Optimization Setup Research Articles

Combined Individual Pitch and Flap Control for Load Reduction of Wind Turbines

In this paper individual pitch control is combined with trailing-edge flap (TEF) control, both designed as multi-loop proportional-integral-derivative (PID) controllers, to significantly reduce blade damage equivalent loads. OpenFAST NREL 5MW aerodynamics are enhanced with dedicated aerodynamic polars of TEF blade elements. The NREL 5MW model, including the TEF extension, is incorporated into Simulink, and PID controller parameters are optimized in a closed-loop optimization setup. The DEL decrease is confirmed via an extensive simulation campaign using the non-linear wind turbine simulation environment.

Mathematical optimization and machine learning to support PCB topology identification

Abstract. In this paper, we study an identification problem for schematics with different concurring topologies. A framework is proposed, that is both supported by mathematical optimization and machine learning algorithms. Through the use of Python libraries, such as scikit-rf, which allows for the emulation of network analyzer measurements, and a physical microstrip line simulation on PCBs, data for training and testing the framework are provided. In addition to an individual treatment of the concurring topologies and subsequent comparison, a method is introduced to tackle the identification of the optimum topology directly via a standard optimization or machine learning setup: An encoder-decoder sequence is trained with schematics of different topologies, to generate a flattened representation of the rated graph representation of the considered schematics. Still containing the relevant topology information in encoded (i.e., flattened) form, the so obtained latent space representations of schematics can be used for standard optimization of machine learning processes. Using now the encoder to map schematics on latent variables or the decoder to reconstruct schematics from their latent space representation, various machine learning and optimization setups can be applied to treat the given identification task. The proposed framework is presented and validated for a small model problem comprising different circuit topologies.

Fuzzy Observer-Based Output Feedback Control of Continuous-Time Nonlinear Two-Dimensional Systems

The fuzzy observer-based output feedback control of continuous-time nonlinear two-dimensional systems is studied by T-S fuzzy models in this work. The plant information of the two-dimensional systems evolves along two independent directions dynamically. The nonlinear two-dimensional systems are firstly expressed by Takagi-Sugeno fuzzy models with parameter uncertainties. By a Lyapunov method together with some convexification techniques, two methods are developed for fuzzy observer-based output feedback controller synthesis of the underlying fuzzy two-dimensional systems, and novel output feedback controller synthesis results are proposed within a convex optimization setup. Simulation studies are provided to illustrate the validity of the proposed methods.

Provably accurate and scalable linear classifiers in hyperbolic spaces

Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces, and one often seeks low-dimensional embeddings in other space forms to perform the required learning tasks. For hierarchical data, the space of choice is a hyperbolic space because it guarantees low-distortion embeddings for tree-like structures. The geometry of hyperbolic spaces has properties not encountered in Euclidean spaces that pose challenges when trying to rigorously analyze algorithmic solutions. We propose a unified framework for learning scalable and simple hyperbolic linear classifiers with provable performance guarantees. The gist of our approach is to focus on Poincaré ball models and formulate the classification problems using tangent space formalisms. Our results include a new hyperbolic perceptron algorithm as well as an efficient and highly accurate convex optimization setup for hyperbolic support vector machine classifiers. Furthermore, we adapt our approach to accommodate second-order perceptrons, where data are preprocessed based on second-order information (correlation) to accelerate convergence, and strategic perceptrons, where potentially manipulated data arrive in an online manner and decisions are made sequentially. The excellent performance of the Poincaré second-order and strategic perceptrons shows that the proposed framework can be extended to general machine learning problems in hyperbolic spaces. Our experimental results, pertaining to synthetic, single-cell RNA-seq expression measurements, CIFAR10, Fashion-MNIST and mini-ImageNet, establish that all algorithms provably converge and have complexity comparable to those of their Euclidean counterparts.

