Nonlinear Optimization Approach Research Articles

Multi-objective Pareto and GAs nonlinear optimization approach for flyback transformer

Design and optimization of high-frequency inductive components is a complex task because of the huge number of variables to manipulate, the strong interdependence and the interaction between variables, the nonlinear variation of some design variables as well as the problem nonlinearity. This paper proposes a multi-objective design methodology of a 200-W flyback transformer in continuous conduction mode using genetic algorithms and Pareto optimality concept. The objective is to minimize loss, volume and cost of the transformer. Design variables such as the duty cycle, the winding configuration and the core shape, which have great effects on the former objectives but were neglected in previous works, are considered in this paper. The optimization is performed in discrete research space at different switching frequencies. In total, 24 magnetic materials, 6 core shapes and 2 winding configurations are considered in the database. Accurate volume and cost models are also developed to deal with the optimization in the discrete research space. The bi-objective (loss–volume) and tri-objective (loss–volume–cost) optimization results are presented, and the variations of the design variables are analyzed for the case of 60 kHz. An example of a design (30 kHz) is experimentally verified. The registered efficiency is 88% at full load.

Optimal Precursors Triggering the Kuroshio Intrusion Into the South China Sea Obtained by the Conditional Nonlinear Optimal Perturbation Approach

AbstractThe Kuroshio Intrusion (KI) into the South China Sea (SCS) is a key process that greatly modulates the variability of dominant phenomena in the northern SCS. Using the Regional Ocean Modeling System, the optimal precursor (OPR) triggering the KI is obtained by the Conditional Nonlinear Optimal Perturbation (CNOP) approach. The OPRs exhibit the anticyclonic eddies (AEs) spatial pattern in the southern region (19°N–20.3°N, 119°E–122°E) of the Luzon Strait. The evolution processes of the OPRs indicate that the northwestward movement and rapid growth of AEs force the Kuroshio to bend westward continuously, which leads to the transition of the Kuroshio path from leaping state to intruding state. Eddy‐energetic analyses suggested that the barotropic instabilities are responsible for the evolution of the OPRs and thus triggering the KI, while the local wind stress plays a minor role in the triggering process. Additional examinations based on satellite altimeter data and ocean reanalysis data further confirm that the AE‐like perturbation similar to the obtained OPR indeed plays a key role in the KI triggering process.

Algorithm development for real-time thin asphalt concrete overlay compaction monitoring using ground-penetrating radar

Ground-penetrating radar (GPR) is an effective, feasible, and non-destructive tool for real-time estimation of the density of asphalt concrete (AC) during compaction. When the AC pavement is thin, however, it is difficult to estimate the density due to the limited GPR signal resolution. In addition, the surface moisture, applied during compaction, has an effect on the GPR signal and hence impacts density prediction accuracy. In this study, a nonlinear optimization approach, based on gradient descent, was used to recover the AC pavement surface reflection. A “modified reference scan” approach was developed to remove the effect of surface moisture on GPR signals during density monitoring. The “modified reference scan” approach was first validated in a laboratory experiment setting, then validated in a field study near Chicago, IL, where GPR antennas were installed on the roller and data were collected during compaction. The results show that GPR is a prospective tool for real-time AC compaction monitoring.

Bearing the bear: Sentiment-based disagreement in multi-criteria portfolio optimization

Employing a nonlinear multi-criteria optimization approach, sentiment-based disagreement is incorporated into portfolio optimization as additional risk factor. A multi-criteria trading strategy outperforms several benchmarks regarding various performance measures. Applying the strategy over a long time period including downturns and upswings, disagreement proves itself especially valuable in bear markets as it is an indicator for future volatility.

Quality cost-based allocation of training hours using learning-forgetting curves

The training of suppliers and inbound quality inspectors is a common strategy to increase the quality performance of the supply chain but, under budget constraints, these actors compete for a limited amount of training hours. The proposed model aims to allocate the available training hours so as to minimise a total quality cost function composed of prevention, appraisal, and failure costs; it also sets the inspection rates defining the inspection policies assigned to suppliers. The relationship between decision variables and costs is expressed through organisational and individual learning-forgetting curves, for suppliers and quality inspectors respectively, and the effect of the training hours on quality improvement is measured in terms of failure rates. To the best of our knowledge, a total quality cost model with such decision variables is new in the related literature, as it is a model including both organisational and individual learning-forgetting phenomena.A nonlinear optimisation approach was adopted to solve this complex problem. The experimental section includes a decision trees analysis of simplified scenarios in order to interpret the model functioning, as well as a complex numerical example to extrapolate managerial insights.

