Nonlinear Optimization Techniques Research Articles

Studying the effects of Türkiye earthquake disaster and its impact on real estate industry: A risk analysis based on input-output & non-linear optimization models

The real estate industry of Türkiye is highly susceptible to seismic activity. The recent earthquakes have severely impacted the industry and the country's economy. This study examines Türkiye's real estate resilience during earthquakes using the Dynamic Inoperability Input-Output Model (DIIM) and a non-linear optimization technique. According to the findings of DIIM, specific industries, including those dealing with the supply of electricity and gas, chemicals, non-metallic minerals, and financial and insurance intermediaries, suffer significant financial losses. The levels of inoperability are highest in the mining and quarrying industries, followed by the chemical and non-metallic mineral product industries, and then by mining support activities. The top nine most inoperable industries account for approximately $9.5 billion in economic losses, with real estate alone accounting for $27.4 billion. The Fuzzy-FUCOM technique was used to identify significant risk factors related to technological, political, and social hazards, assisting policymakers in making more informed decisions. The novelty of this study is in its application of the DIIM model and a non-linear optimization technique to the challenge of seismic hazard mitigation in Türkiye's real estate market. In conclusion, this study's findings provide insight into Türkiye's affected sectors' risks, recovery time, and adaptability.

Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting ‘Cautious Bayesian MPC’ algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems. In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling. Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation. The efficiency of the method is illustrated using numerical examples.

A real-time collision-free maneuver generation algorithm for autonomous driving

In this paper we propose a real-time maneuver generation algorithm for Autonomous Vehicles (AVs). Given a planar road geometry with static and moving obstacles along it, we are interested in finding collision-free maneuvers that satisfied the AV’s dynamics and subject to physical and comfort limits. Based on longitudinal and transverse coordinates, we propose a novel collision avoidance constraint and formulate a suitable maneuver regulation optimal control problem. Maneuver regulation has intrinsic robustness with respect to standard trajectory tracking that stems from the requirement of following a desired path with a desired velocity profile assigned on it. The optimization problem is solved by using a nonlinear optimal control technique that generates (local) optimal trajectories. We demonstrate the efficacy of the proposed algorithm by providing numerical computations on two different scenarios. Finally, experimental results are presented to demonstrate the efficiency of the proposed algorithm both in terms of computational effort and dynamic features captured.

A two-way logistic network design for deteriorating items considering preservation effort and cost minimisation

The deterioration of many items, such as chemicals, volatile liquids, blood banks, and medicines, among other goods, is non-negligible in supply chain management. The transportation and holding of perishable inventories are important issues that need to be addressed by supply chain managers. Considering preservation efforts, this study deals with a two-way logistic network design problem for deteriorating items. A two-way logistic network provides two-way services. First, the collecting points and hubs transport items from customers in region A to those in region B. Second, the items are transported from customers in region B to those in region A. The effort to preserve deteriorating items lowers the deterioration rate but involves preservation costs and is also considered in the model. This model aims to determine the optimal number and location of collecting points, joint replenishment cycle time, and preservation effort while minimising the network cost. A nonlinear optimisation technique is used to solve the proposed problem. Finally, we present an example to illustrate the model and solution approach.

Artificial Intelligence Modeling-Based Optimization of an Industrial-Scale Steam Turbine for Moving toward Net-Zero in the Energy Sector.

