Stochastic Global Optimization Research Articles

The 23–24 March 2021 lava fountain at Mt Etna, Italy

In 2021, more than 50 paroxysmal episodes occurred at the South-East Crater (SEC) of Mt Etna, Italy. The 23–24 March lava fountain was one of the longest episodes and began with weak Strombolian explosions, gradually transitioning to lava fountaining. The eruption intensity then dropped more slowly than in previous episodes, resulting in pulsating Strombolian explosions dominated by ash emission. Thirty-four tephra samples were used to reconstruct the fallout dispersal and estimate the total erupted mass. Grain size, textural, petrological and geochemical analyses indicate different features and were compared with the gas phase (SO2 and HCl) in the volcanic plume. By applying stochastic global optimization to simulations of the temporal evolution of the eruption column height and tephra dispersal and deposition, the total erupted mass retrieved (6.76 × 108 kg) matches well the total erupted mass estimation by the ground-based deposit (8.03 ± 2.38 × 108 kg), reducing the column height throughout the episode from 6.44 to 4.5 km above sea level and resulting in a mass eruption rate ranging from 1.96 × 105 to 8.18 × 103 kg/s. The unusual duration of the March episode and the characteristics of the erupted products point to the change in explosive style and magma fragmentation from fountaining to ash emission phases, associated with a slower magma supply inducing a change in magma rheology and a final, prolonged ash generation. Furthermore, this study showed that using observational data and the variation in eruption source parameters for numerical simulations can improve the accuracy of predicting the dispersal plume, thus mitigating the potential impact of longer paroxysmal episodes.

A Novel Approach to a Recurrent Fuzzy Logic Controller Design Applied to Systems with Multiple Disturbances

In any process, control plays a vital role in the quality of the product. The influence of a controller's operation on a process is linked to its success or failure. However, using a controller that works properly presents several obstacles, such as non-linearity or the lack of a model that adequately represents the behavior of the process. Different approaches have been devised and studied to deal with these difficulties. One of the most promising and widely applied and studied in recent years is fuzzy control due to its ability to operate systems with no precise plant model. Herein, a set of rules and a fuzzy control structure are proposed, with fewer design parameters than a conventional fuzzy controller and better performance. The global stochastic optimization tool Differential Evolution is used to obtain the design parameters of the proposed fuzzy controller.

Evaluation of dropwise condensation from a vertical condenser tube impregnated with semisolid lubricant

AbstractThe quest for augmenting dropwise condensation heat transfer performance has been the driving force behind the exploration of innovative techniques and approaches to fulfill the desired objective. Mostly, earlier research on dropwise condensation was devoted to study condensation from horizontal tubes and plates but, rarely, addressed dropwise condensation from vertical tubes. An interesting topic of current research in dropwise condensation is to explore the application of Slippery Liquid Infused Porous Surfaces (SLIPSs) to improve the condensation performance. The aforesaid facts are the motivation behind the topics of interest in the present study. In this study, we explore the applicability of semisolid lubricant‐impregnated porous surfaces in enhancing dropwise condensation performance of a vertical condenser tube. The experiments conducted over a wide range of subcooling (5°C ≤ ΔT ≤ 65°C) in saturated steam environment showed significant improvement in condensation heat transfer coefficient of a vertical condenser tube impregnated with semisolid lubricants when compared to bare vertical condenser tube. The highest enhancement is found to be 280% at a subcooling of 40°C. Furthermore, these surfaces proficiently sustain dropwise condensation over a period of 72 hours without compromising heat transfer performance. The devised fabrication method is simpler, more cost‐effective, and less time‐consuming than earlier techniques used for creating SLIPSs. Additionally, an approach based on numerical optimization by a stochastic global optimization technique, namely, Genetic Algorithm, is proposed to retrieve the coefficients and the exponent in the mathematical expression of overall resistance, that is being used to compute the tube‐side dropwise convection heat transfer coefficient.

