Nonlinear Optimization Algorithm Research Articles

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].

Conflict Detection and Separation Configuration Method Based on Uncertain Flight Trajectory

Aiming at two aircraft conflict scenario in the pre-tactical stage, by converting the uncertain flight trajectory of the target aircraft into a spatio-temporal trajectory under its performance constraints, a conflict detection model based on truncated normal distribution was proposed,and influencing factors affecting the overall conflict probability were analysed by numerical simulation. For the conflict scenario, nonlinear particle swarm optimisation (NPSO) algorithm was applied to solve the optimal separation configuration strategy for the ownship. The simulation results show that, in comparison to conventional PSO algorithm, the improved NPSO algorithm improves the optimal value by 14.88% and decreases the maximum velocity change by 19.84%. The simulation also shows that the algorithm can maintain the minimum interval requirements under different initial parameters, demonstrating its strong adaptability.

Research on Dynamic Optimization Algorithm of Warehousing Location Layout Based on Nonlinear Optimization

The paper aims to improve the turnover rate and operation efficiency of goods that are shipped out and replenished in the warehouses of electric power enterprises through big data analysis and optimization algorithms.The data is distributed in diverse locations and data nonlinear optimization algorithms certainly helps to understand the patterns for effective management of warehouses.This article focuses on reducing the delay in the operational processes.A multi-objective optimization (MOO) has been proposed which is aiming at improving the efficiency of transition process of commodities, storage, and overall warehouse operations.The study helps in the optimization of the allocation of cargo spaces with the aid of big data analysis optimization technology which collects and manages data in a distributed environment. A multi-objective cargo space optimization algorithm is proposed along with consideration of dynamic constraints.The algorithm is based on the coefficient of variation adaptive differential evolution algorithm.Individual decoding is performed according to the real-time cargo space availability.The simulation results show that the convergence speed of the algorithm is greatly improved.Meanwhile, the efficiency of warehouse transition process, shelf stability and the classification of commodities are remarkably improved.In nutshell, the multi-objective decision-making with the integration of big data analysis optimization technology assists in the effective organization of warehouse allocation system by considering multiple factors and constraints.

Large deformation assessment of three-tower suspension bridges: An enhanced analytical model and solution algorithm

An enhanced nonlinear approach is proposed in this study to address the limitations of traditional deflection theory in analyzing large deformations of three-tower suspension bridges. In this approach, the three-tower suspension bridge is simplified as two quasi-independent bridges for analysis, and detailed considerations are given to the vertical and longitudinal deformations of the main cable, which produce the expression for the relationship between the cable's internal force and deformations. By employing the complementary energy principle and variational calculus, the nonlinear differential equations describing bridge deformations are then established. To ensure the displacement continuity at the middle tower, this paper proposes the use of Chebyshev polynomials to approximate the solutions of the differential equations, and the weighted residual method is then used to transform these differential equations into algebraic equations. On this basis, the developed nonlinear adjustment optimization algorithm enables efficient solving of the nonlinear equation and thus determination of bridge deformation under various load conditions. The accuracy and effectiveness of the proposed scheme are validated through the analysis of two suspension bridges with equal and unequal spans. Finally, the extended applications of the proposed scheme on the other type of multi-span suspension bridges are introduced for further applications.

Pixelwise high-temperature calibration for in-situ temperature measuring in powder bed fusion of metal with laser beam

High-temperature calibration methods in additive manufacturing involve the use of advanced techniques to accurately measure and control the temperature of the build material during the additive manufacturing process. Infrared cameras, blackbody radiation sources and non-linear optimization algorithms are used to correlate the temperature of the material with its emitted thermal radiation. This is essential for ensuring the quality and repeatability of the final product. This paper presents the calibration procedure of an imaging system for in-situ measurement of absolute temperatures and temperature gradients during powder bed fusion of metal with laser beam (PBF-LB/M) in the temperature range of 500 K–1500 K. It describes the design of the optical setup to meet specific requirements in this application area as well as the procedure for accounting the various factors influencing the temperature measurement. These include camera-specific effects such as varying spectral sensitivities of the individual pixels of the sensor as well as influences of the exposure time and the exposed sensor area. Furthermore, influences caused by the complex optical path, such as inhomogeneous transmission properties of the galvanometer scanner as well as angle-dependent transmission properties of the f-theta lens were considered. A two-step fitting algorithm based on Planck's law of radiation was applied to best represent the correlation. With the presented procedure the calibrated thermography system provides the ability to measure absolute temperatures under real process conditions with high accuracy.

