Stochastic Global Optimization Algorithm Research Articles

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.

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.

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).

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.

An adaptively weighted stochastic gradient MCMC algorithm for Monte Carlo simulation and global optimization

An adaptively weighted stochastic gradient MCMC algorithm for Monte Carlo simulation and global optimization

Optimising portfolio diversification and dimensionality

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree. The latter arises naturally due to our requirement that diversification measures should be leverage invariant. We introduce this new framework and argue the benefits relative to existing measures of diversification in the literature, before addressing the question of optimizing diversification or, equivalently, dimensionality. Maximising portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex and potentially have multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size and more akin to asset allocation problems, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate analytically and through numerical experiments that the framework reflects the desired properties often discussed in the literature.

A self-adaptive and gradient-based cuckoo search algorithm for global optimization

The stochastic global optimization (SGO) methods like particle swarm optimization (PSO), genetic algorithm (GA), and cuckoo search (CS) have been widely used in a variety of optimization problems partly because of the ability to find the global optimum. Most existing SGO algorithms are designed for gradient-free problems and ignore the gradient information even if the gradient is readily available, resulting in low efficiency and high computational cost. In this paper, we introduce a hybrid self-adaptive gradient-based cuckoo search (HAGCS) to tackle this limitation. HAGCS first takes a gradient-based local random walk to explore the search space, and then uses gradient-based local optimization (GBLO) to find a local minimum near to the current best solution, which is more efficient and precise than standard CS. Additionally, in order to avoid premature convergence potentially being caused by the use of the gradient, we introduce two novel self-adaptation and diversity promotion strategies onto HAGCS. These help HAGCS find proper control parameters and prevent HAGCS from getting stuck at local minima or stationary points. Lastly, we compare HAGCS with PSO, GA, CS, and 5 refinements of CS on 12 benchmark functions. Compared to the other methods, the experiment results show that the proposed method HAGCS has about 2 times faster convergence speed, higher accuracy, and 27.5% higher success rate of finding the global minimum in high-dimension problems. Even when the dimension of the problem is 1000, HAGCS still offers a success rate of 64% to find the global minima accurately.

Isogeometric Analysis and Bayesian Optimization on Efficient Weld Geometry Design for Remarkable Stress Concentration Reduction

Shape optimization combined with Isogeometric Analysis will be an efficient design method since exact Computer Aided Design geometries can be used for numerical analysis thanks to the same basis functions. In this study, authors developed an in-house research software JWRIAN-IGA and applied it to optimize the weld geometries of two models, namely a T-joint fillet weld and an elongated boxing fillet weld to reduce stress concentration. A gradient-free stochastic global optimization algorithm, Bayesian Optimization was used to sought optimal geometry parameters. It was shown that the optimized geometry was efficiently designed and the stress concentration in the welds for both cases was greatly reduced.

Estimation of parameters for a humidity-dependent compartmental model of the COVID-19 outbreak.

Building an effective and highly usable epidemiology model presents two main challenges: finding the appropriate, realistic enough model that takes into account complex biological, social and environmental parameters and efficiently estimating the parameter values with which the model can accurately match the available outbreak data, provide useful projections. The reproduction number of the novel coronavirus (SARS-CoV-2) has been found to vary over time, potentially being influenced by a multitude of factors such as varying control strategies, changes in public awareness and reaction or, as a recent study suggests, sensitivity to temperature or humidity changes. To take into consideration these constantly evolving factors, the paper introduces a time dynamic, humidity-dependent SEIR-type extended epidemiological model with range-defined parameters. Using primarily the historical data of the outbreak from Northern and Southern Italy and with the help of stochastic global optimization algorithms, we are able to determine a model parameter estimation that provides a high-quality fit to the data. The time-dependent contact rate showed a quick drop to a value slightly below 2. Applying the model for the COVID-19 outbreak in the northern region of Italy, we obtained parameters that suggest a slower shrinkage of the contact rate to a value slightly above 4. These findings indicate that model fitting and validation, even on a limited amount of available data, can provide useful insights and projections, uncover aspects that upon improvement might help mitigate the disease spreading.

