An Integrated Method Based on PSO and EDA for the Max-Cut Problem

The max-cut problem is NP-hard combinatorial optimization problem with many real world applications. In this paper, we propose an integrated method based on particle swarm optimization and estimation of distribution algorithm (PSO-EDA) for solving the max-cut problem. The integrated algorithm overcomes the shortcomings of particle swarm optimization and estimation of distribution algorithm. To enhance the performance of the PSO-EDA, a fast local search procedure is applied. In addition, a path relinking procedure is developed to intensify the search. To evaluate the performance of PSO-EDA, extensive experiments were carried out on two sets of benchmark instances with 800 to 20000 vertices from the literature. Computational results and comparisons show that PSO-EDA significantly outperforms the existing PSO-based and EDA-based algorithms for the max-cut problem. Compared with other best performing algorithms, PSO-EDA is able to find very competitive results in terms of solution quality

An Integrated Method Based on PSO and EDA for the Max-Cut Problem

The max-cut problem is NP-hard combinatorial optimization problem with many real world applications. In this paper, we propose an integrated method based on particle swarm optimization and estimation of distribution algorithm (PSO-EDA) for solving the max-cut problem. The integrated algorithm overcomes the shortcomings of particle swarm optimization and estimation of distribution algorithm. To enhance the performance of the PSO-EDA, a fast local search procedure is applied. In addition, a path relinking procedure is developed to intensify the search. To evaluate the performance of PSO-EDA, extensive experiments were carried out on two sets of benchmark instances with 800 to 20000 vertices from the literature. Computational results and comparisons show that PSO-EDA significantly outperforms the existing PSO-based and EDA-based algorithms for the max-cut problem. Compared with other best performing algorithms, PSO-EDA is able to find very competitive results in terms of solution quality

Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure

Xqx Based Modeling For General Integer Programming Problems

We present a new way to model general integer programming (IP) problems with in- equality and equality constraints using XQX. We begin with the definition of IP problems folloby their practical applications, and then present the existing XQX based models to handle such problems. We then present our XQX model for general IP problems (including binary IP) with equality and inequality constraints, and also show how this model can be applied to problems with just inequality constraints. We then present the local optima based solution procedure for our XQX model. We also present new theorems and their proofs for our XQX model. Next, we present a detailed literature survey on the 0-1 multidimensional knapsack problem (MDKP) and apply our XQX model using our simple heuristic procedure to solve benchmark problems. The 0-1 MDKP is a binary IP problem with inequality con- straints and variables with binary values. We apply our XQX model using a heuristics we developed on 0-1 MDKP problems of various sizes and found that our model can handle any problem sizes and can provide reasonable quality results in reasonable time. Finally, we apply our XQX model developed for general integer programming problems on the general multi-dimensional knapsack problems. The general MDKP is a general IP problem with inequality constraints where the variables are positive integers. We apply our XQX model on GMDKP problems of various sizes and find that it can provide reasonable quality results in reasonable time. We also find that it can handle problems of any size and provide fea- sible and good quality solutions irrespective of the starting solutions. We conclude with a discussion of some issues related with our XQX model

Analog Photonics Computing for Information Processing, Inference and Optimisation

This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

From image co-segmentation to discrete optimization in computer vision - the exploration on graphical model, statistical physics, energy minimization, and integer programming