Multidisciplinary concurrent optimization framework for multi-phase building design process

AbstractModern day building design projects require multidisciplinary expertise from architects and engineers across various phases of the design (conceptual, preliminary, and detailed) and construction processes. The Architecture Engineering and Construction (AEC) community has recently shifted gears toward leveraging design optimization techniques to make well-informed decisions in the design of buildings. However, most of the building design optimization efforts are either multidisciplinary optimization confined to just a specific design phase (conceptual/preliminary/detailed) or single disciplinary optimization (structural/thermal/daylighting/energy) spanning across multiple phases. Complexity in changing the optimization setup as the design progresses through subsequent phases, interoperability issues between modeling and physics-based analysis tools used at later stages, and the lack of an appropriate level of design detail to get meaningful results from these sophisticated analysis tools are few challenges that limit multi-phase multidisciplinary design optimization (MDO) in the AEC field. This paper proposes a computational building design platform leveraging concurrent engineering techniques such as interactive problem structuring, simulation-based optimization using meta models for energy and daylighting (machine learning based) and tradespace visualization. The proposed multi-phase concurrent MDO framework is demonstrated by using it to design and optimize a sample office building for energy and daylighting objectives across multiple phases. Furthermore, limitations of the proposed framework and future avenues of research are listed.

An abstract convergence framework with application to inertial inexact forward–backward methods

In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of several first-order methods designed for nonsmooth nonconvex optimization problems. Such properties guarantee the convergence of the full sequence of iterates to a stationary point, if the objective function satisfies the Kurdyka-Lojasiewicz property. The abstract framework allows for the design of new algorithms. We propose two inertial-type algorithms with implementable inexactness criteria for the main iteration update step. The first algorithm, i$^2$Piano, exploits large steps by adjusting a local Lipschitz constant. The second algorithm, iPila, overcomes the main drawback of line-search based methods by enforcing a descent only on a merit function instead of the objective function. Both algorithms have the potential to escape local minimizers (or stationary points) by leveraging the inertial feature. Moreover, they are proved to enjoy the full convergence guarantees of the abstract descent scheme, which is the best we can expect in such a general nonsmooth nonconvex optimization setup using first-order methods. The efficiency of the proposed algorithms is demonstrated on two exemplary image deblurring problems, where we can appreciate the benefits of performing a linesearch along the descent direction inside an inertial scheme.

Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamics

Bayesian optimization (BO) provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g., in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g., in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common BO algorithms on a range of synthetic test functions to provide general guidance on the design of BO algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo (MC) based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of BO to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics (CFD) are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.

Joint Power Control and Phase Shift Design for Future PD-NOMA IRS-Assisted Drone Communications under Imperfect SIC Decoding.

Intelligent reflecting surfaces (IRS) and power-domain non-orthogonal multiple access (PD-NOMA) have recently gained significant attention for enhancing the performance of next-generation wireless communications networks. More specifically, IRS can smartly reconfigure the incident signal of the source towards the destination node, extending the wireless coverage and improving the channel capacity without consuming additional energy. On the other side, PD-NOMA can enhance the number of devices in the network without using extra spectrum resources. This paper proposes a new optimization framework for IRS-enhanced NOMA communications where multiple drones transmit data to the ground Internet of Things (IoT) devices under successive interference cancellation errors. In particular, the power budget of each drone, PD-NOMA power allocation of IoT devices, and the phase shift matrix of IRS are simultaneously optimized to enhance the total spectral efficiency of the system. Given the system model and optimization setup, the formulated problem is coupled with three variables, making it very complex and non-convex. Thus, this work first transforms and decouples the problem into subproblems and then obtains the efficient solution in two steps. In the first step, the closed-form solutions for the power budget and PD-NOMA power allocation subproblem at each drone are obtained through Karush-Kuhn-Tucker (KKT) conditions. In the second step, the subproblem of efficient phase shift design for each IRS is solved using successive convex approximation and DC programming. Numerical results demonstrate the performance of the proposed optimization scheme in comparison to the benchmark schemes.

Investigation of Efficient Optimization Approach to the Modernization of Francis Turbine Draft Tube Geometry

The installation of new and revitalization of existing hydropower requires the optimal design of hydraulic turbine parts, which were previously mostly based on simplified analytical methods and engineering practices. With the increase in computational power, optimization methods now present an effective approach to the improvement of the geometry of turbine parts, thus enabling fine geometry-tuning adjustments of site specifics. However, despite continually increasing computational power, such numerical optimizations still require substantial resources and time. Therefore, in the proposed paper, extensive analysis of different numerical simplifications was conducted to determine the best trade-off between accuracy and the required computational resources for draft tube optimization. Additionally, the influence of geometry parametrization in terms of greater geometry flexibility, different goal functions, and optimization parameters was investigated. Within the considered constraints, a novel draft tube geometry was obtained, with the elbow displacements toward the draft tube exit, a shape that could not be obtained with the usual draft tube parametrization. It was also observed that geometry improvements for a single operating point did not provide improvements for other operating points. The obtained findings regarding the numerical and optimization setup can be used as guidelines for future optimization research, where multiobjective optimization for multiple operating points should be further investigated.

