We consider a multi-facility location problem in the presence of a line barrier with the starting point of the barrier uniformly distributed. The objective is to locate n new facilities among m existing facilities min...
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We consider a multi-facility location problem in the presence of a line barrier with the starting point of the barrier uniformly distributed. The objective is to locate n new facilities among m existing facilities minimising the summation of the weighted expected rectilinear barrier distances of the locations of new facilities and new and existing facilities. The proposed problem is designed as a mixed-integer nonlinear programming model, conveniently transformed into a mixed-integer quadratic programming model. The computational results show that the LINGO 9.0 software package is effective in solving problems with small sizes. For large problems, we propose two meta-heuristic algorithms, namely the genetic algorithm and the imperialist competitive algorithm for optimisation. The numerical investigations illustrate the effectiveness of the proposed algorithms.
Multiple instance learning (MIL) is a variation of supervised learning, where data consists of labeled bags and each bag contains a set of instances. Unlike traditional supervised learning, labels are not known for th...
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Multiple instance learning (MIL) is a variation of supervised learning, where data consists of labeled bags and each bag contains a set of instances. Unlike traditional supervised learning, labels are not known for the instances in MIL. Existing approaches in the literature make use of certain assumptions regarding the instance labels and propose mixed integer quadratic programs, which introduce computational difficulties. In this study, we present a novel quadratic programming (QP)-based approach to classify bags. Solution of our QP formulation links the instance-level contributions to the bag label estimates, and provides a linear bag classifier along with a decision threshold. Our approach imposes no additional constraints on relating instance labels to bag labels and can be adapted to learning applications with different MIL assumptions. Unlike existing specialized heuristic approaches to solve previous MIL formulations, our QP models can be directly solved to optimality using any commercial QP solver. Also, kindly confirm Our computational experiments show that proposed QP formulation is efficient in terms of solution time, overcoming a main drawback of previous optimization algorithms for MIL. We demonstrate the classification success of our approach compared to the state-of-the-art methods on a wide range of real world datasets.
A new neural network is proposed in this paper for solving quadratic programming problems with equality and inequality constraints. Comparing with the existing neural networks for solving such problems, the proposed n...
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A new neural network is proposed in this paper for solving quadratic programming problems with equality and inequality constraints. Comparing with the existing neural networks for solving such problems, the proposed neural network has fewer neurons and an one-layer architecture. The proposed neural network is proven to be global convergence. Furthermore, illustrative examples are given to show the effectiveness of the proposed neural network. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
Image labelling tasks are usually formulated within the framework of discrete Markov random fields where the optimal labels are recovered by extremising a discrete energy function. The authors present an alternative c...
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Image labelling tasks are usually formulated within the framework of discrete Markov random fields where the optimal labels are recovered by extremising a discrete energy function. The authors present an alternative continuous relaxation approach to image labelling, which makes use of a quadratic cost function over the class labels. The cost function to be minimised is convex and its discrete version is equivalent up to a constant additive factor to the target function used in discrete MRF approaches. Moreover, its corresponding Hessian matrix is given by the graph Laplacian of the adjacency matrix. Therefore the optimisation of the cost function is governed by the pairwise interactions between pixels in the local neighbourhood. This leads to a sparse Hessian matrix for which the global minimum of the continuous relaxation problem can be efficiently found by solving a system of linear equations using the Cholesky factorisation. The authors elaborate on the links between the method and other techniques elsewhere in the literature and provide results on synthetic and real-world imagery. The authors also provide a comparison with competing approaches.
Economic dispatch for micro-grids and district energy systems presents a highly constrained non-linear, mixed-integer optimization problem that scales exponentially with the number of systems. Energy storage technolog...
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Economic dispatch for micro-grids and district energy systems presents a highly constrained non-linear, mixed-integer optimization problem that scales exponentially with the number of systems. Energy storage technologies compound the mixed-integer or unit-commitment problem by necessitating simultaneous optimization over the applicable time horizon of the energy storage. The dispatch problem must be solved repeatedly and reliably to effectively minimize costs in real-world operation. This paper outlines a method that greatly reduces, and under some conditions eliminates, the mixed-integer aspect of the problem using complementary convex quadratic optimizations. The generalized method applies to grid-connected or islanded district energy systems comprised of any variety of electric or combined heat and power generators, electric chillers, heaters, and all varieties of energy storage systems. It incorporates constraints for generator operating bounds, ramping limitations, and energy storage inefficiencies. An open-source platform, EAGERS, implements and investigates this optimization method. Results demonstrate a >99% reduction in computational effort when comparing the newly minted optimization strategy against a benchmark commercial mixed-integer solver applied to the same combined cooling, heating, and power problem. (C) 2018 Elsevier Ltd. All rights reserved.
