Nonlinear Numerical Optimization Research Articles

Improved particle swarm optimization algorithm for multi-reservoir system operation

In this paper, a hybrid improved particle swarm optimization (IPSO) algorithm is proposed for the optimization of hydroelectric power scheduling in multi-reservoir systems. The conventional particle swarm optimization (PSO) algorithm is improved in two ways: (1) The linearly decreasing inertia weight coefficient (LDIWC) is replaced by a self-adaptive exponential inertia weight coefficient (SEIWC), which could make the PSO algorithm more balanceable and more effective in both global and local searches. (2) The crossover and mutation idea inspired by the genetic algorithm (GA) is imported into the particle updating method to enhance the diversity of populations. The potential ability of IPSO in nonlinear numerical function optimization was first tested with three classical benchmark functions. Then, a long-term multi-reservoir system operation model based on IPSO was designed and a case study was carried out in the Minjiang Basin in China, where there is a power system consisting of 26 hydroelectric power plants. The scheduling results of the IPSO algorithm were found to outperform PSO and to be comparable with the results of the dynamic programming successive approximation (DPSA) algorithm.

Verification of very strong coupling in a semiconductor optical microcavity

We study the very strong coupling effect in a semiconductor optical microcavity in which the exciton radius is dramatically modified due to the presence of strong photon–exciton coupling by means of nonlinear numerical optimization. To experimentally verify the features of very strong coupling and distinguish them from those of strong coupling, we propose two schemes and show that our proposals can provide unequivocal experimental proof of the existence of very strong coupling.

Supporting adaptive and irregular parallelism for non-linear numerical optimization

This paper presents an infrastructure for high performance numerical optimization on clusters of multicore systems. Building on a runtime system which implements a programming and execution environment for irregular and adaptive task-based parallelism, we extract and exploit the parallelism of a Multistart optimization strategy at multiple levels, which include second order derivative calculations for Newton-based local optimization. The runtime system can support a dynamically changing hierarchical execution graph, without any assumptions on the levels of parallelization. This enables the optimization practitioners to implement, transparently, even more complicated schemes. We discuss parallelization details and task distribution schemes for managing nested and dynamic parallelism. In addition, we apply our framework to a real-world application case that concerns the protein conformation problem. Finally, we report performance results for all the components of our system on a multicore cluster.

A simple iterative positioning algorithm for client node localization in WLANs

Abstract The ability to determine in real-time the geographic location of client nodes is an important tool in wireless networks, allowing instantaneous mobile tracking, implementation of location-aware services and also efficient channel and power allocation planning. Among existing classical cooperative localization techniques for wireless networks, the maximum likelihood estimator (MLE) is theoretically the best. However, the gradient-based algorithms that are commonly used for maximum likelihood estimation are quite sensitive to the initial values and cannot achieve the theoretical optimal performance. In this paper, we propose a new iterative positioning algorithm based on received signal strength information that employs a location ordering strategy and a numerical nonlinear optimization method. The algorithm performance is evaluated through simulation for different network scenarios. A real wireless network scenario is also implemented in order to demonstrate the algorithm effectiveness. The proposed algorithm, while presenting a simplified implementation, can achieve better positioning estimates than the classical MLE approach based on the conjugated gradient.

Backtracking Search Optimization Algorithm for numerical optimization problems

This paper introduces the Backtracking Search Optimization Algorithm (BSA), a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. EAs are popular stochastic search algorithms that are widely used to solve non-linear, non-differentiable and complex numerical optimization problems. Current research aims at mitigating the effects of problems that are frequently encountered in EAs, such as excessive sensitivity to control parameters, premature convergence and slow computation. In this vein, development of BSA was motivated by studies that attempt to develop simpler and more effective search algorithms. Unlike many search algorithms, BSA has a single control parameter. Moreover, BSA’s problem-solving performance is not over sensitive to the initial value of this parameter. BSA has a simple structure that is effective, fast and capable of solving multimodal problems and that enables it to easily adapt to different numerical optimization problems. BSA’s strategy for generating a trial population includes two new crossover and mutation operators. BSA’s strategies for generating trial populations and controlling the amplitude of the search-direction matrix and search-space boundaries give it very powerful exploration and exploitation capabilities. In particular, BSA possesses a memory in which it stores a population from a randomly chosen previous generation for use in generating the search-direction matrix. Thus, BSA’s memory allows it to take advantage of experiences gained from previous generations when it generates a trial preparation. This paper uses the Wilcoxon Signed-Rank Test to statistically compare BSA’s effectiveness in solving numerical optimization problems with the performances of six widely used EA algorithms: PSO, CMAES, ABC, JDE, CLPSO and SADE. The comparison, which uses 75 boundary-constrained benchmark problems and three constrained real-world benchmark problems, shows that in general, BSA can solve the benchmark problems more successfully than the comparison algorithms.