Augmentation of energy efficiency in the power generation systems can aid in decarbonizing the energy sector, which is also recognized by the International Energy Agency (IEA) as a solution to attain net-zero from the energy sector. With this reference, this article presents a framework incorporating artificial intelligence (AI) for improving the isentropic efficiency of a high-pressure (HP) steam turbine installed at a supercritical power plant. The data of the operating parameters taken from a supercritical 660 MW coal-fired power plant is well-distributed in the input and output spaces of the operating parameters. Based on hyperparameter tuning, two advanced AI modeling algorithms, i.e., artificial neural network (ANN) and support vector machine (SVM), are trained and, subsequently, validated. ANN, as turned out to be a better-performing model, is utilized to conduct the Monte Carlo technique-based sensitivity analysis toward the high-pressure (HP) turbine efficiency. Subsequently, the ANN model is deployed for evaluating the impact of individual or combination of operating parameters on the HP turbine efficiency under three real-power generation capacities of the power plant. The parametric study and nonlinear programming-based optimization techniques are applied to optimize the HP turbine efficiency. It is estimated that the HP turbine efficiency can be improved by 1.43, 5.09, and 3.40% as compared to that of the average values of input parameters for half-load, mid-load, and full-load power generation modes, respectively. The annual reduction in CO2 measuring 58.3, 123.5, and 70.8 kilo ton/year (kt/y) corresponds to half-load, mid-load, and full load, respectively, and noticeable mitigation of SO2, CH4, N2O, and Hg emissions is estimated for the three power generation modes of the power plant. The AI-based modeling and optimization analysis is conducted to enhance the operation excellence of the industrial-scale steam turbine that promotes higher-energy efficiency and contributes to the net-zero target from the energy sector.

Minimum secrecy rate maximization for multiple peer-to-peer communications in two-way relaying networks

We investigate physical layer security for multi-user peer-to-peer relay networks, where a secure user pair and other unclassified users exchange information only through a multi-antenna relay in the presence of a multi-antenna eavesdropper. Our aim is to obtain the optimal values for variables of user transmit power and the relay beamforming matrix by solving the minimum secrecy rate maximization problem under specific constraints. We assume scenarios in which the eavesdropper’s channel state information is and is not available. Mathematically, the optimization problem raised in the first scenario is nonlinear and non-convex. The relay adopts a null space beamforming technique to facilitate the problem and guarantee secrecy. Also, we decouple it into two subproblems and solve them using inequality semi-definite programming and nonlinear optimization techniques to find solutions for variables. Also, the complexity of the proposed algorithms is analyzed and its convergency is proved by simulation. In the second scenario, we utilize an artificial noise-aided secure relay beamforming scheme. The problem is equivalent to the problem of assigning maximum power to the artificial noise evaluated by the secrecy outage probability concept. Finally, simulations demonstrate the validity of the proposed methods.

Distilled neural state-dependent Riccati equation feedback controller for dynamic control of a cable-driven continuum robot

This article presents a novel learning-based optimal control approach for dynamic control of continuum robots. Working and interacting with a confined and unstructured environment, nonlinear coupling, and dynamic uncertainty are only some of the difficulties that make developing and implementing a continuum robot controller challenging. Due to the complexity of the control design process, a number of researchers have used simplified kinematics in the controller design. The nonlinear optimal control technique presented here is based on the state-dependent Riccati equation and developed with consideration of the dynamics of the continuum robot. To address the high computational demand of the state-dependent Riccati equation controller, the distilled neural technique is adopted to facilitate the real-time controller implementation. The efficiency of the control scheme with different neural networks is demonstrated using simulation results.

Solar PV power plant site selection using a GIS-based non-linear multi-criteria optimization technique.

The ongoing rise in energy consumption imposed serious environmental challenges by using fossil fuels. The use of renewable energy sources is being increasingly explored as a potential answer for achieving sustainable energy production and minimizing adverse environmental effects. In the modern day, photovoltaic (PV) systems are viewed as a possible replacement for fossil fuels as a clean energy source. The installation of solar PV power plants requires vast land and huge investment. Therefore, it is necessary to select a suitable site to achieve maximum efficiency and low cost. A feasible location of photovoltaic (PV) system must consider certain criteria including land restrictions, access to roads, and transmission lines. This study analyzed ten factors grouped into four categories: geographic, technical, economic, and flood susceptibility criterion. The data of each factor is extracted from various governments, United Nation (UN), and non-government organizational bodies. Weights were assigned to ten factors by using a non-linear multi-criteria optimization technique called full consistency method (FUCOM). A geographic information system (GIS) software, ESRI ArcGIS pro, performs the weighted overlay analysis of the ten factors with weighted importance calculated by the above technique. A suitability map is created showing that a total of 2.02% of the country's area is suitable for PV power plants, which are further divided into five suitability classes. The results highlight the distribution of suitable sites for the construction of solar PV power plant throughout the country. A sensitivity analysis is performed to highlight the impact of the factor on the final suitability map. These findings can promote the future widespread development and application of solar energy resources.