A large class of separable quadratic programming problems is presented. The problems in the class can be solved in linear time. The class includes the separable convex quadratic transportation problem with a fixed num...
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A large class of separable quadratic programming problems is presented. The problems in the class can be solved in linear time. The class includes the separable convex quadratic transportation problem with a fixed number of sources and separable convex quadratic programming with nonnegativity constraints and a fixed number of linear equality constraints.
The technique of linearization for nonlinear systems around some operating point has been widely used for analysis and synthesis of the system behavior within a certain operating range. Conventional linearization meth...
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The technique of linearization for nonlinear systems around some operating point has been widely used for analysis and synthesis of the system behavior within a certain operating range. Conventional linearization methods include the analytical linearization (AL) method using the Jacobian matrix, the result of which usually works only for a sufficiently small region, as well as the numerical linearization (NL) method based on small perturbation, the accuracy of which is usually not guaranteed. In this letter, we propose an optimal linearization method via quadratic programming (OLQP). We start with uniform data sampling within the neighborhood of the operating point based on the nonlinear ordinary differential equation (ODE). We then find the best linear model that fits to these sample points with a QP formulation. The OLQP solution is derived in closed form with proved convergence to the AL solution. Two examples of nonlinear systems are investigated in terms of linearization and results are compared among these linearization methods, which has shown the proposed OLQP method features a great balance between model accuracy and computational complexity. Moreover, the OLQP method offers additional options in controller design by tuning its parameters.
To handle the large variation issues in fuzzy input-output data, the proposed quadratic programming (QP) method uses a piecewise approach to simultaneously generate the possibility and necessity models, as well as the...
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To handle the large variation issues in fuzzy input-output data, the proposed quadratic programming (QP) method uses a piecewise approach to simultaneously generate the possibility and necessity models, as well as the change-points. According to Tanaka and Lee [ H. Tanaka, H. Lee, Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems 6 ( 1998) 473-481], the QP approach gives more diversely spread coefficients than linear programming ( LP) does. However, their approach only deals with crisp input and fuzzy output data. Moreover, their method is weak in handling fluctuating data. So far, no method has been developed to cope with the large variation problems in fuzzy input-output data. Hence, we propose a piecewise regression for fuzzy input-output data with a QP approach. There are three advantages in our method. First, the QP technique gives a more diversely spread coefficient than does a linear programming technique. Second, the piecewise approach is used to detect the change-points in the estimated model automatically, and handle the large variation data such as outliers well. Third, the possibility and necessity models with better fitness in data processing are obtained at the same time. Two examples are presented to demonstrate the merits of the proposed method. (C) 2009 Elsevier B. V. All rights reserved.
Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this s...
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Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this study, a nonconvex and bound constraint zeroing neural network (NCZNN) model is designed and theorized to solve the time-varying complex-valued QP with linear equation constraint. Besides, we construct several new types of nonconvex and bound constraint complex-valued activation functions by extending real-valued activation functions to the complex domain. Subsequently, corresponding simulation experiments are conducted, and the simulation results verify the effectiveness and robustness of the proposed NCZNN model. Moreover, the model proposed in this article is further applied to solve the issue of small target detection in remote sensing images, which is modeled to QP problem with linear equation constraint by a serial of conversions based on constrained energy minimization algorithm.
The present paper will discuss the efficient, practical and definitive algorithm for dealing with constrained load flow problems. Algorithms based on mathematical programming and algorithms based on the load flow calc...
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The present paper will discuss the efficient, practical and definitive algorithm for dealing with constrained load flow problems. Algorithms based on mathematical programming and algorithms based on the load flow calculation methods have been studied since earlier days. However, on account of numerous control variables to be determined and of inadequate calculating efficiency, the guarantee of unfailing solution is yet to be achieved. In the calculating procedure herein described the extents of adjustments are not determined simultaneously for all the control variables ; the control variables considered likely to produce greater adjusting effect are selected one by one and are adjusted successively. This adjustment method, as a consequence, is useful not only for on-line power system operation but also as simulator software for training system operators.
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