Neural network genetic algorithm optimization of a transient hybrid renewable energy system with solar/wind and hydrogen storage system for zero energy buildings at various climate conditions

This research aims to investigate a hybrid renewable energy system (HRES) and its integration in buildings to create zero-energy buildings. Each location has its specific climate condition that requires a related HRES configuration that can address energy demand in that particular location. Hence, the applicability of HRES in four different case studies has been considered, Tehran, Yazd, Tabriz, and Bandar Abbas. The energy system has been simulated in TRNSYS, which is a powerful transient-simulation software. Although energy system simulation in TRNSYS brings users remarkable benefits, it lacks an optimization setup. To address the mentioned issue, a neural network-genetic algorithm optimization has been proposed. Simulated HRES comprised of PV panels, vertical axis wind turbines, and hydrogen storage. Results of the simulation indicate between 35% and 49% of the required electricity of the buildings in each city can be generated via PV panels and wind turbines, and between 70% and 88% can be encompassed with the combination of renewable resources and a hydrogen storage system depend on the climate. Results indicate that adding a hydrogen storage system to the main system increases the reliability of the HRES and reduces dependency on grid electricity. Afterward, by employing a neural network–genetic algorithm optimization method, an optimized number of PV panels and wind turbines for the building located in Tehran as a final case is computed. The optimized configuration has the lowest installation cost, CO2 production and loss of power supply probability (LPSP). Optimization procedure is implemented in MATLAB. Appraised data indicated that by installing 1 wind turbine and 291 PV panels, total CO2 production, LPSP, and cost are 53.48 ton/year, 0.4057, and 1.422 EUR/hr, respectively.

Robust Value Quantification of Enhanced Oil Recovery Methods Using Ensemble-Based Optimization

Summary Over the last decades, the development of different oil reservoirs with gas or chemical enhanced oil recovery (EOR) methods have been studied, and the EOR effects of the recovery methods are found to be sensitive to fluid and rock properties in the reservoirs. The use of a single reservoir model with the assumption of known reservoir parameters is not enough to guarantee an accurate prediction of EOR effects. The best decision related to the injection strategies of EOR methods can be appropriately found using an optimization setup that accounts for the uncertainty quantification in the reservoir. In this paper, we present mathematical tools for optimizing and ranking the value of the commonly used EOR methods. The methodology is demonstrated with Smartwater, carbon dioxide (CO2), and polymer EOR methods on synthetic 2D and 3D oil reservoirs. To capture the uncertainties in the reservoirs, we use an ensemble of geological realizations obtained by engineering upscaling of the initial model. The usefulness of this study is to improve the understanding of the actual benefit of EOR methods and to provide a methodology that quickly allows users to appropriately predict EOR injection strategies that maximize the annually discounted economic values of the injected and production data. The control variables of optimization problems include EOR gas rate or chemical concentration, water rates, oil rate, or bottomhole pressures. An ensemble-based optimization method with covariance adaptation is used to solve the optimization problem. For the different reservoirs considered, we find the optimal well controls for EOR methods. A comparative study of the economic benefits of the optimal solutions of EOR methods using optimized waterflooding as a reference point is presented. CO2 is found to rank high compared with other EOR methods in both cases. Finally, we investigate the effect of different injection costs of CO2 on the optimization results of CO2 EOR methods for the 3D reservoir field.

A hybrid deep learning framework for urban air quality forecasting

Deep learning models address air quality forecasting problems far more effectively and efficiently than the traditional machine learning models. Specifically, Long Short-Term Memory networks (LSTMs) constitute a significant breakthrough in understanding the complex sequential behavioral dependencies of the time series. Further, LSTM models justify well with the speed–accuracy tradeoff, among other deep learning models. However, there are several limitations of such deep learning models. Firstly, the addition of multiple hidden layers, on the one hand, improves the performance but, on the other hand, requires extensive hardware and computation capabilities. Secondly, most of the previous works that utilized LSTMs for air quality forecasting do not consider the issue of optimal hyperparameter calibration. While deciding the gradient, network learning parameters should be so fixed such that the model does not underfit or overfit. To address these issues, a stochastic optimization algorithm, mimicking the pattern of flocking birds, is utilized to find the most fitting solution in the parameter search space. Particle swarm optimization setup primarily models varying particles representing parameters to reach an optimum state. Furthermore, the Spatio-temporal instabilities of LSTM models are addressed in this work using preprocessing, segmentation and feature engineering to understand seasonal and trend characteristics along with the Spatio-temporal correlation of the time series. The proposed model is employed on the air quality dataset of 15 locations in India. A variety of experiments are performed to prove the superiority of the proposed method. Firstly, a comparison with traditional sequential models and deep learning models is done. Secondly, results are further evaluated over several existing benchmark dataset samples. Results suggest that the proposed method outperforms existing forecasting models when evaluated over a variety of performance metrics.