О гибридизации стохастических алгоритмов глобальной оптимизации с учетом особенностей их архитектуры

The work is devoted to the hybridization of stochastic global optimization algorithms depending on their architecture. The main methods of hybridization of stochastic optimization algorithms are listed. An example of hybridization of the algorithm is given, the modification of which became possible due to taking into account the characteristic architecture of the M-PCA algorithm.

Conjugate Direction Particle Swarm Optimization Based Approach to Determine Kinetic Parameters from Part of Adiabatic Data

Due to the limited detection range of the adiabatic equipment, it is difficult to get complete experimental curve of some materials and calculate the kinetic parameters. In this work, the conjugate direction particle swarm optimization (CDPSO) approach, as a global stochastic optimization algorithm, is proposed to estimate the kinetic parameters and complete experimental curve from part of adiabatic calorimetric data. This algorithm combines the conjugate direction algorithm (CD) which has the ability to escape from the local extremum and the global optimization ability of the particle swarm optimization (PSO) which finds the globally optimal solutions. One case was used to verify this method: 20% DTBP in toluene decompositions under adiabatic conditions. Comparing the experimental and calculated complete temperature curve, the accuracy of the fitted kinetic parameters calculated by no less than 70% temperature rise rate proportion of data is verified. The value of TD24 is well-deviated even used 10% proportion of data. The case reasonably proves the effectiveness of CDPSO algorithm in the estimation of kinetic parameters from part of adiabatic data.

Tree Search versus Optimization Approaches for Map Generation

Search-based procedural content generation uses stochastic global optimization algorithms to search for game content. However, standard tree search algorithms can be competitive with evolution on some optimization problems. We investigate the applicability of several tree search methods to level generation and compare them systematically with several optimization algorithms, including evolutionary algorithms. We compare them on three different game level generation problems: Binary, Zelda, and Sokoban. We introduce two new representations that can help tree search algorithms deal with the large branching factor of the generation problem. We find that in general, optimization algorithms clearly outperform tree search algorithms, but given the right problem representation certain tree search algorithms performs similarly to optimization algorithms, and in one particular problem, we see surprisingly strong results from MCTS.

Filter-based stochastic algorithm for global optimization

We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.

A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs

In this article we propose a new more general calibration of the Heston Stochastic-Local Volatility (HSLV) model. More precisely, the main contribution is to perform the direct calibration of the whole set of parameters at the same time instead of the usual two steps procedure. Moreover, the proposed approach allows to use exotic options to calibrate the HSLV model, thus making it more flexible and general. However, as there are no analytical formulas available to price exotic options to calibrate the model, the cost function (the HSLV pricer) involved in the calibration process must be computed using Monte Carlo methods, thus leading to a highly demanding computational problem. Therefore, we also propose efficient parallel GPU implementations of Monte Carlo techniques for the pricers. Furthermore, for solving the resulting global optimization problem, we develop customized parallel multi-CPU implementations of two of the most common stochastic metaheuristic global optimization algorithms: Differential Evolution and Simulated Annealing. A comparison between both algorithms has been made. This second level of parallelization has been carried out by the implementation of the cost function as a single GPU kernel and keeping the OpenMP parallelization for the optimization algorithm, thus leading to a hybrid multi-GPU implementation of the calibrator. All these implementations have been tested with real market data for European and barrier options in the context of foreign exchange markets.

Global optimization to retrieve borehole-derived petrophysical properties of carbonates

Joint modeling and inversion of frequency-dependent dielectric constant and electrical resistivity well-log measurements has been addressed in literature in recent years. However, this problem is not studied for dual-porosity carbonate formations. Besides, the salinity and matrix dielectric constant are presumed to be known in previous studies. We have combined a model for brine dielectric constant and two laboratory-supported models for the electrical resistivity and dielectric constant of dual-porosity carbonates. Using this methodology, we replicate electrical resistivity and dielectric well-log measurements. Using a stochastic global optimization algorithm, we formulate a joint inversion workflow to estimate petrophysical properties of interest. For a constructed dual-porosity carbonate reservoir, we determine that the inversion workflow matches the forward-modeled data for the oil column, water column, and transition zone. We also found that our inversion workflow is capable to retrieve local model parameters (water-filled intergranular porosity and water-filled vuggy porosity) and global model parameters (matrix dielectric constant, lithology exponents for intergranular and vuggy pores, and salinity) with reasonable accuracy.