An Algorithm Based on Compute Unified Device Architecture for Estimating Covering Functionals of Convex Bodies

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. and Yu et al. provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

Control of Aerodynamic Characteristics of Thick Airfoils at Low Reynolds Numbers Using Methods of Boundary Layer Control

The article explores flow behavior around thick airfoils at low Reynolds numbers and the potential application of energy methods to manipulate the flow field for increased lift and reduced drag. The study relies on a set of propulsion airfoils calculated using a combined approach of solving the inverse problem of aerodynamics and applying stochastic global optimization methods. The calculations consider the transition from laminar to turbulent flow regimes, which significantly affects lift and airfoil drag. The suitability of different turbulence models for airfoil modeling in low Reynolds numbers is discussed, and numerical simulation results determine the lift coefficient dependence on angle of attack and the optimal air flow rate taken from the airfoil surface for each angle of attack. The accuracy of different turbulence models is analyzed by comparing numerical simulation results to physical experiment data.

On assessing the carbon capture performance of graphynes with particle swarm optimization.

Tackling climate change is one of the greatest challenges of current times and therefore the development of efficient technologies to limit anthropogenic emissions is of utmost urgency. Recent research towards this goal has alluded to the use of carbon-based solid sorbents for carbon capture. Graphynes (GYs), an interesting class of porous carbon membranes, have recently proven their potential as excellent membranes for gas adsorption and separation. Herein, we explored the CO2 and N2 adsorption characteristics and CO2/N2 selectivities of a class of GYs, namely γ-GY-1, γ-GY-2 and γ-GY-4. We investigated the putative global minimum geometries of adsorbed unary (n = 2-10) and binary (n : m; n, m ∈ [1, 8]) clusters of CO2 and N2 by employing a stochastic global optimization method called particle swarm optimization in conjunction with empirical intermolecular force field formulations. The intervening interactions are modeled using various pairwise potentials, including Lennard-Jones potential, improved Lennard-Jones potential, Buckingham potential and Coulombic potential. The binding energies for both unary and binary clusters are highest for adsorption on γ-GY-1, followed by γ-GY-2. The putative global minimum geometries suggested that N2 molecules preferred binding over the pore centres while CO2 molecules showed higher clustering propensity than any binding site preference. The predicted interaction energies suggested higher selectivity for CO2 over N2 for all the three γ-GYs.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease Part II: Extension for Variable Metabolic Rates.

Recently, we developed a systems engineering model of the human cardiorespiratory system [Kurian et al. ACS Omega2023, 8 (23), 20524-20535. DOI: 10.1021/acsomega.3c00854] based on existing models of physiological processes and adapted it for chronic obstructive pulmonary disease (COPD)-an inflammatory lung disease with multiple manifestations and one of the leading causes of death in the world. This control engineering-based model is extended here to allow for variable metabolic rates established at different levels of physical activity. This required several changes to the original model: the model of the controller was enhanced to include the feedforward loop that is responsible for cardiorespiratory control under varying metabolic rates (activity level, characterized as metabolic equivalent of the task-Rm-and normalized to one at rest). In addition, a few refinements were made to the cardiorespiratory mechanics, primarily to introduce physiological processes that were not modeled earlier but became important at high metabolic rates. The extended model is verified by analyzing the impact of exercise (Rm > 1) on the cardiorespiratory system of healthy individuals. We further formally justify our previously proposed adaptation of the model for COPD patients through sensitivity analysis and refine the parameter tuning through the use of a parallel tempering stochastic global optimization method. The extended model successfully replicates experimentally observed abnormalities in COPD-the drop in arterial oxygen tension and dynamic hyperinflation under high metabolic rates-without being explicitly trained on any related data. It also supports the prospects of remote patient monitoring in COPD.

Simulated Annealing Search Technique

Simulated Annealing is a stochastic global search optimization algorithm. The algorithm is inspired by annealing in metallurgy where metal is heated to a high temperature quickly, then cooled slowly, which increases its strength and makes it easier to work with. algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Keywords: optimization, bound-constrained, local minima, travelling salesman problem.