Model Predictive Path Planning for an Autonomous Ground Vehicle in Rough Terrain

An autonomous ground vehicle (AGV) in rough terrain typically experiences uncertain environment. Because the uncertainty makes overall performance of autonomous navigation degrade, the AGV requires a suitable path to maintain or improve the performance against the uncertainty. In order to handle this problem, this study proposes a model predictive path planning algorithm by employing a passivity-based model predictive control (MPC) optimization setup. The model predictive path planning method is formulated as a finite optimization problem with an objective function and several constraints. In the cost function, environment perception result about the AGV’s own neighborhood is included and the only traversable region has low cost value. To reflect dynamic characteristics of the AGV, the proposed method utilizes dynamic and kinematic models of the AGV as equality constraints and limited range of states and control input as inequality constraints. In addition, the stability of the path planning method is improved by a passivity constraint. The solution of the optimization problem is obtained using the particle swarm optimization (PSO) method. Finally, field tests are conducted to validate the performance of the proposed algorithm, and satisfactory results of the autonomous navigation were obtained.

Spatiotemporal Memories for Missing Samples Reconstruction.

We develop a systematic theory to reconstruct missing samples in a time series using a spatiotemporal memory based on artificial neural networks. The Markov order of the input process is learned and subsequently used for learning temporal correlations from data difference sequences. We enforce the Lipschitz continuity criterion in our algorithm, leading to a regularized optimization framework for learning. The performance of the algorithm is analyzed using both theory and simulations. The efficacy of the technique is tested on synthetic and real life data sets. Our technique is analytic and uses nonlinear feedback within an optimization setup. Simulation results show that the algorithm presented in this article significantly outperforms the state-of-the-art algorithms for missing samples reconstruction with the same data set and similar training conditions.

Stabilizing instability‐suboptimality‐and‐chaos‐prone fluctuations at crisis junctures: Stochastic possibilities for crisis management

AbstractThere is a rich array of ways in which unstable, suboptimal and chaos‐prone fluctuations could appear at crisis junctures. The richness of the patterns associated with such fluctuations presents considerable challenges to the theory of crises as well as the policies targeting various tendencies induced by crises. Dealing with complexly interwoven unstable, suboptimal and potentially chaotic tendencies is not an easy task, which may require new combinations of methods analysing the causal connections and feedback relations embedded in the web of relations characterizing the crisis‐junctures. In this paper, we develop an illustrative dynamic model that takes into account such causally connected feedback relations so as to construct and simulate stochastic policy options, which can influence and help stabilize unstable, suboptimal and chaotic trajectories of exchange rates at financial crisis junctures. For reasons of convenience and practical relevance, we exemplified such policies using taxes. One of the constructed examples makes use a stochastic taxing policy to influence the coefficient of adjustment, which influences the amount of adjustments and hence fluctuations in the market. We incorporate a software‐based optimization setup into the simulation model to find the optimal values of the policy parameter to be used for the purpose of simulating the trajectories of the exchange rates. It turns out that the suggested policies could influence/reduce the fluctuations in the market and hence help stabilize unstable or chaotic exchange rate trajectories. The second example in the paper is concerned with an empirical case relating to a particular financial crisis juncture of Turkey during May–November 2018.

Genetic algorithm applied to discrete optimization of band-pass microwave filter

We propose a design approach for band-pass microwave filters based on optimization of discrete-valued parameters of filters using an implementation of (1 + (l, l)) genetic algorithm. If the filter is made of SMD components then only discrete values are allowed. The proposed design approach yields a solution with feasible components values in the end, without further need for tuning and adjustments of component values that is needed in the case when real numbers are used during optimization. The optimization setup is run for 20 times and obtained (suboptimal) solutions are presented. One of the best optimized solutions of a band-pass filter is chosen for further analysis. The found filter design is verified using a circuit solver including the yield analysis, 3D electromagnetic simulations and by measurements of the manufactured prototype. The presented results as well as the optimization run-time show that the proposed approach based on discrete optimization can be used to design microwave filters.