Flexible job shop scheduling with stochastic machine breakdowns by an improved tuna swarm optimization algorithm

In job-shop production environments, machine breakdowns are a significant factor in reducing productivity. Existing approaches seldom consider algorithm improvement and rescheduling scheme design in an integrated manner, and lack stability considerations. This paper addresses the flexible job shop scheduling problem with random machine breakdowns, aiming to produce a stable rescheduling scheme that minimizes a combined index of maximum completion time and stability. The paper innovatively applies the tuna swarm optimization algorithm to the flexible job shop scheduling problem, proposing an efficient and superior improved version called the genetic chaos levy nonlinear tuna swarm optimization (GCLNTSO) algorithm. Three stability metrics are designed to guide the generation of efficient and stable rescheduling schemes. A rescheduling scheme is proposed that combines right-shift rescheduling with complete rescheduling. The proposed scheme is benchmarked against Brandymalter and Kacem’s problems, and compared with other algorithms from the literature. The results demonstrate that the GCLNTSO algorithm outperforms other algorithms in terms of both performance and stability.

A Hybrid Forecasting Model for Self-Similar Traffic in LEO Mega-Constellation Networks

Mega-constellation network traffic forecasting provides key information for routing and resource allocation, which is of great significance to the performance of satellite networks. However, due to the self-similarity and long-range dependence (LRD) of mega-constellation network traffic, traditional linear/non-linear forecasting models cannot achieve sufficient forecasting accuracy. In order to resolve this problem, a mega-constellation network traffic forecasting model based on EMD (empirical mode decomposition)-ARIMA (autoregressive integrated moving average) and IGWO (improved grey wolf optimizer) optimized BPNN (back-propagation neural network) is proposed in this paper, which makes comprehensive utilization of linear model ARIMA, non-linear model BPNN and optimization algorithm IGWO. With the enhancement of the global optimization capability of a BPNN, the proposed hybrid model can fully realize the potential of mining linear and non-linear laws of mega-constellation network traffic, hence improving the forecasting accuracy. This paper utilizes an ON/OFF model to generate historical self-similar traffic to forecast. RMSE (root mean square error), MAE (mean absolute error), R-square and MAPE (mean absolute percentage error) are adopted as evaluation indexes for the forecasting effect. Comprehensive experimental results show that the proposed method outperforms traditional constellation network traffic forecasting schemes, with several improvements in forecasting accuracy and efficiency.

Structure optimisation of cathode parallel polar plate PEMFC based on topology optimisation

Polar plate design can directly affect the performance of the proton exchange membrane fuel cell(PEMFC). A novel topology parallel polar plate design is proposed to improve cell performance. We used the sparse nonlinear optimisation (SNOPT) algorithm to freely evolve the 2D model and obtain the output material factor distribution map. While keeping the height of the gas diffusion layer constant, the channel height is stretched proportionally to the output material factor to obtain 3D models. By analyzing the mass transfer, water management, and cell performance, the results indicate that increasing the selection range of material output factors is beneficial for the diffusion of reactive gases, reducing pressure loss, and improving cell performance. Reducing the selection range of material output factors helps increase the reaction gas flow rate and enhancing drainage performance. The optimisation model with lower limits benefits oxygen diffusion, increasing gas flow rate and pressure loss, and has little impact on drainage. Case 6 performs well in mass transfer and drainage performance, and the pressure loss is relatively small. The quantitative evaluation shows that Case 6 has an improvement of 22.2% compared to the parallel polar plate and 26.5% compared to the serpentine polar plate in cell efficiency.

A Co-Evolutionary Dual Niching Differential Evolution Algorithm for Nonlinear Equation Systems Optimization

A Co-Evolutionary Dual Niching Differential Evolution Algorithm for Nonlinear Equation Systems Optimization

A Nonlinear Adaptive Weight-Based Mutated Whale Optimization Algorithm and Its Application for Solving Engineering Problems

A Nonlinear Adaptive Weight-Based Mutated Whale Optimization Algorithm and Its Application for Solving Engineering Problems

Research on vegetable sales decision-making based on single-objective nonlinear optimization and genetic algorithm

Research on vegetable sales decision-making based on single-objective nonlinear optimization and genetic algorithm

Thermometrical determination of the postmortem interval by non-linear optimization method

