Random Search Method Research Articles

APPLICATION OF HYBRID RANDOM SEARCH METHOD TO OPTIMISATION OF ENGINEERING SYSTEMS’ PARAMETERS

This paper presents a modification of the Luus-Jaakola global optimization method, which belongs to the class of metaheuristic algorithms. A hybrid method is suggested, using a combination of random search methods: Luus-Jaakola method, adaptive random search method and best trial method. The obtained method is applied to the optimization of parameters of different engineering systems. This class of problems appears during the design of aerospace and aeronautical structures; its goal is the cost or weight minimization of the construction. These problems belong to the class of constrained global optimization problems, where the level surface of the objective function has uneven relief and there is a large number of variables. This means that the classical optimization methods prove to be inefficient and these problems should be solved using metaheuristic optimization methods, which provide sufficient accuracy at reasonable operating time. In this paper, the constrained global optimization problem is solved using the penalty method. Thus, the problem of exterior penalty function optimization is considered, where the penalty coefficients are chosen in such a way as to avoid the violation of the constraints. Two applied problems are considered in the paper: the determination of the high-pressure vessel parameters and the anti rattle spring parameters determination. Using the suggested algorithm, a software complex was developed, which allows us to solve engineering optimization problems. The results obtained using the suggested methods were compared with the results obtained using the non-modified Luus-Jaakola method in order to demonstrate the efficiency of the suggested hybrid random search method.

ОПТИМИЗАЦИЯ ЛИНЕЙНЫХ ФУНКЦИЙ НА МНОЖЕСТВЕ ЦИКЛИЧЕСКИХ ПЕРЕСТАНОВОК С ЛИНЕЙНЫМИ ОГРАНИЧЕНИЯМИ

Предметом статьи является процесс решения задач дискретной оптимизации на комбинаторных множествах различных классов. Целью является разработка методов решения задачи оптимизации линейной функции с линейными ограничениями на множестве циклических перестановок, погруженном в евклидово пространство. Задачи: найти точное или приближенное решение задачи оптимизации линейной функции с линейными ограничениями на множестве циклических перестановок, погруженном в евклидово пространство. Исследовать свойства задачи оптимизации, оценить приближенное решение. Основные результаты работы. Предложена стратегия решения с использованием алгоритма на основе случайного поиска. Для решения задачи оптимизации линейной функции на множестве циклических перестановок используется подход, основанный на идеологии случайного поиска и аналитическом решении систем линейных неравенств, описывающих ограничения задачи. В процессе решения исходной задачи необходимо многократное решение вспомогательной задачи оптимизации линейной функции на множестве циклических перестановок без ограничений. В работе приводится два подхода к решению вспомогательной задачи. Первый подход позволяет получить точное решение вспомогательной задачи методом ветвей и границ или приближенное решение при использовании дополнительных эвристик с оценкой полученного решения. Второй подход – эвристический метод на основе транспозиций специального вида. Для реализации подхода введен класс транспозиций, представители которого соответствуют критерию смежности в перестановочном многограннике. Предложенные стратегии реализованы программно и протестированы на задачах различной размерности с исходными данными, генерируемыми случайным образом. Проведены вычислительные эксперименты с целью сравнения точности и времени решения исходной задачи методом случайного поиска с использованием предложенных подходов к решению вспомогательной задачи. Выводы. Эксперименты показывают преимущество решения вспомогательной задачи методом ветвей и границ на малых размерностях. При этом на задачах больших размерностей метод на основе транспозиций существенно выигрывает в плане экономии вычислительных мощностей.

Performance Comparison of Algorithms for Real-Time Rate-of-Penetration Optimization in Drilling Using Data-Driven Models

Summary Real-time drilling optimization is a topic of significant interest because of its economic value, and its importance increases particularly during periods of low oil prices. This paper evaluates different optimization strategies and algorithms for real-time optimization of an objective function (function to be optimized) specific to drilling. The objective function optimized here is derived from a data-driven (or machine-learning) model with an unknown functional form. A data-driven model has been used to calculate the objective function [rate of penetration (ROP)] because it has been shown to be more efficient in ROP prediction relative to deterministic models (Hegde and Gray 2017). The data-driven ROP model is built using machine-learning algorithms; measured drilling parameters [weight on bit (WOB), revolutions per minute (rev/min), strength of rock, and flow rate] are used as inputs to predict the ROP. Real-time drilling optimization that is data-driven is challenging because of run-time constraints. This is perceived as a handicap for data-driven models because their functional form is unknown, making them more difficult to optimize. This paper evaluates algorithms depending on their ability to best maximize the objective (ROP) and their time effectiveness. Two simple yet robust algorithms, the eyeball method and the random-search method, are presented as plausible solutions to this problem. These methods are then compared with popular metaheuristic algorithms, evaluating the tradeoff between improvement in the objective (search for a global optimal) and the computational time of run. Using results from the simulations conducted in this paper, we concluded that data-driven models can be used for real-time drilling despite their computational constraints by choosing the right optimization algorithm. The best tradeoff in terms of ROP increase as well as computational efficiency evaluated in this paper is the simplex algorithm. The ROP was improved by 30% on average with a variance of 2.5% in the test set over 14 formations that were tested.