Global optimization for data assimilation in landslide tsunami models

The goal of this article is to make automatic data assimilation for a landslide tsunami model, given by the coupling between a non-hydrostatic multi-layer shallow-water and a Savage-Hutter granular landslide model for submarine avalanches. The coupled model is discretized using a positivity preserving second-order path-conservative finite volume scheme. Then, the data assimilation problem is posed in a global optimization framework. Later, multi-path parallel metaheuristic stochastic global optimization algorithms are developed. More precisely, a multi-path Simulated Annealing algorithm is compared with a multi-path hybrid global optimization algorithm based on coupling Simulated Annealing with gradient local searchers.

Fuzzy clustering algorithm based on modified whale optimization algorithm for automobile insurance fraud detection

Fuzzy c-means (FCM) clustering method is used for performing the task of clustering. This method is the most widely used among various clustering techniques. However, it gets easily stuck in the local optima. whale optimization algorithm (WOA) is a stochastic global optimization algorithm, which is used to find out global optima of a provided dataset. The WOA is further modified to achieve better global optimum. In this paper, a fuzzy clustering method has been proposed by using the strengths of both modified whale optimization algorithm (MWOA) and FCM. The effectiveness of the proposed clustering technique is evaluated by considering some of the well-known existing metrics. The proposed hybrid clustering method based on MWOA is employed as an under sampling method to optimize the cluster centroids in the proposed automobile insurance fraud detection system (AIFDS). In the AIFDS, first the majority sample data set is trimmed by removing the outliers using proposed fuzzy clustering method, and then the modified dataset is undergone with some advanced classifiers such as CATBoost, XGBoost, Random Forest, LightGBM and Decision Tree. The classifiers are evaluated by measuring the performance parameters such as sensitivity, specificity and accuracy. The proposed AIFDS consisting of fuzzy clustering based on MWOA and CATBoost performs better than other compared methods.

Conjugate direction particle swarm optimization based approach to determine kinetic parameters from differential scanning calorimetric data

Optimization of the kinetic parameters with thermal analysis data is an essential issue. In this work, the conjugate direction particle swarm optimization (CDPSO) approach, as a global stochastic optimization algorithm that is suitable to high-dimension optimization problem, is first employed to estimate the kinetic parameters with DSC data. This algorithm combines the global optimization ability of the particle swarm optimization (PSO) and the ability to escape from the local extremum by the conjugate direction algorithm (CD) to find the globally optimal solutions. This algorithm does not require estimation of the initial values of the kinetic parameters. The validation of this method is verified by two cases: DCPO decomposition and CHP decomposition. By comparing the experimental and calculated heat flow results, the accuracy of the fitted kinetic parameters is verified. These two cases prove the effectiveness of CDPSO algorithm in the estimation of high-dimension kinetic parameters using DSC data.

Stochastic global optimization algorithms: A systematic formal approach

Up to now, different algorithmic methods have been developed to find ’good’ solutions (near to the optimal solution) for global optimization problems that cannot be solved using analytical methods. In particular, algorithmic methods such as differential evolution, evolutionary algorithms, and hill climbing belong to the class of Stochastic Global Optimization Algorithms (SGoals). In general, an SGoal iteratively applies stochastic operations to a set of candidate solutions (population), following, in some cases, a heuristic/metaheuristic. Although some research works have tried to formalize SGoals using Markov kernels, such formalization is not general and sometimes is blurred. In this paper, we propose a comprehensive, systematic and formal approach for studying SGoals. First, we present concepts of probability theory that are required to perform such formalization and we demonstrate that the swapping, sorting, and permutation functions, among others, can be represented by Markov kernels. Then, we introduce the joint Markov kernel as a way of characterizing the combination of stochastic methods. Next, we define the optimization space, a σ-algebra that contains ϵ-optimal states, and develop Markov kernels for stochastic methods like swapping, sorting and permutation. Finally, we introduce sufficient convergence conditions for SGoals and present some popular SGoals in terms of the developed theory.