Large-scale Nonlinear Optimization Problems Research Articles

A Spectral Dai-Yuan-Type Conjugate Gradient Method for Unconstrained Optimization

A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems.

Efficient parallel solution of large-scale nonlinear dynamic optimization problems

This paper presents a decomposition strategy applicable to DAE constrained optimization problems. A common solution method for such problems is to apply a direct transcription method and solve the resulting nonlinear program using an interior-point algorithm. For this approach, the time to solve the linearized KKT system at each iteration typically dominates the total solution time. In our proposed method, we exploit the structure of the KKT system resulting from a direct collocation scheme for approximating the DAE constraints in order to compute the necessary linear algebra operations on multiple processors. This approach is applied to find the optimal control profile of a combined cycle power plant with promising results on both distributed memory and shared memory computing architectures with speedups of over 50 times possible.

Scheduling short-term hydrothermal generation using predator prey optimization technique

Paper presents predator–prey based optimization (PPO) technique to obtain optimal generation scheduling of short-term hydrothermal system. PPO is a part of the swarm intelligence family and is capable to solve large scale non-linear optimization problems. PPO based algorithm combines the idea of particle swarm optimization concept with predator effect that helps to, maintain diversity in the swarm and preventing premature convergence to local sub-optimal. In this paper first of all feasible solution is obtained through random heuristic search and then thermal and hydro power generations are searched for optimum hydrothermal scheduling problem using PPO. Variable elimination method is implemented to handle the equality constraint by eliminating variable explicitly. These eliminated variables are considered by penalty method restricts slack units with in limits. Slack thermal generating unit for each sub-interval handles power balance equality constraint and slack hydro units handle water equality constraint. The performance of the proposed approach is illustrated on, fixed-head and variable-head hydrothermal power systems. The results obtained from the proposed technique are compared with the existing technique. From the numerical results, it is experienced that the PPO based approach is able to provide a better solution.

A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods

The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.

An efficient harmony search with new pitch adjustment for dynamic economic dispatch

A simple yet efficient harmony search (HS) method with a new pitch adjustment rule (NPAHS) is proposed for dynamic economic dispatch (DED) of electrical power systems, a large-scale non-linear real time optimization problem imposed by a number of complex constraints. The new pitch adjustment rule is based on the perturbation information and the mean value of the harmony memory, which is simple to implement and helps to enhance solution quality and convergence speed. A new constraint handling technique is also developed to effectively handle various constraints in the DED problem, and the violation of ramp rate limits between the first and last scheduling intervals that is often ignored by existing approaches for DED problems is effectively eliminated. To validate the effectiveness, the NPAHS is first tested on 10 popular benchmark functions with 100 dimensions, in comparison with four HS variants and five state-of-the-art evolutionary algorithms. Then, NPAHS is used to solve three 24-h DED systems with 5, 15 and 54 units, which consider the valve point effects, transmission loss, emission and prohibited operating zones. Simulation results on all these systems show the scalability and superiority of the proposed NPAHS on various large scale problems.

The Distribution Network Reconfiguration Based on Spatial Data Mining

Distribution network reconfiguration is one of the essential functions of the DMS system; it can be attributed to a number of constraints of large-scale nonlinear combinatorial optimization problem in mathematics. The characteristic of load change of time and space will affect the results of load forecasting. Distribution network reconfiguration relies on the load forecasting results. This paper proposes the more realistic distribution reconfiguration scheme based on the GIS system with space information through spatial data mining. For the real-time and efficiency of effective assurance data, the interface design in GIS system and distribution automation system are also proposed. The geographical information and real-time information are connected seamlessly, so that this two system information is highly unified. The solution can provide the data basis for distribution reconfiguration scheme accurately, and improve power supply reliability of distribution network. It shows that through the example: GIS based on the spatial data mining can provide load in quantity, time, space prediction for the deeper research of distribution network reconfiguration.