Nonlinear optimization for drift removal in estimation of gait kinematics based on accelerometers

A new data processing method is described for estimation of angles of leg segments, joint angles, and trajectories in the sagittal plane from data recorded by sensors units mounted at the lateral side of leg segments. Each sensor unit comprises a pair of three-dimensional accelerometers which send data wirelessly to a PC. The accelerometer signals comprise time-varying and temperature-dependent offset, which leads to drift and diverged signals after integration. The key features of the proposed method are to model the offset by a slowly varying function of time (a cubic spline polynomial) and evaluate the polynomial coefficients by nonlinear numerical simplex optimization with the goal to reduce the drift in processed signals (angles and movement displacements). The angles and trajectories estimated by our method were compared with angles measured by an optical motion capture system. The comparison shows that the errors for angles (rms) were below 4° and the errors in stride length were below 2%. The algorithm developed is applicable for real-time and off-line analysis of gait. The method does not need any adaptation with respect to gait velocity or individuality of gait.

임무기반 태양동기궤도 운영궤도 설계에 관한 연구

This paper presents a mission orbit design method for spacecraft which use the sun-synchronous and ground repeat orbits. In this work, we have proposed a new design procedure, “Nonlinear simulation-based numerical optimization technique” using the commercial S/W’s such as STK (Satellite Tool kit) and Matlab, which are widely adopted S/W’s in the area of orbital mechanics and engineering analysis. Inclusion of all the perturbation effects on the spacecraft not only can more precisely satisfy the mission requirements for sun-synchronicity and repeated ground track, and also operational requirements such as minimum change in the S/C local time, maximization of the contact time with a specified ground station, etc. can be appropriately considered. Design examples for LEO sun-synchronous mission are presented to demonstrate the usefulness of the proposed method in this paper.

A note on teaching–learning-based optimization algorithm

Teaching–Learning-Based Optimization (TLBO) seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances. It is reported that it outperforms some of the well-known metaheuristics regarding constrained benchmark functions, constrained mechanical design, and continuous non-linear numerical optimization problems. Such a breakthrough has steered us towards investigating the secrets of TLBO’s dominance. This paper reports our findings on TLBO qualitatively and quantitatively through code-reviews and experiments, respectively. Our findings have revealed three important mistakes regarding TLBO: (1) at least one unreported but important step; (2) incorrect formulae on a number of fitness function evaluations; and (3) misconceptions about parameter-less control. Additionally, unfair experimental settings/conditions were used to conduct experimental comparisons (e.g., different stopping criteria). The experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy. The ultimate goal of this paper is to provide reminders for metaheuristics’ researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects, and to allow fair comparisons of the TLBO algorithm to be made with other metaheuristic algorithms.

Preconditioning Large Indefinite Linear Systems

After briefly recalling some relevant approaches for preconditioning large symmetric linear systems, we describe a novel class of preconditioners. Our proposal is tailored for large indefinite linear systems, which arise very frequently in many different contexts of numerical analysis and nonlinear optimization. Our preconditioners are built as a byproduct of the Krylov subspace method used to solve the system. We describe theoretical properties of the proposed class of preconditioners, namely their capability of both shifting some eigenvalues of the system’s matrix to controlled values, and reducing the modulus of the other ones. The results of a numerical experimentation give evidence of the good performance of our proposal.

Determination of cohesive parameters for a mixed-mode cohesive zone model

The mechanical behaviour and failure properties of adhesive joints are influenced not only by adhesive properties but also by interface characteristics. Various modelling methods have been proposed to predict the failure behaviour of adhesive joints. Among those methods, cohesive zone modelling, which consists of introducing a cohesive law in the numerical models to reproduce the adhesive layer, is widely used to simulate the behaviour of adhesive joints. The cohesive parameters of the traction–separation laws in each pure mode should be determined for application of this technique. It is known that the cohesive parameters are affected by both adhesive properties and interface characteristics so, in most cases, these parameters are iteratively obtained by matching numerical results to experimental results. In this paper, a systematic procedure for the determination of the cohesive parameters is proposed by introducing an optimization technique (design of experiment and the kriging metamodel). The first step is to identify design variables affecting a response of a system. In this study, the cohesive parameters are selected as the design variables. Once the design variables are identified, design ranges or sampling ranges of the design variables are determined in order to result in a near optimal response with the determined sampling ranges. If the design variables and the sampling ranges are obtained then the design of experiment is performed to determine appropriate sampling points in the sampling ranges and a minimum number of simulations. Then, the load difference between numerical and experimental load–displacement results at several values of displacements are defined as an error, and the kriging metamodel, which surrogates the error, is constructed based on the sampling points. Cohesive parameters are determined by applying the numerical nonlinear optimization algorithm to minimize the error. The proposed procedure is applied to a co-cured Single Leg Bending (SLB) joint under mode I and mode II-dominant modes and the cohesive parameters are determined. From these parameters, the mixed-mode cohesive zone model is constructed and applied to the simulation of the co-cured SLB joint under varying mode-mixities. Simulation results are compared with the experimental results. It is shown that the failure behaviour of the SLB joint is well-described by using the mixed-mode cohesive zone model with the determined parameters.

