An approximate approach to the Unsplittable flow Edge-Load factor Balancing problem with the Lagrangian relaxation

This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

This paper presents an application of combined Lagrangian relaxation (LR) method and particle swarm optimization (PSO) technique for the Unit Commitment (UC) problem. This hybrid technique uses LR as the main algorithm. The LR method provides a fast solution, but it may suffer from numerical convergence and solution quality problem. The proposed algorithm uses PSO to update the Lagrangian multipliers and improve the performance of LR method. In this paper, ramp rate limit is also considered besides taking minimum up time and minimum down time of thermal units. The proposed method is implemented for solving two examples of UC test problems. The study results have shown that the approach developed is feasible and efficient.

The problem of multilocation facility modernization is described. An integer multicommodity flow formulation is presented. Because of the problem size, exact solutions are not practical, and approximate solution methods are examined. Upper bounds are obtained by LP and Lagrangian relaxation. Near-optimal feasible solutions are obtained by heuristic procedures. The relaxation methods and the heuristics are compared in terms of the computation cost and the quality of the modernization policies produced, where quality is measured by the net present value of cash flows for a number of test problems. Also included is an evaluation of an aggregate modeling approach to multilocation planning, where average costs are employed in a single-location model to determine a homogeneous multilocation modernization policy. This assessment is important, as aggregate models have been employed widely in practice.

Utilization of a dependency-tracking language to reduce computational time during multidisciplinary design optimization

The AC-DC hybrid microgrid is a credible evolution path for the microgrid. State estimation in complex distribution network is a significant foundation for the safe operation. In AC-DC hybrid microgrid, centralised state estimation algorithms have quite a few deficiencies such as large communication capacity and privacy protection. In response to these obstacles, this paper proposed a novel distributed state estimation algorithm. First, a three-stage state estimation model was established for AC-DC hybrid microgrid, in which the second stage is a nonlinear transform for the linearisation of the nonlinear state estimation progress so that the first and third stage can solve the linear state estimation problem. Furthermore, the Lagrangian relaxation method was ultilised for the distributed problem solution. In the proposed algorithm, AC subsystems and DC subsystems respectively execute state estimation through local information, and the overall consistency of the system state estimation can be eventually achieved according to the transfer iteration of the boundary information. The computational efficiency and convergence of the proposed method was ensured owing to the combination of bilinear theory and Lagrangian relaxation. Simulation results indicate that the proposed method can achieve its goal and be superior to existing method in efficiency.

Toward flexible and persistent UAV service: Multi-period and multi-objective system design with task assignment for disaster management

A central problem in multitarget, multisensor, and multiplatform tracking remains that of data association. Lagrangian relaxation methods have shown themselves to yield near optimal answers in real-time. The necessary improvement in the quality of these solutions warrants a continuing interest in these methods. These problems are NP-hard; the only known methods for solving them optimally are enumerative in nature with branch-and-bound being most efficient. Thus, the development of methods less than a full branch-and-bound are needed for improving the quality. Such methods as K-best, local search, and randomized search have been proposed to improve the quality of the relaxation solution. Here, a partial branch-and-bound technique along with adequate branching and ordering rules are developed. Lagrangian relaxation is used as a branching method and as a method to calculate the lower bound for subproblems. The result shows that the branch-and-bound framework greatly improves the resolution quality of the Lagrangian relaxation algorithm and yields better multiple solutions in less time than relaxation alone.

An inverse dynamics method is introduced for constructing exact special-case solutions for hybrid coordinate ordinary/partial systems of differential equations (hybrid ODE/PDE systems). The solution is constructed such that it lies near a given approximate numerical solution, and therefore the special-case solutions can be generated in a versatile and physically meaningful fashion and can serve as a benchmark problem to validate approximate solution methods. The exact solution is constructed such that it is a differentiable, continuous-function neighbor of the given approximate numerical solution. This continuous solution is then substituted into the governing system of ODEs/PDEs and a full complement of distributed and boundary forces is determined algebraically to exactly satisfy the differential equations. This process has been automated by computer symbol manipulation. Since the exact special-case algebraic solutions can be evaluated anywhere in space and time, this approach is ideally suited to providing a true exact motion and the corresponding forces for studying the convergence errors in a family of approximate solutions. This methodology makes it possible for one to rigorously determine exact solution errors for a significant class of ODE/PDE systems for which the initial-value problem is not, in general, exactly solvable. We explore the utility of this method in validating numerical solution methods.