This dissertation aims to explore the ideas and frameworks for solving the discrete optimization problem in computer vision. Much of the work is inspired by the study of the image co-segmentation problem. It is through the research on this topic that the author has become very familiar with the graphical model and energy minimization point of view in handling computer vision problems - that is, how to combine the local information with the neighborhood interaction information in the graphical system for the inference; and also the author has come to the realization that many problems in and beyond computer vision can be solved in that way. At the beginning of this dissertation, we first give a comprehensive background review on graphical model, energy minimization, integer programming, as well as all their connections with the fundamental statistical physics. We aim to review the various aspects of the concepts, models, algorithms, etc., in a systematic way and from a different perspective. For instance, we review the correspondences between the commonly used unary/binary energy objective terms in computer vision with those of the fundamental Ising model in statistical physics; and also we summarize several widely used discrete energy minimization algorithms in computer vision under a unified framework in statistical physics; in addition we stress the close connections between the graphical model energy minimization and the integer programming problems, and especially we point out the central role of Mixed-Integer Quadratic Programming in discrete optimization in and beyond computer vision. Moreover, we explore the relationship between integer programming and energy minimization experimentally. We test integer programming methods on randomly generated energy formulations (as those would appear in computer vision problems), and similarly energy minimization methods on the integer programming problem of Graph K-coloring. Therefore we can easily compare the optimization performance of various methods (no matter whether they are designed for energy minimization or integer programming) on one platform. We come to the conclusion that sharing the methods across the fields (energy minimization in computer vision and integer programming in applied mathematics) is very helpful and beneficial. Based on the statistical physics inspired energy minimization framework we obtained, we formulate the task of density based clustering into this formulation. Energy is defined in terms of inhomogeneity in local point density. A sequence of energy minima are found to recursively partition the points, and thus we find a hierarchical embedding of clusters that are increasingly homogeneous in density. Energy is expressed as the sum of a unary (data) term and a binary (smoothness) term. The only parameter required to be specified by the user is a homogeneity criterion - the degree of acceptable fluctuation in density within a cluster. Thus, we do not have to specify, for example, the number of clusters present. Disjoint clusters with the same density are identified separately. Experimental results show that our method is able to handle clusters of different shapes, sizes and densities. We present the performance of our approach using the energy optimization algorithms ICM, LBP, Graph-cut, and Mean field theory algorithm. We also show that the family of commonly used spectral, graph clustering algorithms (such as Normalized-cut) is a special case of our formulation, using only the binary energy term while ignoring the unary term. After all the discussions above on the general framework for solving the discrete optimization problem in computer vision, the dissertation then focuses on the study of image co-segmentation, which is in fact carried out before the above topics. Image co-segmentation is the task of automatically discovering, locating and segmenting some unknown common object in a set of images. It has become a popular research topic in computer vision during recent years. The unsupervised nature is an important characteristic of the problem; i.e., the common object is a priori unknown. Moreover, the common object may be subject to viewpoint change, lighting condition change, occlusion, and deformation across the images; all these conditions make the co-segmentation task very challenging. In this part of the study we focus on the research of image co-segmentation and propose various approaches for addressing this problem. Most existing co-segmentation methods focus on co-segmenting the images with a very dominant common object, where the background interference is very limited. Such images are not realistic for the co-segmentation task, since in practice we may always encounter images with very rich and complex content where the common object is not dominant and appears simultaneously along with a large number of other objects. In this work we aim to address the image co-segmentation problem on this kind of image that cannot be handled properly with many previous methods. Two distinct approaches have been proposed in this work for image co-segmentation; the key difference lies in the method of common object discovery. The first approach is a "topology" based approach (also called a "point-region" approach) while the second one is a "sparse optimization" based approach. Specifically, in the first approach we combine the image key point features with the segment features together to discover the common object, while relying on the local topology consistency of both key point and segment layout for the robust recognition. The obtained initial foreground (the common object) in each image is refined through graphical model energy minimization based on a global appearance model extracted from the entire image dataset. The second approach is inspired by sparse optimization techniques; in this approach we use a sparse approximation scheme to find the optimal correspondence of the segments in two images as the initial estimation of the common object, based on some linear additive features extracted from the segments. In both proposed approaches, we emphasize the exploration of inter-image information in all steps of the algorithms; therefore, the common object need not to be dominant or salient in each individual image, as long as it is "common" across the image set. Extensive experiments have been conducted in this study to validate the performance of the proposed approaches. We carry out experiments on the widely used benchmark datasets for image co-segmentation, including iCoseg dataset, the multi-view co-segmentation dataset, Oxford flower dataset and so forth. Besides the above datasets, in order to better evaluate the performance on the rich and complex images with non-dominant common object, we also propose a new dataset in this work called richCoseg. Experiments are also conducted on this new dataset and qualitative and quantitative comparisons with the recent methods are provided. Finally, this dissertation also discusses very briefly some other vision problems the author has studied in previously published works