Nonlinear Numerical Optimization Design Applied to Wall-Thickness of Welding T Shaped Connecting HDPE Tube

There are two reasons to enlarge the thickness of welding HDPE tri-branch tube. Firstly, welding weakens the HDPE material properties. Secondly, stress concentration occurs at the joint of tri-branch tube. The material properties of HDPE and the tensile strength of welding HDPE were tested. Based on the test results, the wall-thickness of HDPE tri-branch tube was investigated by numerical optimization design with particle swarm optimization (PSO). Two material constitutive models of elasto-palstic and Ramberg-Osgood for HDPE are adopted in FEM. Some valuable conclusions of pipeline design are concluded by the distribution of stress contour curves and optimization curves of welding joint of HDPE tri-branch tube.

1A1-A13 二慣性系における疲労破壊回避のための機械要素と制御系の混合設計(動作計画と制御の新展開)

We propose a mixed design of machine elements and control systems which aims at avoiding metal fatigue in two-inertia systems. On the basis of an elementary knowledge of material mechanics and machine design, we derive an allowable torsional angle of rotary shafts. Using the ciritical control design framework and the method of inequalities, we design both the diameter of shafts and a feedback controller so as to bound the torsional angle within the allowable value and achieve satisfactory closed-loop performance. An iterative design procedure using bisection algorithm and numerical nonlinear optimization is developed. We finally give a numerical example to evaluate the proposed mixed design method.

Narrow-band low-noise amplifier synthesis for high-performance system-on-chip design

In this paper, we present a systematic synthesis methodology for fully integrated narrow-band CMOS low-noise amplifiers (LNAs) in high-performance system-on-chip (SoC) designs. The methodology is based on deterministic gradient-based numerical nonlinear optimization and the normal boundary intersection (NBI) method for Pareto optimization. We simultaneously optimize transistor widths, bias voltages, and input and output matching network passive components, which yields integrated inductor values that are more than one order of magnitude less than those generated by several existing equation-based LNA design techniques. By generating significantly smaller inductor values, we enable the SoC integration of the complete LNA. When the synthesized LNAs are characterized using circuit-level simulation, our methodology yields up to 35% and 58% improvement in noise figure and gain, respectively.

MANAGING COMPLEXITY IN LARGE SCALE CONTROL SYSTEMS

This paper presents a data-based iterative tuning technique for large systems with multiple parameters. The method uses multivariate statistical regression methods to capture the dependencies between the system parameters and the quality measures determining the performance of the system. Nonlinear numerical optimization methods are applied for parameter tuning. Complementary tools to support the tuning procedure are suggested. Results from a simulated case study on a continuous pulp digester model are presented.

Wakeby Distribution and the Maximum Likelihood Estimation Algorithm in Which Probability Density Function Is Not Explicitly Expressed

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

Polygonal surface mesh optimization

A procedure has been developed to improve polygonal surface mesh quality while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices so that they remain on the original discrete surface. The repositioning is performed in a series of triangular-facet-based local parametric spaces. The movement of the mesh vertices is driven by a nonlinear numerical optimization process. Two optimization approaches are described, one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh.

Generation of enhanced initial estimates for Hammerstein Systems

Hammerstein systems are nonlinear models that are used in many domains for their simplicity and physical meaning. This paper presents a simple iterative method for generating good starting values which can be used to initialize the numerical nonlinear optimization of the cost function. In the absence of model errors, the presented method is proven to converge locally to the true model values in the noise-less case.

Triangular and quadrilateral surface mesh quality optimization using local parametrization

A procedure is presented to improve the quality of surface meshes while maintaining the essential characteristics of the discrete surface. The surface characteristics are preserved by repositioning mesh vertices in a series of element-based local parametric spaces such that the vertices remain on the original discrete surface. The movement of the mesh vertices is driven by a non-linear numerical optimization process. Two optimization approaches are described, one which improves the quality of elements as much as possible and the other which improves element quality but also keeps the new mesh as close as possible to the original mesh.

Generation of enhanced initial estimates for wiener systems and harnrnerstein systems

Wiener systems and Hammerstein systems are nonlinear models that are used in many domains for their simplicity and physical meaning. However, when these systems are identified, a cost function which is highly non-quadratic in the system parameters needs to be minimized. This paper presents a simple iterative method for generating good starting values which can be used to initialize the numerical nonlinear optimization of the cost function.

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.