Cycle-based formulations in Distance Geometry

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the edge weights. The problem is often modelled as a mathematical programming formulation involving decision variables that determine the position of the vertices in the given Euclidean space. Solution algorithms are generally constructed using local or global nonlinear optimization techniques. We present a new modelling technique for this problem where, instead of deciding vertex positions, the formulations decide the length of the segments representing the edges in each cycle in the graph, projected in every dimension. We propose an exact formulation and a relaxation based on a Eulerian cycle. We then compare computational results from protein conformation instances obtained with stochastic global optimization techniques on the new cycle-based formulation and on the existing edge-based formulation. While edge-based formulations take less time to reach termination, cycle-based formulations are generally better on solution quality measures.

Real-Time Global Localization of a Mobile Robot by Exploiting RFID Technology

This work addresses the problem of the global localization of a mobile robot by exploiting RFID technology. The robot is equipped with kinematic sensors capable of measuring the incremental distances covered by each wheel and an RFID reader which measures the phase of the signal that is backscattered by reference RFID tags situated inside the environment at known positions. The motion of the robot with respect to the tags enables the collection of measurements from multiple antenna-locations, in a synthetic-aperture sense. Localization of the mobile robot over time is accomplished by processing short segments of trajectory during each iteration. The odometry-data are exploited to estimate each segment of the vehicle’s trajectory relative to an unknown initial position. The odometry-based estimation, the known positions of the reference tags, the unwrapped phase measurements and a phase-to-distance model represent the input to a data-fit problem, the solution of which reveals the unknown initial position and orientation of the trajectory segment in the absolute frame. Thanks to phase unwrapping, the data-fit problem features convexity-type properties and the solution is rapidly found by non-linear optimization techniques. The influence of different algorithmic features on the performance of the method is investigated in a simulative context. An experimental campaign that employs a prototype robotic agent equipped with two antennas reports a mean absolute localization error of less than 0.1m, while the execution time stays below the measurements’ collection-time such that the real-time capability of the method is preserved.

Nonlinear Optimization Techniques for Signal Processing

Nonlinear Optimization Techniques for Signal Processing

Consistent FDTD Modeling of Dispersive Dielectric Media via Multiple Debye Terms Derived Rigorously by Padé Approximants

An finite-difference time-domain (FDTD) scheme for simulating wave propagation inside Cole-Cole (CC), Havriliak-Negami (HN), or Raicu (R) dispersive media is proposed. The main difficulty in FDTD implementations for such media is the fact that the time-domain polarization relations are fractional integro-differential equations. To circumvent this difficulty, the dispersive susceptibility of the medium is modeled by Padé approximants. It is proven that under certain conditions the Padé approximant is equal to a weighted sum of Debye terms, while the physical restrictions for positive weights and relaxation times are fulfilled with certainty. Hence, a set of first-order auxiliary differential equations (ADEs), which approximate the original fractional polarization relation, is derived and directly embedded in the FDTD scheme. In contrast to previous works, the derivation of the Debye expansion of the original dispersive permittivity is carried out in a straightforward manner without involving nonlinear optimization techniques. Comparisons between analytical and FDTD results of the reflection and transmission coefficients as well as of the transfer functions inside the dispersive media illustrate the efficiency of the proposed scheme, over wideband frequency domains.

Game Theory–Based Parameter Tuning for Energy-Efficient Path Planning on Modern UAVs

Present-day path planning algorithms for UAVs rely on various parameters that need to be tuned at runtime to be able to plan the best possible route. For example, for a sampling-based algorithm, the number of samples plays a crucial role. The dimension of the space that is being searched to plan the path, the minimum distance for extending a path in a direction, and the minimum distance that the drone should maintain with respect to obstacles while traversing the planned path are all important variables. Along with this, we have a choice of vision algorithms, their parameters, and platforms. Finding a suitable configuration for all these parameters at runtime is very challenging because we need to solve a complicated optimization problem, and that too within tens of milliseconds. The area of theoretical exploration of the optimization problems that arise in such settings is dominated by traditional approaches that use regular nonlinear optimization techniques often enhanced with AI-based techniques such as genetic algorithms. These techniques are sadly rather slow, have convergence issues, and are typically not suitable for use at runtime. In this article, we leverage recent and promising research results that propose to solve complex optimization problems by converting them into approximately equivalent game-theoretic problems. The computed equilibrium strategies can then be mapped to the optimal values of the tunable parameters. With simulation studies in virtual worlds, we show that our solutions are 5-21% better than those produced by traditional methods, and our approach is 10× faster.