Gesture Recognition With the Linear Optical Sensor and Recurrent Neural Networks

In this paper, the optical linear sensor, a representative of low-resolution sensors, was investigated in the multiclass recognition of near-field hand gestures. The recurrent neural network (RNN) with a gated recurrent unit (GRU) memory cell was utilized as a gestures classifier. A set of 27 gestures was collected from a group of volunteers. The 27 000 sequences obtained were divided into training, validation, and test subsets. The primary research goal was to define the most appropriate model architecture in terms of the accurate recognition of each gesture. An additional aim of the research was to investigate the kind of input data, i.e., raw data or preprocessed (feature) data, which generally produces better results. Therefore, three datasets were generated: raw data, simple features data, and high-level features data. (This includes information about hand poses which are already recognized.) The random search method was applied to achieve hyperparameter optimization to find the best possible topology for the neural network. The analysis performed shows that selected models were characterized by a test score at a level of 96.89% for the raw data, 95.75% for simple features, and 93.38% for high-level features. Results indicate that the direct use of raw data obtained from the optical linear sensor evaluated on the RNN with GRU memory cells allows for the reliable recognition of even complex gestures. Therefore, such solutions may have the potential to serve as a support to or as an alternative to video-based sensors especially for mobile devices.

An Improved Tent Map-Adaptive Chaotic Particle Swarm Optimization (ITM-CPSO)-Based Novel Approach Toward Security Constraint Optimal Congestion Management

The introduction of deregulation into the electric utility industry has led to the transmission dispatch and congestion problem becoming more severe and complex to manage. This paper presents the implementation of an improved tent map-embedded chaotic particle swarm optimization (ITM-CPSO) algorithm to the nonlinear congestion management cost problem. To prevent the particle swarm optimization (PSO) plugging into the local minima with low convergence rate at later stages of iterations in case of nonlinear problems, a novel approach comprising a combination of PSO with tent map-adaptive chaotic particle swarm optimization has been implemented on nonlinear congestion management cost problem in this work. ITM-CPSO is a hybrid evolutionary algorithm, whose search procedure performs within a normalized plane of search space for all the chosen optimization variables for population-based procedures. The dual and full benefits of the characteristics of chaotic variables (i.e., periodicity and randomness) and tent map (i.e., more flat distribution than logistic maps) have been taken while formulating the congestion management cost problem. Further, to preserve the diversity of the proposed algorithm the inequality constraints have been handled by constraint prior optimal dominance method which is more efficient than the traditional penalty function method. Main contributions of the paper are twofold: Firstly, participating generators are selected using power flow tracing algorithm which is superior than sensitivity-based approach stated in the literature and secondly the implementation of proposed algorithm to the nonlinear congestion management cost problem further minimizes deviations of the rescheduled generator outputs from the scheduled levels as well as reduces the overall load shedding amount and cost. The simulation results of proposed algorithm are compared with those using classical PSO, random search method, simulated annealing, flower pollination algorithm, symbiotic organism search, firefly algorithm and ant lion optimizer for various line outage cases of IEEE-30, IEEE-57 and IEEE-118 bus system to prove the quality of results in terms of number of participating generators for rescheduling process and overall congestion management cost to relieve congestion.

Modeling an intelligent system for the estimation of technical state of construction structures

The study investigates issues related to modeling and development of intelligent systems for estimation of the technical state of building constructions. The study considers mathematical bases of modeling of an estimation system based on a fuzzy knowledge base and one of modifications of Takagi-Sugeno-Kang fuzzy network. It describes the structure of a network in detail and substantiates a choice of the algorithm for its learning. The main criteria for choosing this modification were its ability to solve a classification problem under conditions of uncertainty and the ability to set rules by the function of inputs. We adapted the structure of a network to the task of estimation of the technical state of real building constructions. We showed that it is advisable to learn a network with a use if an algorithm with a trainer. In this case, we suggested to use a direct method of random search, which is adapted to the solution of this problem, to minimize an error. In order to identify the state of structures, we suggested to use membership measures obtained by the clustering method. Implementation and introduction of neural network technologies in solution of tasks of estimation of the technical state of building constructions expands and improves capabilities of intelligent systems, reduces risks of making incorrect decisions by increasing reliability and speed of modeling.