The risk of making decisions from data through the lens of the scenario approach

Abstract In previous contributions, it has been shown that the “complexity” is a key indicator to quantify the “risk” associated to data-driven scenario-based solutions. Depending on the context of application, risk is interpreted as probability of misprediction, or probability of underperforming or meeting shortfalls in various control endeavors, and the acquired ability to tightly evaluate the risk is a vital element in a world where data-driven methods are being increasingly used not only for decision support but also for automated decision making. The present contribution is meant to significantly expand the area of applicability of these results: all achievements so far have been based on an assumption, called “non-degeneracy”, that hardly applies e.g. to optimization problems that are not convex. Here, we show that these results maintain their integrity in a non-convex optimization setup, and beyond into a broad domain of decision making that contains non-convex optimization as a particular case.

Proton or photon radiosurgery for cardiac ablation of ventricular tachycardia? Breath and ECG gated robust optimization.

Ventricular tachycardia (VT) is a life-threatening heart disorder. The aim of this preliminary study is to assess the feasibility of stereotactic body radiation therapy (SBRT) photon and proton therapy (PT) plans for the treatment of VT, adopting robust optimization technique for both irradiation techniques. ECG gated CT images (in breath hold) were acquired for one patient. Conventional planning target volume (PTV) and robust optimized plans (25GyE in single fraction) were simulated for both photon (IMRT, 5 and 9 beams) and proton (SFO, 2 beams) plans. Robust optimized plans were obtained both for protons and photons considering in the optimization setup errors (5mm in the three orthogonal directions), range (±3.5%) and the clinical target volume (CTV) motion due to heartbeat and breath-hold variability. The photon robust optimization method, compared to PTV-based plans, showed a reduction in the average dose to the heart by about 25%; robust optimization allowed also reducing the mean dose to the left lung from 3.4. to 2.8Gy for 9-beams configuration and from 4.1 to 2.9Gy for 5-beams configuration. Robust optimization with protons, allowed further reducing the OAR doses: average dose to the heart and to the left lung decreased from 7.3Gy to 5.2 GyE and from 2.9Gy to 2.2 GyE, respectively. Our study demonstrates the importance of the optimization technique adopted in the treatment planning system for VT treatment. It has been shown that robust optimization can significantly reduce the dose to healthy cardiac tissues and that PT further increases this gain.

Kinetic modeling and development of optimal trajectories for biodiesel production using multi-objective optimization

A kinetic model has been developed based on the experimental data in the open literature for the simultaneous esterification of myristic acid and transesterification of rapeseed oil with methanol by using sulphated zirconia catalyst at three different temperatures (120 °C, 150 °C, 170 °C) and methanol to oil ratio (20:1). The developed kinetic model has been utilized for the cross-validation of methanol to oil ratio of 10:1 and 4:1 and at a temperature of 170 °C, which is in accordance with the experimental data. Furthermore, the validated kinetic model has been extended to find the optimal process conditions for the desired conflicting objectives. Trade-off solutions for this process are obtained by utilizing the non-dominated sorting genetic algorithm (NSGA-II). The objective is to obtain maximum FAME (fatty acid methyl ester) in minimum methanol to oil ratio and minimum reaction temperature. Addition of oil, methanol, myristic acid and temperature are considered as decision variables with relevant process constraints. A wide range of choices have been obtained for the present optimization setup. The yield of FAME is strongly depends on the reaction temperature, reaction time and methanol to oil ratio. The optimal methanol to oil ratio of 10–15 is sufficient to enhance the FAME yield. • Kinetic modeling of simultaneous Transesterification and esterification. • Kinetic parameter estimation using RCGA. • Formulation of Multi-objective optimization. • Pareto optimal set obtained for the desired conflicting objectives.

Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the latter involving all the decision variables. We propose a novel fully distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation, based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node finds a primal-dual optimal solution pair of a local relaxed version of the original problem and then updates suitable auxiliary local variables. We prove that agents asymptotically compute their portion of an optimal (feasible) solution of the original problem. This primal recovery property is obtained without any averaging mechanism typically used in dual decomposition methods. To corroborate the theoretical results, we show how the methodology applies to an instance of a distributed model-predictive control scheme in a microgrid control scenario.