Evaluating intraocular lens power formula constant robustness using bootstrap algorithms.

Bootstrapping is a modern technique mostly used in statistics to evaluate the robustness of model parameters. The purpose of this study was to develop a method for evaluation of formula constant uncertainties and the effect on the prediction error (PE) in intraocular lens power calculation with theoretical-optical formulae using bootstrap techniques. In a dataset with N=888 clinical cases treated with the monofocal aspherical intraocular lens (Vivinex, Hoya) constants for the Haigis, the Castrop and the SRKT formula were optimised for the sum of squared PE using nonlinear iterative optimisation (interior point method), and the formula predicted spherical equivalent refraction (predSEQ) and the PE were derived. The PE was bootstrapped NB=1000 times and added to predSEQ, and formula constants were derived for each bootstrap. The robustness of the constants was calculated from the NB bootstrapped models, and the predSEQ was back-calculated from the NB formula constants. With bootstrapping, the 90% confidence intervals for the a0/a1/a2 constants of the Haigis formula were -0.8317 to -0.5301/0.3203 to 0.3617/0.1954 to 0.2100, for the C/H/R constants of the Castrop formula they were 0.3113 to 0.3272/0.1237 to 0.2149/0.0980 to 0.1621, and for the A constant of the SRKT formula they were 119.2320 to 119.3028. The back-calculated PE from the NB bootstrapped formula constants standard deviation for the mean/median/mean absolute/root mean squared PE were 5.677/5.735/0.401/0.318 e-3 dpt for the Haigis formula, 5.677/5.735/0.401/0.31829 e-3 dpt for the Castrop formula and 14.748/14.790/0.561/0.370 e-3 dpt for the SRKT formula. We have been able to prove with bootstrapping that nonlinear iterative formula constant optimisation techniques for the Haigis, the Castrop and the SRKT formulae yield consistent results with low uncertainties of the formula constants and low variations in the back-calculated mean, median, mean absolute and root mean squared formula prediction error.

Magnetic particle tracking: A semi-algebraic solution

Magnetic Particle Tracking (MPT) is a relatively new non-invasive measurement technique which is often used to study dense granular flow. Its basic principle relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength at a suitable distance from the tracer. By assumption of a magnetic dipole and the use of minimization techniques, both location and orientation of the tracer can be determined. MPT is therefore uniquely suited for the study of non-spherical particles. The performance of the localization is largely dependent on the signal-to-noise ratio and very often relies on nonlinear optimization techniques, as the definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. In this paper, we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach is in the speed and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques.

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium.

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g_{2}(r) or corresponding structure factor S(k) in d-dimensional Euclidean space R^{d} is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)2470-004510.1103/PhysRevE.101.032124] conjectured that any realizable g_{2}(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g_{2}(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L_{2}-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.

Hybrid Nonlinear Transceiver Optimization for the RIS-Aided MIMO Downlink

The hybrid nonlinear transceiver optimization problem of reconfigurable intelligent surface (RIS)-aided multi-user multiple-input multiple-output (MU-MIMO) downlink is investigated. Specifically, the Tomlinson-Harashima precoder (THP) and the hybrid transmit precoder (TPC) of the base station are jointly optimized with the linear digital receivers of mobile users. The triangular feedback matrix of the THP is optimized and the optimal solution is derived in closed form based on a matrix inequality. Moreover, in order to tackle the nonconvexity of the constant-modulus constraints imposed on the analog TPC, the Majorization-Minimization (MM) based reconfigurable optimization framework is proposed, which strikes a trade-off between the implementation complexity and system performance in a reconfigurable manner. Explicitly, our MM-based reconfigurable optimization framework is capable of optimizing the analog TPC in a dynamically reconfigurable manner on an element-by-element, column-by-column, row-by-row or block-by-block basis. Moreover, an MM-based reconfigurable algorithm is proposed for the optimization of the phase shifting matrix at RIS, which also suffers from constant-modulus constraints. In the proposed MM-based reconfigurable algorithm, the RIS can be partitioned into a series of subarrays for striking different performance vs. complexity tradeoffs. Finally, our numerical results demonstrate the performance advantages of the proposed nonlinear hybrid transceiver optimization techniques.

