Quadratic Programming Technique Research Articles

A swept volume approach based on hermite interpolation for optimization in collision‐free motion planning

The recursive quadratic programming (RQP) technique has been successfully applied for the motion planning problem. This paper inherits the RQP optimization formulation to solve collision‐free motion planning problems. The focus of the paper is to develop a more accurate approach to represent the swept volume based on Hermite interpolation. The non‐convex swept volume may be described by parametric representation. Based on this idea, the non‐convex limitation of the motion planning by the previous RQP technique can be overcome and it has yielded accurate answers in distance calculation. Also, have been presented to illustrate and demonstrate this approach in the paper.

Distribution Grid Voltage Control Using Cascaded Multi-level Inverter-based Static Synchronous Compensator

In this article, the voltage control performance of the cascaded multi-level inverter based static synchronous compensator was studied, specifically, a 21-level cascaded multi-level inverter based static synchronous compensator was considered. The switching angles of the cascaded multi-level inverter based static synchronous compensator have been determined by an optimization methodology based on the sequential quadratic programming technique for minimizing the total harmonic distortion of the static synchronous compensator output voltage. To achieve satisfactory performance of the static synchronous compensator voltage controller, two different fuzzy logic control schemes, namely, indirect and direct control systems, have been developed. The performances of these two developed control schemes for controlling the bus voltage were investigated with detailed non-linear fault simulation studies in a practical power distribution system using PSCAD/EMTDC (Manitoba HVDC Research Center, Winnipeg, Manitoba, Canada) software and have been found satisfactory. Furthermore, the performances of the proposed fuzzy controllers have also been found to be superior to that obtained with an indirect proportional-integral controller.

Identification and characterization of H10 enzymes isolated from Bacillus cereus H10 with keratinolytic and proteolytic activities

Two types of extracellular proteases with molecular mass of 50.0 and 44.8 kDa were found in H10 enzymes partially purified from Bacillus cereus H10. Further identification using liquid chromatography-tandem mass spectrometry, the enzyme with 50.0 kDa was identified as being similar to leucine dehydrogenase; while the enzyme with 44.8 kDa might be a novel keratinolytic enzyme with little similarity to other proteins. To maximize the keratinolytic and proteolytic abilities in the H10 enzymes, a combination of response surface methodology and sequential quadratic programming technique was used to study the hydrolytic pH and temperature. Results showed that the H10 enzymes could produce optimal proteolytic and keratinolytic activities at a hydrolysis temperature of 59°C at pH 7.57. Testing the protease activity on various protein substrates and temperatures indicated that the H10 enzymes showed high thermal stability and were very effective in porcine hair.

Spectral upper bounds for the order of a k-regular induced subgraph

Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which induce a subgraph with mean degree k. We use a quadratic programming technique in conjunction with the main angles of G to establish an upper bound of the form | S | ⩽ inf { ( k + t ) q G ( t ) : t > - λ } where q G is a rational function determined by the spectra of G and its complement. In the case k = 0 we obtain improved bounds for the independence number of various benchmark graphs.

Modelling the likely impact of healthy eating guidelines on agricultural production and land use in England and Wales

Quadratic programming techniques were applied to household food consumption data in England and Wales to estimate likely changes in diet under healthy eating guidelines, and the consequences this would have on agriculture and land use in England and Wales. The first step entailed imposing nutrient restrictions on food consumption following dietary recommendations suggested by the UK Department of Health. The resulting diet was used, in a second step as a proxy for demand in agricultural commodities, to test the impact of such a scenario on food production and land use in England and Wales and the impacts of this on agricultural landscapes. Results of the diet optimisation indicated a large drop in consumption of foods rich in saturated fats and sugar, essentially cheese and sugar-based products, along with lesser cuts of fat and meat products. Conversely, consumption of fruit and vegetables, cereals, and flour would increase to meet dietary fibre recommendations. Such a shift in demand would dramatically affect production patterns: the financial net margin of England and Wales agriculture would rise, due to increased production of high market value and high economic margin crops. Some regions would, however, be negatively affected, mostly those dependent on beef cattle and sheep production that could not benefit from an increased demand for cereals and horticultural crops. The effects of these changes would also be felt in upstream industries, such as animal feed suppliers. While arable dominated landscapes would be little affected, pastoral landscapes would suffer through loss of grazing management and, possibly, land abandonment, especially in upland areas.