To develop and implement an online application for the numerical method of determination of the postmortem interval and its limiting faults, caused by errors of measurement processes, based on the Marshall-Hoare law of cooling and dual thermometry of the corpse's core. The numerical search for a minimum of two variables' target function, obtained from the system of non-linear Marshall-Hoare equations, reflecting the dual thermometry of the corpse's core was performed. The code of online program was written in Python 3 programming language. The method for determination of the postmortem interval, based on iterative algorithm of non-linear optimization, allowing by dual thermometry of the corpse to consider the uniqueness of its cooling conditions, as well as to calculate the degree of uncertainty of computational estimations, caused by the impact of measurement errors, has been developed. The method is implemented in the format of the Warm Bodies Z online application. The developed numerical method and its online application are recommended for determining of the postmortem interval.

Method for prediction and control by uncertain microsatellite magnetic cleanliness based on calculation and compensation magnetic field spatial harmonics

Aim. Development of method for prediction and control the microsatellite magnetic cleanliness taking into account the uncertainties of the magnetic characteristics of the microsatellite, based on calculation the magnetic field spatial spherical harmonics in the area of the onboard magnetometer installation and using compensating multipoles. Methodology. Spatial spherical harmonics of microsatellite magnetic field in the area of the onboard magnetometer installation calculated as solution of nonlinear minimax optimization problem based on near field measurements for prediction far spacecraft magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field. Values of the compensating dipoles, quadrupoles and octupoles and coordinates of them placement inside the spaceship for compensation of the dipoles, quadrupoles and octupoles components of the microsatellite initial magnetic field also calculated as solution of nonlinear minimax optimization problem. Both solutions of this nonlinear minimax optimization problems calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction spacecraft far magnetic field magnitude based on spacecraft spatial spherical harmonics of the magnetic field using near field measurements and compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of spacecraft magnetic characteristics uncertainty for ensuring the microsatellite magnetic cleanliness. Originality. The method for prediction and control by spacecraft magnetic cleanliness based on calculation spatial spherical harmonics of the magnetic field in the area of the onboard magnetometer installation using compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of ensuring the magnetic cleanliness of the «Sich-2» microsatellite family based on the spatial spherical harmonics of the magnetic field model using the compensation of the dipole, quadrupole and octupole components of the output magnetic field of the sensor for the kinetic parameters of the neutral component of the space plasma at the point of installation of the on-board magnetometer LEMI-016 by setting the compensating dipole, quadrupole and octupole with consideration of spacecraft magnetic characteristics uncertainty solved.

A computer code for optimizing the neutronics model parameters based on results of reactor physics experiments

The paper describes in brief the functional capabilities of a computer code for optimizing the neutronics model parameters (neutron data, technological parameters, and their covariance matrices) based on results of reactor physics experiments using conditional nonlinear multi-parameter optimization algorithms. The code’s application scope includes adjustment of neutron constants, technological parameters and their covariance matrices based on integral measurement results, formulation of requiremen117198ts with respect to the neutron data uncertainties for achieving the target accuracies in calculation of the reactor functionals, and estimation of the reactor performance prediction accuracy, as well as the informativity and similarity metrics of reactor physics experiments with respect to each other and in relation to the target reactor system. The paper also considers some examples of using the code to refine the neutronics models of nuclear reactor and fuel cycle systems based on results of reactor physics experiments.

A Comparison of Nonlinear Optimization Methods for Rosenbrock, Booth, and Matyas Functions

There is increasing interest in the application of nonlinear optimization techniques across a broad range of real-world problems that is linked to rapid advances in novel technologies and renewed interest in areas like sustainable development. While many algorithms for nonlinear optimization have been developed, they differ widely in their methods of convergence to the solution. Consequently, matching the function to be optimized with the right optimization algorithm is essential. To further explore this relationship, we studied two nonlinear optimization methods – the Nelder-Mead simplex method that only performs function evaluations and the quasi-Newton method which requires estimation of derivatives. These algorithms were used to find the global minima of the Rosenbrock, Booth, and Matyas functions from multiple starting points. The convergence paths for each starting point across both optimization methods for all 3 functions were visualized on contour plots. While convergence on the global minima was observed in all instances, our analysis indicated that the quasi-Newton method was consistently more efficient and needed fewer iterations than the Simplex method. This was especially pronounced for the Booth and Matyas functions where ~10-fold and 20-fold fewer iterations, respectively, were necessary for convergence. Our analysis reinforces the need to carefully match properties of the function being minimized with the performance characteristics of the optimization approach to obtain fast convergence on the global minimum.