Predictive Modeling and Non-linear Optimization Techniques for Composite Materials Design

With the rise in the use of composite materials for product design, research has been performed in determining the optimal way to produce materials for given desired outputs. As of now response surface methodology and the Taguchi method are the front running methods for optimizing material production methods at the design level. This research investigates why these methods are not a one size fits all solution to optimizing composite materials production for material properties. It proposes utilizing predictive modeling and non-linear optimization techniques from historical manufacturing data of a non-highly controlled manufacturing process. The method is examined with the manufacturing and testing data of a local concrete product manufacturer. The models and optimization methods are validated with residual values to the true data and sensitivity analysis of the problem. The initial testing of the method offers promise to companies who have not found Taguchi or surface response methodology, applicable to their specific business solutions.

Constrained Fourier estimation of short-term time-series gene expression data reduces noise and improves clustering and gene regulatory network predictions

BackgroundBiological data suffers from noise that is inherent in the measurements. This is particularly true for time-series gene expression measurements. Nevertheless, in order to to explore cellular dynamics, scientists employ such noisy measurements in predictive and clustering tools. However, noisy data can not only obscure the genes temporal patterns, but applying predictive and clustering tools on noisy data may yield inconsistent, and potentially incorrect, results.ResultsTo reduce the noise of short-term (< 48 h) time-series expression data, we relied on the three basic temporal patterns of gene expression: waves, impulses and sustained responses. We constrained the estimation of the true signals to these patterns by estimating the parameters of first and second-order Fourier functions and using the nonlinear least-squares trust-region optimization technique. Our approach lowered the noise in at least 85% of synthetic time-series expression data, significantly more than the spline method (p<10^{-6}). When the data contained a higher signal-to-noise ratio, our method allowed downstream network component analyses to calculate consistent and accurate predictions, particularly when the noise variance was high. Conversely, these tools led to erroneous results from untreated noisy data. Our results suggest that at least 5–7 time points are required to efficiently de-noise logarithmic scaled time-series expression data. Investing in sampling additional time points provides little benefit to clustering and prediction accuracy.ConclusionsOur constrained Fourier de-noising method helps to cluster noisy gene expression and interpret dynamic gene networks more accurately. The benefit of noise reduction is large and can constitute the difference between a successful application and a failing one.

Differential SfM and image correction for a rolling shutter stereo rig

• A simple and flexible generalized RS stereo differential SfM algorithm over two consecutive frames. • Two effective and effcient RS-stereo non-linear optimization techniques based on the maximum likelihood criterion. • An RS-stereo image correction method to remove the inaccuracies induced by the RS effect. • The proposed model and method are universal and tractable. Most modern consumer-grade cameras are equipped with an electronic rolling shutter (RS), leading to image distortions when the camera moves during image acquisition. We explore the first structure and motion estimation problem of a dynamic generalized RS stereo camera. Such a general configuration is commonplace in robots and autonomous driving applications. We propose a tractable RS stereo differential structure from motion (SfM) algorithm, taking into account the RS effect during consecutive imaging, which effectively compensates for the RS-stereo image distortion by a linear scaling operation on each optical flow. We further propose embedding the cheirality into RANSAC and develop a robust RS-stereo-aware full-motion estimation framework. We demonstrate that the RS stereo motion and depth map refined by our non-linear optimization schemes within the maximum likelihood criterion can be used for image correction to recover high-quality global shutter (GS) stereo images. Moreover, using the proposed generalized RS stereo differential SfM pipeline, the corrected images produce an accurate 3D scene structure as the ground-truth structure. Extensive experiments on both synthetic and real RS stereo data demonstrate the effectiveness of our model and method in various configurations.