Large-scale Constrained Optimization Problems Research Articles

Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblemQPlat each iteration instead of theQPl0of the SQP-type PVD algorithm proposed by C. A. Sagastizábal and M. V. Solodov in 2002. The algorithm can circumvent the difficulties associated with the possible inconsistency ofQPl0subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit).

Efficient computation of nonparametric survival functions via a hierarchical mixture formulation

We propose a new algorithm for computing the maximum likelihood estimate of a nonparametric survival function for interval-censored data, by extending the recently-proposed constrained Newton method in a hierarchical fashion. The new algorithm makes use of the fact that a mixture distribution can be recursively written as a mixture of mixtures, and takes a divide-and-conquer approach to break down a large-scale constrained optimization problem into many small-scale ones, which can be solved rapidly. During the course of optimization, the new algorithm, which we call the hierarchical constrained Newton method, can efficiently reallocate the probability mass, both locally and globally, among potential support intervals. Its convergence is theoretically established based on an equilibrium analysis. Numerical study results suggest that the new algorithm is the best choice for data sets of any size and for solutions with any number of support intervals.

Reliability based generator maintenance scheduling using hybrid evolutionary approach

With the growth of electrical energy demand, providing reliable energy without interruption has become very important nowadays. Maintenance scheduling of generating units is one of the crucial factors in delivering reliable electrical energy to the vital industrial and urban loads. As number of generating units and constraints over their operation is increasing, there is growing need for developing new methods for planning optimal outage of generating units for maintenance. This paper presents a hybrid evolutionary algorithm to tackle the reliability based generator maintenance scheduling problem. Uncertainties in the generating units and the load variations are included so that a more realistic scheduling is obtained. Maintenance scheduling problem is a large scale constrained optimization problem with a large number of variables which needs novel methods to cope with it. A new local search method which is derived from Extremal Optimization (EO) and Genetic Algorithm (GA) is presented to tackle the problem. The proposed method can be used as a local optimizer to further improve the potential solutions in the GA. The proposed method, Hill Climbing Technique (HCT), GA and their hybrid approaches are applied to the IEEE Reliability Test System (RTS) and the obtained results are discussed.

Parallel MR Image Reconstruction Using Augmented Lagrangian Methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data--SENSE-reconstruction--using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.

An Efficient Algorithm for Solving BCOP and Implementation

The distributed constrained state estimation (DCSE) and distributed optimal power flow (DOPF) problems are some kinds of large-scale block-additive constrained optimization problem (BCOP) in their exact formulation. In this paper, we propose a general form methodology, an efficient distributed asynchronous dual-type method, to cope with the computational difficulty of these problems. Our method achieves some attractive features, including being computationally efficient and numerically stable. The computational formulae of our method are explicit, compact, and easy to be programmed. We have demonstrated the computational efficiency of our method, by comparing with the state-of-the-art algorithm through the implementation of two real different types PC-networks in asynchronous computing environment on the IEEE 118-bus and IEEE 244-bus systems

A Decomposition-Technique-Based Algorithm for Nonlinear Large Scale Mesh-Interconnected System and Application

In this paper, we propose two techniques to solve the nonlinear constrained optimization problem in large scale mesh-interconnected system. The first one is a diagram-method-based decomposition technique which decomposes the large scale system into some small subsystems. The second technique is a projected-Jacobi-based parallel dual-type method which can solve the optimization problems in the decomposed subsystems efficiently. We have used the proposed algorithm to solve numerous examples of large scale constrained optimization problems in power system. The test results show that the proposed algorithm has computational efficiency with respect to the conventional approach of the centralized Newton method and the state-of-the-art Block-Parallel Newton method.

A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction.

Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variables. Owing to the large size of our problem, we compute approximate reduced Newton steps by using the conjugate gradient (CG) iteration. We introduce a limited-memory, quasi-Newton preconditioner that speeds up CG convergence. A numerical comparison is presented that demonstrates the effectiveness of this preconditioner.

A hybrid evolutionary approach for solving constrained optimization problems over finite domains

A novel approach for the integration of evolution programs and constraint-solving techniques over finite domains is presented. This integration provides a problem-independent optimization strategy for large-scale constrained optimization problems over finite domains. In this approach, genetic operators are based on an arc-consistency algorithm, and chromosomes are arc-consistent portions of the search space of the problem. The paper describes the main issues arising in this integration: chromosome representation and evaluation, selection and replacement strategies, and the design of genetic operators. We also present a parallel execution model for a distributed memory architecture of the previous integration. We have adopted a global parallelization approach that preserves the properties, behavior, and fundamentals of the sequential algorithm. Linear speedup is achieved since genetic operators are coarse grained as they perform a search in a discrete space carrying out arc consistency. The implementation has been tested on a GRAY T3E multiprocessor using a complex constrained optimization problem.

Exploiting Sparsity in the Direct Transcription Method for OptimalControl

In the direct transcription method an approximation to an optimal control problem is constructed by discretization of the state and control variables. The control problem is thus transcribed into a large scale constrained optimization problem with a finite number of variables. It is necessary to solve the nonlinear programming (NLP) problem produced by the discretization as efficiently as possible, and research has focused on methods for solving the underlying NLP when the relevant Jacobian and Hessian matrices are sparse. However little attention has been given to computing the Jacobian and Hessian, particularly for applications that require finite difference techniques. Typically it is assumed that these matrices have a block structure, and when standard finite difference estimates are used this operation is a major computational expense. This paper describes how to actually construct the Jacobian and Hessian matrices efficiently, and exploit sparsity inherent in the problem. This new technique can significantly reduce the computational costs when the original optimal control problem has many state and control variables.

A security-constrained bid-clearing system for the New Zealand wholesale electricity market

This paper reports upon the mathematical models and implementation of the Scheduling, Pricing and Dispatch (SPD) application for the New Zealand Electricity Market (NZEM). SPD analyzes bids for energy offers, reserve offers and energy demands, and recognizes explicitly the effects on bid clearing due to transmission congestion, network losses, reserve requirements, and ramp rate limits. Advanced LP solution methods are utilized to solve the large-scale constrained optimization problem. Results on a 67-bus test system and the NZEM are included.

Optimization technique based on learning automata

Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.