Neural‐Network Potential Simulation of Defect Formation Induced by Knock‐On Irradiation Damage in GaN

AbstractUnderstanding the irradiation damage mechanisms of GaN is of great importance for improving irradiation resistance and the ion implantation processes of GaN‐based devices. The understanding of the damage mechanisms, which are normally simulated using molecular dynamics (MD), is bottlenecked by the dilemma that ab initio MD is limited by relatively high computational cost, whereas classical MD suffers from low accuracy. In this paper, a global neural network (G‐NN) potential is constructed for GaN using random stochastic surface walking global optimization combined with global neural network potential (SSW‐NN). By benchmarking the properties of intrinsic defects and defect‐pairs, as well as the threshold displacement energies along different crystallographic directions, this potential is found to provide accuracy similar to ab initio calculations. Furthermore, based on the large‐scale simulations of the knock‐on process, Ga and N vacancies, as well as N interstitials are found to be the major generated defects, whereas only Ga vacancies are predicted in the previous device simulation studies that have been widely recognized. This potential provides an efficient and accurate tool to gain a fundamental understanding of the irradiation damage mechanisms of GaN and refine the parameters in the related device simulations.

Phase stability analysis and phase equilibrium calculations in reactive and nonreactive systems using new hybrids of Pelican and Gorilla troops algorithms

Phase stability and equilibrium calculations are very significant in the process industries, ranging from process simulation, equipment design, operation and design. These problems involve several systems of complex and nonlinear equations, which are mathematically challenging. An alternative solution is formulating the problems into a global optimisation problem. A robust and reliable optimisation technique is required to solve these global optimisation problems. In this study, two recently developed stochastic global optimisation algorithms, POA and GTO were applied to phase stability and equilibrium problems. The need to enhance their performance necessitated the development of two modified algorithms, PGOA1 and PGOA2, which are the hybridisation of POA and GTO. All the algorithms' abilities were explored for solving computationally challenging and multidimensional phase stability and equilibrium problems, and their performances were compared. The implementation of POA and GTO was good in solving most problems, though GTO slightly outperformed POA. The hybridisation of both to develop PGOA1 and PGOA2 was worthwhile as both outperformed the POA and GTO. PGOA2 is more robust and reliable in solving phase stability and equilibrium, and its performance superseded the performances of the other algorithms.

Simulation of COVID-19 Spread Scenarios in the Republic of Kazakhstan Based on Regularization of the Agent-Based Model

We propose an algorithm for modeling scenarios for newly diagnosed cases of COVID-19 in the Republic of Kazakhstan. The algorithm is based on treating incomplete epidemiological data and solving the inverse problem of reconstructing the parameters of the agent-based model (ABM) using the set of available epidemiological data. The main tool for constructing the ABM is the Covasim open library. In the event of a drastic change in the situation (appearance of a new strain, removal or introduction of restrictive measures, etc.), the model parameters are updated taking into account additional information for the previous month (online data assimilation). The inverse problem is solved by stochastic global optimization (of tree-structured Parzen estimators). As an example, we give two scenarios of COVID-19 propagation calculated on December 12, 2021 for the period up to January 20, 2022. The scenario that took into account the New Year holidays (published on December 12, 2021 on http://covid19-modeling.ru ) almost coincided with what happened in reality (the error was 0.2%).

Coupled oxygen desorption and structural reconstruction accompanying reduction of copper oxide.

Understanding structural transformation and phase transition accompanying reactions in a solid as a catalyst or oxygen carrier is important to the design and optimization of many catalytic or chemical looping reaction processes. Herein, we combined density functional theory calculation with the stochastic surface walking global optimization approach to track the structural transformation accompanying the reduction of CuO upon releasing oxygen. We then used machine learning (ML) methods to correlate the structural properties of CuOx with varying x. By decomposing a reduction step into oxygen detachment and structural reconstruction, we identified two types of pathways: (1) uniform reduction with minimal structural changes; (2) segregated reduction with significant reconstruction. The results of ML analysis showed that the most important feature is the radial distribution functions of Cu-O at a percentage of oxygen vacancy [C(OV)] < 50% and Cu-Cu at C(OV) > 50% for CuOx formation. These features reflect the underlying physicochemical origin, i.e., Cu-O breaking and Cu-Cu formation in the respective stage of reduction. Phase diagram analysis indicates that CuO will be reduced to Cu2O under a typical oxygen uncoupling condition. This work demonstrates the complexity of solid structural transformation and the potential of ML methods in studying solid state materials involved in many chemical processes.