Process Yield Index and Variable Sampling Plans for Autocorrelation Between Nonlinear Profiles

In this paper, a process yield-index for autocorrelation between nonlinear profiles is proposed. Applying a one-dimensional Taylor series expansion, the mean and variance of the estimator of the yield index are derived. To evaluate the performance of the proposed yield index a simulation study is conducted. The new index is employed to design three acceptance sampling plans for quality characteristics described by auto-correlated nonlinear profiles. The first sampling plan is based on resubmission. The remaining two follow the repetitive group and multiple dependent repetitive sampling schemes respectively. For all sampling plans, the operating characteristic function is developed. A non-linear optimization approach with search algorithm is employed to determine the number of profiles required for inspection and to decide critical values for acceptance, rejection, and resubmission criteria. The performance of the new methods is investigated and compared with traditional single sampling plan. The comparison confirms all of the three proposed methods possess higher efficiency than a single sampling plan in terms of sample size. For practical applications tables are provided. Two numerical examples from the automobile engine testing and particleboard manufacturing process are used to demonstrate the applicability of the proposed methods.

Regionalized Design Rainfall Estimation: an Appraisal of Inundation Mapping for Flood Management Under Data-Scarce Situations

Availability of regionalized design rainfall is crucial for flood modeling, particularly over the regions with sparse raingauge networks. This study proposes a new comprehensive framework for generating regionalized design rainfall time series for data-poor catchments involving non-linear and non-parametric optimization approaches. A large set of parametric and non-parametric families of distribution were considered for multivariate rainfall frequency analysis using at-site station data, while a unique design temporal pattern over the region was derived by quantifying the flood causing potential of design hyetographs. The regionalized design rainfall time series was used as one of the inputs to a two-dimensional (2D) flood model. The accuracy and performance of the derived regionalized design rainfall for flood inundation modeling were evaluated by comparing with those derived from different spatial interpolation methods. There was a high consensus of the former with those of widely used kriging and spline interpolation methods. A severely flood-prone and data-poor (no raingauge available within study area) large coastal catchment lying along the coast of the Bay of Bengal, India, was chosen for a demonstration of the proposed framework. The study showed that the framework can be used for extreme events arising due to floods, even under changing climatic scenarios. It further invokes the necessity for incorporating the proposed framework into various commercially and freely available flood models along with other existing interpolation techniques to support improved flood management.

A fully non-linear optimization approach to acousto-electric tomography

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric tomography, in which the measurement setup in electrical impedance tomography is modulated by ultrasonic waves thus giving rise to a method potentially having both high contrast and high resolution. We formulate the inverse problem as a regularized non-linear optimization problem, show the existence of a minimizer, and derive optimality conditions. We propose a non-linear conjugate gradient scheme for finding a minimizer based on the optimality conditions. All our numerical experiments are done in two-dimensions. The experiments reveal new insight into the non-linear effects in the reconstruction. One of the interesting features we observe is that, depending on the choice of regularization, there is a trade-off between high resolution and high contrast in the reconstructed images. Our proposed non-linear optimization framework can be generalized to other hybrid imaging modalities.

Prediction of thin asphalt concrete overlay thickness and density using nonlinear optimization of GPR data

The processing of ground-penetration radar (GPR) signals collected from thin asphalt concrete (AC) overlay is a challenging task due to the limitation of GPR signal resolution. In this study, a gradient descent based nonlinear optimization approach was developed to analyze GPR signals collected from thin AC overlays to estimate their thickness and density. Both finite difference time domain (FDTD) simulation and field tests were conducted to validate the proposed algorithm. The simulation showed that the accuracy of dielectric constant estimation increased after the nonlinear gradient descent method was applied. This resulted in a thickness estimation error of less than 1 mm. When nonlinear gradient descent was applied to field test measured signals, the average AC overlay thickness prediction and AC density estimation errors were 3 mm and 1.81%, respectively. This study demonstrates that the nonlinear gradient descent is an effective approach for estimating thin AC overlay thickness and density from GPR data.