Optimal Power Flow by Interior Point and Non Interior Point Modern Optimization Algorithms

The idea of optimal power flow (OPF) is to determine the optimal settings for control variables while respecting various constraints, and in general it is related to power system operational and planning optimization problems. A vast number of optimization methods have been applied to solve the OPF problem, but their performance is highly dependent on the size of a power system being optimized. The development of the OPF recently has tracked significant progress both in numerical optimization techniques and computer techniques application. In recent years, application of interior point methods to solve OPF problem has been paid great attention. This is due to the fact that IP methods are among the fastest algorithms, well suited to solve large-scale nonlinear optimization problems. This paper presents the primal-dual interior point method based optimal power flow algorithm and new variant of the non interior point method algorithm with application to optimal power flow problem. Described algorithms were implemented in custom software. The experiments show the usefulness of computational software and implemented algorithms for solving the optimal power flow problem, including the system model sizes comparable to the size of the National Power System. DOI: 10.12736/issn.2300-3022.2013112

Particle swarm optimization based selection of optimal polymeric blend

This paper presents a novel and efficient method to estimate the optimal blend of Silicone Rubber (SiR) and Ethylene Propylene Diene Monomer (EPDM). The SiR and EPDM are widely used insulating materials. Blending of these polymers is one way of obtaining a new material with superior properties of both. Hence blending of SiR/EPDM with different blend ratios has been done. These blends are tested for their electrical and mechanical characteristics as per ASTM and IEC standards. The mechanical properties investigated are tensile strength (TS) and elongation at break (EB). The electrical properties like volume resistivity (VRY) and surface resistivity (SRY), arc resistance (AR) and comparative tracking index (CTI) are also analyzed. Amidst various electro-mechanical parameters, it is really hard to choose a suitable blend ratio for a specific application. In order to identify the suitable blend with superior properties compared to that of the constituent polymers, optimization technique is used. The problem of determining the optimal blend is formulated as a multiobjective optimization problem with the objective of maximizing the electrical and mechanical properties. The problem of finding the optimal blend ratio for improved performance is based on the weights assigned for various electrical and mechanical parameters. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. In this paper, the PSO is used to find the suitable blend ratio for cable applications. A comparison has been made with Genetic Algorithm (GA) technique, in order to validate the result. To have an overview about the thermal behavior of these blends under a practical situation, thermal analysis using Differential Scanning Calorimetry (DSC) and Thermo-gravimetric Analysis (TGA) has been done.

A Conjugate Gradient Method with Global Convergence for Large-Scale Unconstrained Optimization Problems

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. This paper proposes a conjugate gradient method which is similar to Dai-Liao conjugate gradient method (Dai and Liao, 2001) but has stronger convergence properties. The given method possesses the sufficient descent condition, and is globally convergent under strong Wolfe-Powell (SWP) line search for general function. Our numerical results show that the proposed method is very efficient for the test problems.

A Hybrid Modified Particle Swarm Optimization for Heterogeneous Radio Access Technology (RAT) Selection

ABSTRAC Next Generation wireless networks are heterogeneous in nature where a variety of Radio Access Technologies (RATs) coexist in the same coverage area. It is important to select the most appropriate Radio Access Network (RAN) according to the requested service of each user. Hence, this paper proposes a Hybrid Modified Particle Swarm Optimization (PSO) algorithm to select the best access network among Wireless Wide Area Network (WWAN) and Wireless Local Area Network (WLAN). Particle Swarm Optimization is a global optimization algorithm, is known to effectively solve large scale nonlinear optimization problems. A variant of PSO called as Modified PSO is used in this paper where a constriction coefficient (  ) has been introduced in the velocity update equation and this factor improves the convergence of the particle over time and this optimization algorithm has been hybridized with multi-objective decision making algorithm and weighing function to achieve better solutions. The performance of the proposed algorithm is evaluated using 1000 datasets. From the simulation study, it is found that the proposed approach gives higher user satisfaction ratio compared with the other approaches.

Convergence of the descent Dai–Yuan conjugate gradient method for unconstrained optimization

The conjugate gradient method is one of the most useful and the earliest-discovered techniques for solving large-scale nonlinear optimization problems. Many variants of this method have been proposed, and some are widely used in practice. In this article, we study the descent Dai–Yuan conjugate gradient method which guarantees the sufficient descent condition for any line search. With exact line search, the introduced conjugate gradient method reduces to the Dai–Yuan conjugate gradient method. Finally, a global convergence result is established when the line search fulfils the Goldstein conditions.