Global sensitivity analysis and stochastic optimization of multi-energy complementary distributed energy system considering multiple uncertainties

Multiple uncertainties exist in the planning and design of multi-energy complementary distributed energy system (DES). In order to solve this problem, a more complete framework of two-stage stochastic programming (TSP) approach for optimal multi-energy complementary DES planning and design under multiple uncertainties is proposed. The developed TSP model is formulated as a mixed integer linear programming, which is intended to minimize the equivalent annual cost (EAC) of the multi-energy complementary DES. Probability scenarios of key uncertain parameters selected by treed Gaussian process method for the TSP model are generated and reduced using discrete approximations of probability distributions method and random vector sampling method. The developed method framework is applied to a case study high-rise office building in planning stage to illustrate the TSP model's output. And multiple evaluation indicators including configuration, economy, energy and environment are used to compare and analyze the optimal schemes obtained by deterministic model and TSP model under different building load scenarios. The results show that of the 26 uncertain parameters considered only 7 are selected as the key parameters for the TSP model in this paper. EAC of the optimal multi-energy complementary DES may be overestimated if without considering key uncertain parameters. Thus, the deterministic optimization practices and the cost estimates resulting from them can be considered unreliable. Moreover, the multi-energy complementary DES would want to increase CO2 emission to achieve better economic performance. Finally, the energy share distribution of all scenarios in the stochastic model provides more reliable and more accurate information for decision-makers.

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.

Neural Network Accelerated Investigation of the Dynamic Structure-Performance Relations of Electrochemical CO2 Reduction over SnO x Surfaces.

Heterogeneous catalysts, especially metal oxides, play a curial role in improving energy conversion efficiency and production of valuable chemicals. However, the surface structure at the atomic level and the nature of active sites are still ambiguous due to the dynamism of surface structure and difficulty in structure characterization under electrochemical conditions. This paper describes a strategy of the multiscale simulation to investigate the SnO x reduction process and to build a structure-performance relation of SnO x for CO2 electroreduction. Employing high-dimensional neural network potential accelerated molecular dynamics and stochastic surface walking global optimization, coupled with density functional theory calculations, we propose that SnO2 reduction is accompanied by surface reconstruction and charge density redistribution of active sites. A regulatory factor, the net charge, is identified to predict the adsorption capability for key intermediates on active sites. Systematic electronic analyses reveal the origin of the interaction between the adsorbates and the active sites. These findings uncover the quantitative correlation between electronic structure properties and the catalytic performance of SnO x so that Sn sites with moderate charge could achieve the optimally catalytic performance of the CO2 electroreduction to formate.

Efficient Adaptive Monte Carlo Uncertainty Forecasting for High Dimensional Nonlinear Dynamic Systems

The problem of uncertainty forecasting for complex dynamical systems in the framework of particle methods can be effectively addressed through the solution methodology known as adaptive Monte Carlo (AMC). Monte Carlo (MC) methods involve discretizing the initial probability density function (pdf) followed by forward propagation of particles through system dynamics to obtain an approximate particle representation of the evolved state uncertainty. While simple to implement, MC faces questions surrounding transient statistical consistency and rate of convergence. AMC (adopted here) addresses these issues on-the-fly using defined bounds on estimation accuracy alongside ensemble enrichment routines. This paper presents several improvements in the ensemble enrichment module of AMC. The AMC platform is re-engineered to include the novel implementation of a parallel global stochastic optimization routine in conjunction with additional module enhancements that work together towards the goal of efficient forecasting. Moreover, the efficacy of algorithms utilized within every submodule of AMC are detailed and improved upon under the framework of arithmetic minimization and parallelization. Each submodule is profiled to determine computational bottlenecks, optimized or replaced with more efficient methods such as simulated annealing (SA), and parallelized ultimately leading to a clock time reduction of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200 - 400\%$ </tex-math></inline-formula> for benchmark entry descent and landing, Lorenz-96, and Lotka-Volterra models.