Covariance matrix adapted evolution strategy-based decentralised congestion management for multilateral transactions

This study proposes AC load flow-based decentralised model for congestion management in the forward markets using resource allocation technique. In this model, each transaction maximises its profit under the limits of transmission line capacities allocated by independent system operator. The voltage and reactive power impact of the system are also incorporated in the model. A covariance matrix adapted evolution strategy (CMAES) algorithm is used to solve decentralised congestion management problem for multilateral transactions. The proposed approach is tested on IEEE 30 bus, IEEE 118 bus and practical Indian utility 62 bus systems for three, six and two multilateral transactions, respectively, with smooth and non-smooth cost functions. The results obtained for decentralised model using CMAES algorithm is compared with particle swarm optimisation (PSO) algorithm and sequential quadratic programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare for 20 independent trials are given. To prove the validity of the proposed improved decentralised model, the results obtained are also compared with centralised model. Simulation results clearly demonstrate the better performance of CMAES algorithm over PSO and SQP.

A simple method for designing quadrature mirror filter banks via quadratic constrained optimisation

This paper proposes a simple algorithm for the design of a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is formulated as a quadratic constrained least square minimisation that optimises the performance of a prototype filter (PF) and distortion transfer function of filter bank at quadrature frequency. A new method is developed for the design of a low pass prototype filter for QMF banks. For solving the given optimisation problem, a sequential quadratic programming (SQP) technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and the effectiveness of the proposed method. An application of this method is considered in the area of subband coding of the images.

A quadratic programming based cluster correspondence projection algorithm for fast point matching

Point matching is a challenging problem in the fields of computer vision, pattern recognition and medical image analysis, and correspondence estimation is the key step in point matching. This paper presents a quadratic programming based cluster correspondence projection (QPCCP) algorithm, where the optimal correspondences are searched via gradient descent and the constraints on the correspondence are satisfied by projection onto appropriate convex set. In the iterative projection process of the proposed algorithm, the quadratic programming technique, instead of the traditional POCS based scheme, is employed to improve the accuracy. To further reduce the computational cost, a point clustering technique is introduced and the projection is conducted on the point clusters instead of the original points. Compared with the well-known robust point matching (RPM) algorithm, no explicit annealing process is required in the proposed QPCCP scheme. Comprehensive experiments are performed to verify the effectiveness and efficiency of the QPCCP algorithm in comparison with existing representative and state-of-the-art schemes. The results show that it can achieve good matching accuracy while reducing greatly the computational complexity.

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem.

Dsoa: The implementation of a dynamic system optimization algorithm

AbstractThis paper describes the ANSI C/C++ computer program dsoa, which implements an algorithm for the approximate solution of dynamics system optimization problems. The algorithm is a direct method that can be applied to the optimization of dynamic systems described by index‐1 differential‐algebraic equations (DAEs). The types of problems considered include optimal control problems and parameter identification problems. The numerical techniques are employed to transform the dynamic system optimization problem into a parameter optimization problem by: (i) parameterizing the control input as piecewise constant on a fixed mesh, and (ii) approximating the DAEs using a linearly implicit Runge‐Kutta method. The resultant nonlinear programming (NLP) problem is solved via a sequential quadratic programming technique. The program dsoa is evaluated using 83 nontrivial optimal control problems that have appeared in the literature. Here we compare the performance of the algorithm using two different NLP problem solvers, and two techniques for computing the derivatives of the functions that define the problem. Copyright © 2009 John Wiley & Sons, Ltd.

Piecewise regression for fuzzy input–output data with automatic change-point detection by quadratic programming

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.

On the accurate prediction of interfacial micro-slip in frictional joints using distributed dislocations and quadratic programming techniques

Relative displacement between pre-stressed and frictionally interlocked components can play a major role in the failure of mechanical assemblies. The undesired relative motion between the mating parts constituting the coupling may be the result of the accumulation of interfacial micro-slip along a preferred direction. Classical approaches for the design of these systems are based on macroscopic criteria, where potentially severe localised stress conditions giving rise to micro-slip are not considered. A quadratic programming approach which enables to resolve interfacial micro-slip adopting the distributed dislocation technique is proposed here to overcome the limitation of existing formulations.

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.

Primal-dual interior-point method for thermodynamic gas-particle partitioning

A mathematical model for the computation of the phase equilibrium and gas-particle partitioning in atmospheric organic aerosols is presented. The thermodynamic equilibrium is determined by the global minimum of the Gibbs free energy under equality and inequality constraints for a system that involves one gas phase and many liquid phases. A primal-dual interior-point algorithm is presented for the efficient solution of the phase equilibrium problem and the determination of the active constraints. The first order optimality conditions are solved with a Newton iteration. Sequential quadratic programming techniques are incorporated to decouple the different scales of the problem. Decomposition methods that control the inertia of the matrices arising in the resolution of the Newton system are proposed. A least-squares initialization of the algorithm is proposed to favor the convergence to a global minimum of the Gibbs free energy. Numerical results show the efficiency of the approach for the prediction of gas-liquid-liquid equilibrium for atmospheric organic aerosol particles.