Simultaneously optimizing the capacity and configuration of biorefineries

Abstract Advanced biomass conversion plants can replace fossil resources in the electricity, heat, transportation fuels and chemicals sectors, but they face specific challenges with regard to their economic operation. When choosing a capacity for a biomass conversion plant, economies of scale must be weighed against the transportation costs for the widely-distributed input materials. Here, we model the problem of determining the optimal capacity for plants with a single product or a fixed set of products using a single optimization variable and two alternative economic objective functions. To identify the factors that most strongly influence economic plant operation, we perform a sensitivity analysis of various model parameters to determine their impact on the optimal solution using the Envelope Theorem. We also present an optimization approach for simultaneously planning the capacity and configuration of multi-product plants. By modeling economies of scale on a process-specific level, our nonlinear optimization approach makes it possible to determine the optimal configurations, and thus ranges of products, for changing plant capacities. An examination of the obtained feasible solutions shows that the optimization problem is neither convex nor concave.

ENSO Predictions in an Intermediate Coupled Model Influenced by Removing Initial Condition Errors in Sensitive Areas: A Target Observation Perspective

Previous studies indicate that ENSO predictions are particularly sensitive to the initial conditions in some key areas (socalled "sensitive areas"). And yet, few studies have quantified improvements in prediction skill in the context of an optimal observing system. In this study, the impact on prediction skill is explored using an intermediate coupled model in which errors in initial conditions formed to make ENSO predictions are removed in certain areas. Based on ideal observing system simulation experiments, the importance of various observational networks on improvement of El Nio prediction skill is examined. The results indicate that the initial states in the central and eastern equatorial Pacific are important to improve El NiEeno prediction skill effectively. When removing the initial condition errors in the central equatorial Pacific, ENSO prediction errors can be reduced by 25%. Furthermore, combinations of various subregions are considered to demonstrate the efficiency on ENSO prediction skill. Particularly, seasonally varying observational networks are suggested to improve the prediction skill more effectively. For example, in addition to observing in the central equatorial Pacific and its north throughout the year, increasing observations in the eastern equatorial Pacific during April to October is crucially important, which can improve the prediction accuracy by 62%. These results also demonstrate the effectiveness of the conditional nonlinear optimal perturbation approach on detecting sensitive areas for target observations.

Integration of distributed generation technologies on sustainable buildings

This work addresses the optimal sizing and selection of the most used technologies reported in literature for energy and water supply of sustainable buildings. The addressed technologies includes Combined Heat and Power units, solar collectors, photovoltaic panels, conventional boilers, wind turbines, Organic Rankine Cycles, biogas production and water treatment systems. The selection technology problem is cast as an optimization model which takes into account embedded nonlinear behavior of the addressed equipment, especially the ones associated with operative efficiency, and dynamics of the storage units. The renewable energy generation, total annual cost, emissions generated and water consumption of the system are used as objective functions. Since some of these objective functions are contradictory, a multi-objective and multi-scenario Mixed Integer nonlinear optimization approach was used to reach trade-off solutions. The multi-objective approach presented allows to define the preferences of the designer based on predefined weights for reaching trade-off solutions using a dimensional approach. The environmental and energy profiles of a residential building in the Pacific Coast of Mexico are presented as Case Study. The results show the importance of including the nonlinear behavior of the technologies for defining a suitable operational policy as well as the effect of using different criteria about the design of water-energy systems.

Nonlinear impulsive optimal control synthesis with optimal impulse timing: A pseudo-spectral approach

Following the philosophy of pseudo-spectral approach, a nonlinear variable-time impulsive optimal control system design approach is presented in this paper for a class of problem with hard terminal constraint. In this approach the impulse application time instants are also take as ‘decision variables’ and are fixed through an optimization process in addition to the magnitudes of control at those instants. This gives additional freedom for optimization and hence leads to better performance than the fixed timing approach. Three benchmark problems which include a scalar linear problem, the Van-der Pol’s oscillator problem and an inverted pendulum problem are solved to demonstrate the effectiveness of the new technique. The proposed approach is also computationally efficient owing to the usage of the pseudo-spectral philosophy.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

A nonlinear optimal (H-infinity) control approach is proposed for the problem ofstabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic developmentmodel is divided in two parts. The first one describes economic activities in a developed country andthe second part describes variation of economic activities in a country under development which tries tomodify its production so as to serve the needs of the developed country. The article shows that throughcontrol of the macroeconomic model of the developed country, one can finally control the dynamicsof the economy in the country under development. The control method through which this is achievedis the nonlinear H-infinity control. The macroeconomic model for the country under developmentundergoes approximate linearization round a temporary operating point. This is defined at each timeinstant by the present value of the system’s state vector and the last value of the control input vectorthat was exerted on it. The linearization is based on Taylor series expansion and the computation of theassociated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed.The controller’s gain is calculated by solving an algebraic Riccati equation at each iteration of thecontrol method. The asymptotic stability of the control approach is proven through Lyapunov analysis.This assures that the state variables of the macroeconomic model of the country under developmentwill finally converge to the designated reference values.