DEVELOPMENT OF OPTICAL SYSTEMS OF 16-LENS ORTHOSCOPIC TELEPHOTO LENSES

In this work, the possibilities of creating multi-lens optical systems of telephoto lenses with a fixed focal length and high image quality with the help of a computer have been experimentally investigated. The effectiveness of the automated procedure for creating new optical systems of orthoscopic telephoto lenses was repeatedly examined. The design procedure utilizes a modified version of the modern stochastic global optimization algorithm. In particular, we carried out the aberration synthesis of several optical systems of 16-lens orthoscopic telephoto lenses having the effective focal length of 300 mm and a F-number equal to 2.8, and designed to work in the visible spectral range with 35-mm full-frame image matrix detectors. Multiple computer simulations of the design process have shown that the global optimization procedure with a total number of variables of around 90 requires significant computing power. Specifically, when running on the Intel Core i9-9900K processor in multi-threaded mode and optimizing the values of the modulation transfer functions, the design procedure can exceed 50 hours. The maximum value of the relative distortion of synthesized variants of telephoto lenses does not exceed 0.017%. In all considered cases, the values of polychromatic modulation transfer functions for a spatial frequency of 30 lines/mm are not smaller than 0.5 over the entire image field. The design results obtained for the specified telephoto lenses confirm the effectiveness of the proposed approach and the practical possibility of achieving high-quality correction of aberrations in the above-mentioned multi-lens telephoto systems even without the use of fluorite (calcium fluoride).

Stochastic efficient global optimization with high noise variance and mixed design variables

Stochastic efficient global optimization with high noise variance and mixed design variables

Design of Irregularly Distributed Antenna Array towards Smart 6G Networks

The integration of sensing, computing, storage, and communications is one of the main research directions of current network development. To achieve the integration, an innovative design in the antenna array is essential. This paper presents a novel design of an irregularly distributed antenna array for smart 6G networks. Firstly, to solve the problem of fast amplitude and phase distribution of conformal arrays, the fast electromagnetic code of the multilevel fast multipole (MLFMA) based on volume surface integral equations (VSIE) is used to simulate the radiation characteristics of the irregularly distributed antenna arrays. Secondly, another stochastic global optimization algorithm, Simulated Annealing (SA), has been widely used to solve multiscale nonlinear problems. Finally, the performance of the proposed antenna array is given by simulation results and tests, to prove the effectiveness and correctness.

Non-Stationary Stochastic Global Optimization Algorithms

Studying the theoretical properties of optimization algorithms such as genetic algorithms and evolutionary strategies allows us to determine when they are suitable for solving a particular type of optimization problem. Such a study consists of three main steps. The first step is considering such algorithms as Stochastic Global Optimization Algorithms (SGoals ), i.e., iterative algorithm that applies stochastic operations to a set of candidate solutions. The second step is to define a formal characterization of the iterative process in terms of measure theory and define some of such stochastic operations as stationary Markov kernels (defined in terms of transition probabilities that do not change over time). The third step is to characterize non-stationary SGoals, i.e., SGoals having stochastic operations with transition probabilities that may change over time. In this paper, we develop the third step of this study. First, we generalize the sufficient conditions convergence from stationary to non-stationary Markov processes. Second, we introduce the necessary theory to define kernels for arithmetic operations between measurable functions. Third, we develop Markov kernels for some selection and recombination schemes. Finally, we formalize the simulated annealing algorithm and evolutionary strategies using the systematic formal approach.