Teaching–Learning-Based Optimization: An optimization method for continuous non-linear large scale problems

An efficient optimization method called ‘Teaching–Learning-Based Optimization (TLBO)’ is proposed in this paper for large scale non-linear optimization problems for finding the global solutions. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The effectiveness of the method is tested on many benchmark problems with different characteristics and the results are compared with other population based methods.

Decomposed Predictor-Corrector Interior Point Method for Dynamic Optimal Power Flow

In this paper, a decomposed predictor-corrector interior point method (DPCIPM) is proposed for solving the dynamic optimal power flow (DOPF) problem, which is a large-scale nonlinear optimization problem. The Karush-Kuhn-Tucker (KKT) system in DPCIPM is decomposed into many subsystems based on its special block structure, where the size of each subsystem depends on the network size only. In the iterative process, slack variables and Lagrange multipliers of dynamic constraints are first predicted and corrected, and then other variables in each time interval are predicted and corrected. The parameters, such as step length and barrier parameter, are independently estimated in each subsystem. Besides, an inequality iteration strategy is introduced to avoid unnecessary computation. Implementation of the proposed DPCIPM is described in detail. The effectiveness of the proposed method has been demonstrated on the IEEE 14-bus and IEEE 118-bus systems with up to 24 time intervals. It has been found that compared with a decomposed pure primal dual interior point method (DIPM), the proposed DPCIPM is more attractive, especially when dynamic constraints become active.

A new self –scaling VM-algorithm with an adaptive line search

In this study, a new self-scaling VM algorithm for solving large-scale nonlinear unconstrained optimization problems is proposed. The new algorithm is a kind of line search procedure .The local convergence theory for the BFGS matrix implementation of this variable metric is applied to achieve a globally convergent property.Numerical experiments have been done with the standard BFGS algorithm with very promising results.

Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems

In this paper, we deal with conjugate gradient methods for solving nonlinear least squares problems. Several Newton-like methods have been studied for solving nonlinear least squares problems, which include the Gauss–Newton method, the Levenberg–Marquardt method and the structured quasi-Newton methods. On the other hand, conjugate gradient methods are appealing for general large-scale nonlinear optimization problems. By combining the structured secant condition and the idea of Dai and Liao (2001) [20], the present paper proposes conjugate gradient methods that make use of the structure of the Hessian of the objective function of nonlinear least squares problems. The proposed methods are shown to be globally convergent under some assumptions. Finally, some numerical results are given.

A hybrid PSO technique for procuring VAR ancillary service in the deregulated electricity markets

This paper develops a new market-based technique for acquiring VAR ancillary service in the electricity market. The main objective of the developed market is to enable transmission operator “TO” to procure VAR service in a long term contract from the critical VAR providers that satisfy minimum VAR service payment while maintaining system security. Reactive power control problem for voltage stability is introduced into the VAR market problem in an explicit manner for normal and emergency states. An integration of particle swarm optimization “PSO” is presented with successive linear programming “SLP” for dealing with the VAR ancillary service problem. The problem is formulated as a large-scale nonlinear constrained optimization problem with a non-differentiable objective function representing VAR payment and operational costs. This type of problem is hard to be treated straightforwardly by the classical optimization methods. Therefore, we propose here a two-layer hybrid PSO/SLP approach, which is suited for carrying out the difficulties associated with non-differentiable and discontinuous objective functions. The proposed method has been examined on the standard IEEE 57 bus-system and compared with GA/SLP method to demonstrate its capability.

On the linear convergence of Newton–Krylov methods

Solution of large-scale nonlinear optimization problems and systems of nonlinear equations continues to be a difficult problem. One of the main classes of algorithms for solving these problems is the class of Newton–Krylov methods. In this article the number of iterations of a Krylov subspace method needed to guarantee at least a linear convergence of the respective Newton–Krylov method is studied. The problem is especially complicated if the matrix of the linear system to be solved is nonsymmetric. In the article, explicit estimates for the number of iterations for the Krylov subspace methods are obtained.

Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

Multi-step nonlinear conjugate gradient methods for unconstrained minimization

Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87---101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput. Optim. Appl. 28:203---225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357---370, 1993; J. Comput. Appl. Math. 50:305---323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent under certain assumptions. Numerical results are reported.