The prediction of protein-protein interactions (PPIs) is essential to understand the cellular processes from a medical perspective. Among the various machine learning techniques, kernel-based Support Vector Machine (SVM) has been commonly employed to discriminate between interacting and non-interacting protein pairs. The main drawback of employing the kernel-based SVM to datasets with many features, such as the primary sequence-based protein-protein dataset, is the significant increase in computational time of training stage. This increase in computational time is mainly due to the presence of the kernel in solving the quadratic optimisation problem (QOP) involved in nonlinear SVM. In order to fix this issue, we propose a novel and efficient computational algorithm by approximating the kernel-based SVM using a low-rank truncated Mercer series as well as desired. As a result, the QOP for the approximated kernel-based SVM will be very tractable in the sense that there is a significant reduction in computational time of training and validating stages. We illustrate the novelty of the proposed method by predicting the PPIs of “S. Cerevisiae” where the protein features extracted using the multiscale local descriptor (MLD), and then we compare the predictive performance of the proposed low-rank approximation with the existing methods. Finally, the new method results in significant reduction in computational time for predicting PPIs with almost as accuracy as kernel-based SVM.

Dynamic economic dispatch (DED) over multiple time periods is a large-scale coupled spatial-temporal optimization problem. Therefore, the Lagrangian relaxation method has been widely used to split the large-scale optimization problem with coupled structure into several small sub-problems. In order to bring robustness for updating the dual multipliers and yielding convergence without strong assumptions, the augmented Lagrangian relaxation method is introduced in this paper. However, the added penalty term in an augmented Lagrangian function is non-separable, which leads to the difficulty in achieving full decomposition for parallel computation. To address this problem, a diagonal quadratic approximation method is employed to yield an approximated block separation of the non-separable penalty term. Furthermore, the ramp rate constraints are relaxed in this paper, so that the DED model is decomposed into several single-period economic dispatch models that can be efficiently handled in parallel, called the parallel augmented Lagrangian relaxation method. Particularly, the proposed relaxation strategy has a high separability feature which theoretically leads to sound convergence property. Numerical results on the IEEE 118-bus and a practical Polish 2383-bus test system over a different number of time periods show the effectiveness of the proposed method. In addition, the proposed method can be extended to other coupled spatial-temporal scheduling problems in power systems, such as energy storage dispatch.

Database sequencing applications including sequence comparison, searching, and analysis are considered among the most computation power and time consumers. Heuristic algorithms suffer from sensitivity while traditional sequencing methods, require searching the whole database to find the most matched sequences, which requires high computation power and time. This paper introduces a dynamic programming technique based-on a measure of similarity between two sequential objects in the database using two components, namely frequency and mean. Additionally, database sequences that have the lowest scores in the comparison process were excluded such that the similarity algorithm between a query sequence and other database sequences is applied to meaningful parts of the database. The proposed technique was implemented and validated using a heterogeneous HW/SW FPGA-based embedded system platform. The implementation was partitioned into (1) hardware part (running on logic gates of FPGA) and (2) software part (running on ARM processor of FPGA). The validation study showed a significant reduction in computation time by accelerating the database sequencing processes by 60% comparing to traditional known methods.

A simple algorithm for solving the finite-difference (FD) equations for the mode eigenvalues and field distributions of a linear waveguide is presented. By applying the discretized Helmholtz operator column-by-column to an index distribution defined on an N x N grid, a matrix whose size is only a few times N x N is obtained. This yields a reduction in computation time and space compared with the other classical FD approaches which involve an N2 x N2 matrix. Our method is tested against problems for which the exact solutions are known, and we find a high degree of accuracy. Despite the existence of fast algorithms for the treatment of the classical N2 x N2 matrix, our new algorithm presents some advantages over existing FD methods of comparable speed, including: the ability to find all the modes and associated field profiles, very high numerical stability, and no numerical approximations in the procedure. In addition, some general optimum expressions for the domain size and density of grid points which are consistent with the desired precision are provided, and apply to any FD method including ours.

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

In the zonal method, considerable computational resources are needed to calculate the direct exchange areas (DEA) among the isothermal zones due to integrals with up to six dimensions, while strong singularities occur in the integrands when two zones are adjacent or overlaping (self-irradiation). A special transformation of variables to reduce a double integral into several single integrals is discussed in this paper. This technique was originally presented by Erkku (1959) for calculation of DEA using a uniform zone system in a cylindrical enclosure. However, nonuniform zones are needed for applications with large thermal gradients. Thus we extended this technique to calculate the DEA for non-uniform zones in an axisymmetrical cylinder system. A six-fold reduction in computational time was observed in calculating DEA compared with cases without a variable transformation. It is shown that accuracy and efficiency of estimation of radiation heat flux is improved when using a nonuniform zone system. Reasonable accuracy of all DEA are calculated without resorting to the conservative equations. Results compared well with analytical solutions and numerical results of previous researchers. This technique can be readily extended to rectangular enclosures with similar reduction in computation time expected.

Parallel processing of chemical information in a local area network—III. Using genetic algorithms for conformational analysis of biomacromolecules