Image-Based Benchmarking and Visualization for Large-Scale Global Optimization

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.

Multi-objective Optimal Control of Dynamic Integrated Model of Climate and Economy: Evolution in Action

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 Origami Optimization (SOO): A Novel Approach for Solving Large-scale Expensive Optimization Problems Efficiently

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. In this paper, we propose a simple novel algorithm called Shahryar Origami Optimization (SOO) algorithm 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 SOO algorithm in lower dimensions. The results show that SOO is beneficial not only in large-scale problems, but also in low-scale optimization problems.

Learning Autoencoded Radon Projections

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.

Opposition based Ensemble Micro Differential Evolution

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.

Classification and Retrieval of Digital Pathology Scans: A New Dataset

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.

Diversity Enhancement for Micro-Differential Evolution

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.

Learning Opposites Using Neural Networks

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.

Automated Resolution Selection for Image Segmentation

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.

Evolutionary Projection Selection for Radon Barcodes

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.