly assigning a mutation scheme to each individual in each generation, and diversifying individuals selection using opposition-based learning. This approach is easy to implement and does not require the setting of mutation scheme selection and mutation scale factor. Experimental results are conducted for a variety of objective functions with low and high dimensionality on the CEC Black- Box Optimization Benchmarking 2015 (CEC-BBOB 2015). The results show superior performance of the proposed algorithm compared to the other micro-DE algorithms.

Morteza Babaie, Shivam Kalra, Aditya Sriram et al.

In this paper, we introduce a new dataset, \textbf{Kimia Path24}, for image classification and retrieval in digital pathology. We use the whole scan images of 24 different tissue textures to generate 1,325 test patches of size 1000$\times$1000 (0.5mm$\times$0.5mm). Training data can be generated according to preferences of algorithm designer and can range from approximately 27,000 to over 50,000 patches if the preset parameters are adopted. We propose a compound patch-and-scan accuracy measurement that makes achieving high accuracies quite challenging. In addition, we set the benchmarking line by applying LBP, dictionary approach and convolutional neural nets (CNNs) and report their results. The highest accuracy was 41.80\% for CNN.

Shivam Kalra, Aditya Sriram, Shahryar Rahnamayan et al.

Many research works have successfully extended algorithms such as evolutionary algorithms, reinforcement agents and neural networks using "opposition-based learning" (OBL). Two types of the "opposites" have been defined in the literature, namely \textit{type-I} and \textit{type-II}. The former are linear in nature and applicable to the variable space, hence easy to calculate. On the other hand, type-II opposites capture the "oppositeness" in the output space. In fact, type-I opposites are considered a special case of type-II opposites where inputs and outputs have a linear relationship. However, in many real-world problems, inputs and outputs do in fact exhibit a nonlinear relationship. Therefore, type-II opposites are expected to be better in capturing the sense of "opposition" in terms of the input-output relation. In the absence of any knowledge about the problem at hand, there seems to be no intuitive way to calculate the type-II opposites. In this paper, we introduce an approach to learn type-II opposites from the given inputs and their outputs using the artificial neural networks (ANNs). We first perform \emph{opposition mining} on the sample data, and then use the mined data to learn the relationship between input $x$ and its opposite $\breve{x}$. We have validated our algorithm using various benchmark functions to compare it against an evolving fuzzy inference approach that has been recently introduced. The results show the better performance of a neural approach to learn the opposites. This will create new possibilities for integrating oppositional schemes within existing algorithms promising a potential increase in convergence speed and/or accuracy.

Fares Al-Qunaieer, Hamid R. Tizhoosh, Shahryar Rahnamayan

It is well-known in image processing that computational cost increases rapidly with the number and dimensions of the images to be processed. Several fields, such as medical imaging, routinely use numerous very large images, which might also be 3D and/or captured at several frequency bands, all adding to the computational expense. Multiresolution analysis is a method of increasing the efficiency of the segmentation process. One multiresolution approach is the coarse-to-fine segmentation strategy, whereby the segmentation starts at a coarse resolution and is then fine-tuned during subsequent steps. The starting resolution for segmentation is generally selected arbitrarily with no clear selection criteria. The research reported in this paper showed that starting from different resolutions for image segmentation results in different accuracies and computational times, even for images of the same category (depicting similar scenes or objects). An automated method for resolution selection for an input image would thus be beneficial. This paper introduces a framework for the automated selection of the best resolution for image segmentation. We propose a measure for defining the best resolution based on user/system criteria, offering a trade-off between accuracy and computation time. A learning approach is then introduced for the selection of the resolution, whereby extracted image features are mapped to the previously determined best resolution. In the learning process, class (i.e., resolution) distribution is generally imbalanced, making effective learning from the data difficult. Experiments conducted with three datasets using two different segmentation algorithms show that the resolutions selected through learning enable much faster segmentation than the original ones, while retaining at least the original accuracy.

Hamid R. Tizhoosh, Shahryar Rahnamayan

Recently, Radon transformation has been used to generate barcodes for tagging medical images. The under-sampled image is projected in certain directions, and each projection is binarized using a local threshold. The concatenation of the thresholded projections creates a barcode that can be used for tagging or annotating medical images. A small number of equidistant projections, e.g., 4 or 8, is generally used to generate short barcodes. However, due to the diverse nature of digital images, and since we are only working with a small number of projections (to keep the barcode short), taking equidistant projections may not be the best course of action. In this paper, we proposed to find $n$ optimal projections, whereas $n\!<\!180$, in order to increase the expressiveness of Radon barcodes. We show examples for the exhaustive search for the simple case when we attempt to find 4 best projections out of 16 equidistant projections and compare it with the evolutionary approach in order to establish the benefit of the latter when operating on a small population size as in the case of micro-DE. We randomly selected 10 different classes from IRMA dataset (14,400 x-ray images in 58 classes) and further randomly selected 5 images per class for our tests.

Hojjat Salehinejad, Shahryar Rahnamayan, Hamid R. Tizhoosh

The differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. In contrast, micro-DE (MDE) algorithms employ a very small population size, which can converge faster to a reasonable solution. However, these algorithms are vulnerable to a premature convergence as well as to high risk of stagnation. In this paper, MDE algorithm with vectorized random mutation factor (MDEVM) is proposed, which utilizes the small size population benefit while empowers the exploration ability of mutation factor through randomizing it in the decision variable level. The idea is supported by analyzing mutation factor using Monte-Carlo based simulations. To facilitate the usage of MDE algorithms with very-small population sizes, new mutation schemes for population sizes less than four are also proposed. Furthermore, comprehensive comparative simulations and analysis on performance of the MDE algorithms over various mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, and mutation factor ranges are conducted by considering population diversity analysis for stagnation and trapping in local optimum situations. The studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance and convergence speed of the proposed MDEVM algorithm.

Hamid R. Tizhoosh, Shahryar Rahnamayan

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.