Data-driven product-process optimization of N-isopropylacrylamide microgel flow-synthesis

Microgels are cross-linked, colloidal polymer networks with great potential for stimuli-response release in drug-delivery applications, as their small size allows them to pass human cell boundaries. For applications with specified requirements regarding size, producing tailored microgels in a continuous flow reactor is advantageous because the microgel properties can be controlled tightly. However, no fully-specified mechanistic models are available for continuous microgel synthesis, as the physical properties of the included components are only studied partly. To address this gap and accelerate tailor-made microgel development, we propose a data-driven optimization in a hardware-in-the-loop approach to efficiently synthesize microgels with defined sizes. We optimize the synthesis regarding conflicting objectives (maximum production efficiency, minimum energy consumption, and the desired microgel radius) by applying Bayesian optimization via the solver “Thompson sampling efficient multi-objective optimization” (TS-EMO). We validate the optimization using the deterministic global solver “McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization” (MAiNGO) and verify three computed Pareto optimal solutions via experiments. The proposed framework can be applied to other desired microgel properties and reactor setups and has the potential of efficient development by minimizing number of experiments and modeling effort needed.

Kernel function with BFGS quasi-newton methods for solving nonlinear semi-definite problems

In this paper, we will improve the practical performance of an interior points algorithm for convex nonlinear semi-definite optimization, where to minimize a nonlinear convex objective function subject to nonlinear convex constraints. We will propose a new method for solving this kind of problem by using a straightforward kernel function and the iterative Newton directions combined with the Broyden-Fletcher-Goldfarb-Shanno (BFGS in short) quasi-Newton method. Further, a best polynomial complexity for solving nonlinear convex problems will be found until now.

SMIwiz: An integrated toolbox for multidimensional seismic modelling and imaging

This paper contributes an open source software - SMIwiz, which integrates seismic modelling, reverse time migration (RTM), and full waveform inversion (FWI) into a unified computer implementation. SMIwiz has the machinery to do both 2D and 3D simulation in a consistent manner. The package features a number of computational recipes for efficient calculation of imaging condition and inversion gradient: a dynamic evolving computing box to limit the simulation cube and a well-designed wavefield reconstruction strategy to reduce the memory consumption when dealing with 3D problems. The modelling in SMIwiz runs independently: each shot corresponds to one processor in a bijective manner to maximize the scalability. A batchwise job scheduling strategy is designed to handle large 3D imaging tasks on computer with limited number of cores. The viability of SMIwiz is demonstrated by a number of applications on benchmark models. Program summaryProgram Title: SMIwizCPC Library link to program files:https://doi.org/10.17632/tygszns27k.1Developer's repository link:https://github.com/yangpl/SMIwizLicensing provisions: GNU General Public License v3.0Programming language: C, Shell, FortranExternal dependencies: MPI [1], FFTW [2]Nature of problem: Seismic modelling and imaging (FWI and RTM)Solution method: High-order finite-difference time-domain (FDTD) for modelling on staggered grid; Quasi-Newton LBFGS algorithm for nonlinear optimization; line search to estimate step length based on Wolfe condition References[1]https://www.mpich.org/[2]http://fftw.org/

A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms

A Unit Root Test with Markov Switching Deterministic Components: A Special Emphasis on Nonlinear Optimization Algorithms

Comparing optimization schemes for solving case studies with multiple heat exchangers using high-order pinch point temperature difference methods

Heat exchangers (HEs) are often modeled using pinch point temperature difference (ΔTpinch) methods when optimizing systems with HEs. However, even small inaccuracies in model predictions of HEs will introduce numerical noise that can cause optimization algorithms to fail. A recent study of single HEs suggests that high-order interpolation methods can compute ΔTpinch much faster than conventional methods. However, the performance of such methods when optimizing HE systems have not previously been tested.Heat pumps with 2 and 3 HEs, with and without an ejector are optimized using different schemes. Results from these case studies show that non-linear constrained gradient-based optimization algorithms are more than 5 times faster than particle swarm (PS), and that the conventional genetic algorithm (GA) should not be used. However, the main conclusion is that the case study optimizations are solved 5–10 times faster if ΔTpinch is calculated using hybrid high and low-order interpolation methods.