Optimal Control of an Optical System for Material Testing

We implement a prototype for an application of automatic optical material testing in the manufacturing of glass panels. Based on a nonlinear optimal control approach, we present a numerical method for optimal control at run time. The algorithm will be demonstrated and tested with the help of an illustrative example where it turns out that the optimal control is of bang-bang or bang-zero-bang type, depending on the state constraints.

A nonlinear optimization model on the reinforcement length of a modular block wall by varying surcharge and soil strength parameters

This study proposes a nonlinear optimization approach in designing a modular block wall which is atype of the mechanical stabilized earth wall. A nonlinear optimization model is proposed based on minimizing the reinforcement length where the constraints considered are the external stability and the internal stability. Theoptimum reinforcement length can be determined based on available soil strength parameters and the maximum surcharge. This study also includes the parametric study of the reinforced soil, retained soil, and foundation soil by varying the ranges of the wall height, surcharge, and soil strength parameters in density and friction angle to see the behaviours of the aforementioned external stability and internal stability. This can be beneficial in designing thismodular block wall encountering a poor soil condition or a large amount surcharge.

A Nonlinear Optimal Control Approach to Stabilization of Business Cycles of Finance Agents

The article proposes a new nonlinear optimal control method for the stabilization of the business cycles of interconnected finance agents. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a model of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system’s state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme is globally asymptotically stable.

A Gradient-Based Coverage Optimization Strategy for Mobile Sensor Networks

A Voronoi-based strategy is proposed to maximize the sensing coverage in a mobile sensor network. Each sensor is moved to a point inside its Voronoi cell using a coverage improvement scheme. To this end, a gradient-based nonlinear optimization approach is utilized to find a target point for each sensor such that the local coverage increases as much as possible, if the sensor moves to this point. The algorithm is implemented in a distributed fashion using local information exchange among sensors. Analytical results are first developed for the single sensor case, and are subsequently extended to a network of mobile sensors, where it is desirable to maximize network-wide coverage with fast convergence. It is shown that under some mild conditions, the positions of the sensors converge to a stationary point of the objective function, which is the overall weighted coverage of the sensors. Simulations demonstrate the effectiveness of the proposed strategy.

Logistic Regression: From Art to Science

A high quality logistic regression model contains various desirable properties: predictive power, interpretability, significance, robustness to error in data and sparsity, among others. To achieve these competing goals, modelers incorporate these properties iteratively as they hone in on a final model. In the period 1991–2015, algorithmic advances in Mixed- Integer Linear Optimization (MILO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MILO problems. Motivated by this speedup, we propose modeling logistic regression problems algorithmically with a mixed integer nonlinear optimization (MINLO) approach in order to explicitly incorporate these properties in a joint, rather than sequential, fashion. The resulting MINLO is flexible and can be adjusted based on the needs of the modeler. Using both real and synthetic data, we demonstrate that the overall approach is generally applicable and provides high quality solutions in realistic timelines as well as a guarantee of suboptimality. When the MINLO is infeasible, we obtain a guarantee that imposing distinct statistical properties is simply not feasible.

Implementation of regularization for separable nonlinear least squares problems

This paper considers a class of separable nonlinear least squares problems in which a model can be represented as a linear combination of nonlinear functions. A regularized nonlinear parameter optimization approach is presented for coping with the potential ill-conditioned problem of parameter divergence. Together with a regularization parameter detection technique, Tikhonov regularization and truncated singular value decomposition are utilized in the estimation of the linear parameters if the nonlinear parameters are changed during the parameter optimization process, which centers on a nonlinear parameter search using the Levenberg-Marquardt algorithm. Benefiting from the regularization in parameter optimization, the potential ill-conditioned issue can be avoided, and the multi-step-ahead forecasting accuracy of the estimated model may be largely improved. The usefulness of this approach is illustrated by means of a chaotic time-series prediction and nonlinear industrial process modeling.