System protection scheme for mitigation of cascaded voltage collapses

A system protection scheme is proposed to mitigate cascaded voltage collapses. Based on the post-contingency conditions of either existence or non-existence of an equilibrium solution, and with regard to the stability and security criteria, the proposed scheme finds the optimal set of remedies. The proposed stabilising scheme brings the non-equilibrium post-contingency operating point back inside a stable region, and then passes this point to the securing scheme. Also, to enhance the performance of the stabilising scheme, a sensitivity analysis method is presented to detect the most effective remedies. The proposed securing scheme converts the stable, but insecure operating point, to a secure and stable one. Inclusion of the contingencies in the voltage security problem increases its difficult and, hence, the Benders decomposition method is used for this purpose. Also, a voltage stability indicator is proposed to monitor the available margin to the collapse point. Both the mathematical models of the stabilising and securing schemes are solved using the sequential quadratic programming technique over the IEEE 30-bus and IEEE 118-bus test cases.

THE DYNAMICAL STRUCTURE OF DARK MATTER HALOS WITH UNIVERSAL PROPERTIES

$N$-body simulations have unveiled several apparently universal properties of dark matter halos, including a cusped density profile, a power-law pseudo phase-space density $\rho/\sigma_r^3$, and a linear $\beta-\gamma$ relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions $F(E,L)$, based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These distribution functions, derived using a quadratic programming technique, are analytical, positive and smooth over the entire phase space and are able to generate four-parameter velocity anisotropy profiles $\beta(r)$ with arbitrary asymptotic values $\beta_0$ and $\beta_\infty$. We discuss the orbital structure of six radially anisotropic systems in detail and argue that, apart from its use for generating initial conditions for $N$-body studies, our dynamical modeling provides a valuable complementary approach to understand the processes involved in the formation of dark matter halos.

Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification

Wavelet theory has a profound impact on signal processing as it offers a rigorous mathematical framework to the treatment of multiresolution problems. The combination of soft computing and wavelet theory has led to a number of new techniques. On the other hand, as a new generation of learning algorithms, support vector regression (SVR) was developed by Vapnik et al. recently, in which ɛ-insensitive loss function was defined as a trade-off between the robust loss function of Huber and one that enables sparsity within the SVs. The use of support vector kernel expansion also provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, for the support vector regression with the standard quadratic programming technique, the implementation is computationally expensive and sufficient model sparsity cannot be guaranteed. In this article, from the perspective of model sparsity, the linear programming support vector regression (LP-SVR) with wavelet kernel was proposed, and the connection between LP-SVR with wavelet kernel and wavelet networks was analyzed. In particular, the potential of the LP-SVR for nonlinear dynamical system identification was investigated.

Development of Probiotic Candies with Optimal Viability by Using Response Surface Methodology and Sequential Quadratic Programming

The objective of this research was to create a new probiotic candy with good flavor and healthy benefits by using the response surface method and a sequential quadratic programming technique. The endpoint was to increase the varieties of dairy products and enhance their market values. In this study, milk was mixed with yogurt cultures (Lactobacillus bulgaricus, Streptococcus thermophilus) and probiotics (L. paracasei, Bifidobacterium longum) and incubated at 37°C for 20 h. The samples were blended with lyoprotectants (galactose, skim milk powder and sucrose), freeze dried and then mixed with sweeteners (lactose and xylitol) to improve the texture for forming tablets. The processing conditions were optimized in two steps: the first step constructed a surface model using response surface methodology; the second step optimized the model with a sequential quadratic programming procedure. Results indicated that skim milk inoculated with L. delbrueckii subsp. Bulgaricus, S. thermophilus, L. paracasei subsp. paracasei and B. longum and blended with 6.9% of galactose, 7.0% of sucrose and 8.0% of skim milk powder would produce a new probiotic candy with the highest viability of probiotics and good flavor. A relatively higher survival of probiotics can be achieved by placing the probiotic candy product in a glass bottle with deoxidant and desiccant at 4°C. These probiotic counts remained at 10 6 -10 8 CFU/g after being stored for two months.

Influence of Wall Slip on the Dynamic Properties of a Rotor-Bearing System

Based on the limiting shear stress model, we used a multi-linearity finite element algorithm and quadratic programming technique to study the influence of wall slip (boundary slip) on the operation stability of a rigid rotor-bearing system. The shaft surface is designed as a no-slip surface. The bearing sleeve surface is designed as three types of surfaces: (a) no slip is allowed (traditional no-slip rotor-bearing system), (b) the entire sleeve surface has the same slip property (the homogeneous slip bearing), and (c) the sleeve surface is optimized to have an optimized slip zone (the optimized slip bearing). It is found that if the sleeve surface has a single slip property, the wall slip generally reduces the system operation stability, as well as the load-carrying capacity. However, if the sleeve surface is designed as the optimized slip surface, the wall slip enhances the system operation stability as well as the load-carrying capacity. Furthermore, the smaller the surface limiting shear stress, the better the dynamic stability and the higher the load-carrying capacity.