Bayesian optimization for computationally extensive probability distributions.

An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.

Optimization by Self-Organized Criticality

Self-organized criticality (SOC) is a phenomenon observed in certain complex systems of multiple interacting components, e.g., neural networks, forest fires, and power grids, that produce power-law distributed avalanche sizes. Here, we report the surprising result that the avalanches from an SOC process can be used to solve non-convex optimization problems. To generate avalanches, we use the Abelian sandpile model on a graph that mirrors the graph of the optimization problem. For optimization, we map the avalanche areas onto search patterns for optimization, while the SOC process receives no feedback from the optimization itself. The resulting method can be applied without parameter tuning to a wide range of optimization problems, as demonstrated on three problems: finding the ground-state of an Ising spin glass, graph coloring, and image segmentation. We find that SOC search is more efficient compared to other random search methods, including simulated annealing, and unlike annealing, it is parameter free, thereby eliminating the time-consuming requirement to tune an annealing temperature schedule.

Математическая модель для параметрического исследования аммиачной двигательной установки в составе микроспутниковой платформы методом случайного поиска

Математическая модель для параметрического исследования аммиачной двигательной установки в составе микроспутниковой платформы методом случайного поиска

Presenting a Mathematical Model for Joint Production and Purchasing in a Multi-Product Problem and Determining the Optimal Order Value under Practical Constraints

Production and economic order is one of the most important topics in problems of production and inventory control, and it has long been of interest to researchers. Economic and profitable production requires that a comprehensive and detailed plan is taken and implemented for all stages of production. In the manufacturing companies that are producing a group of products, it is possible that in some periods, customers' demands exceed the production rate. In such conditions, the companies can response to such demand by more production, purchase, or accepting shortage of backordering. In case of purchase, the products stock in the warehouse at the beginning of programing period. In this study, a model is presented to determine the optimal amount of production and purchase in a multi-product system and with the objective of optimizing the costs of inventory system under the limitations of warehouse space and budget. Also, the start production time and the optimal amount of the shortage are determined. The presented mathematical model is of nonlinear integer type. The metaheuristic algorithm was used to solve the models, and the method of design of the experiments has been used to configure the parameters of the proposed method. At the end, the proper performance of the proposed methods will be proved by some numerical examples and comparing with random search method.

Piecewise continuous approach to nonlinear differential equations approximation problem of computational structural mechanics

This paper presents a nonlinear differential equations system piecewise continuous approximation. The piecewise continuous approximation improves piecewise linear approximation through reducing the errors at the boundaries of different linear differential equations systems areas. The matrices of piecewise continuous differential and algebraic equations systems are estimated using nonlinear differential equations system time responses and random search method. The results of proposed approach application are presented.

Bee colony optimization with Taguchi method for solving the dynamic economic dispatch

Dynamic economic dispatch is to minimize the cost of power production of all the participating generators over a time horizon of 24 hours in one day. The dynamic economic dispatch with non-smooth cost functions, for which is formulated the optimal dispatch model of generations by considering the ramp up/down scheduling of power. This paper presents a Bee Colony Optimization (BCO) that applies the Taguchi Method (TM) to solve the Dynamic Economic Dispatch problem. The Taguchi method that involves the use of orthogonal arrays in estimating of the non-smooth cost function and Bee Colony Optimization is used to find the objective function under the operational of system constraints. The Taguchi method can global optimization for fast local convergence by minimizing the cost function in a few iterations. The effectiveness and efficiency of the TM-BCO is demonstrated by using a 10 unit of IEEE case with non-smooth fuel cost functions and is more effective than other previously developed algorithms. Moreover, the proposed approach presents significant computational benefits than traditional random search method especially for multi-unit systems with larger numbers of non-smooth cost functions and more complicated dynamic economic dispatch.

A peak-over-threshold search method for global optimization

In this paper, we propose a random search method, called peak-over-threshold search (POTS), for solving global optimization problems. An important feature of POTS is that it combines the existing partition-based random search framework (e.g., Shi and Ólafsson 2000a; Chen et al. 2011) with the peak-over-threshold statistical reference (Coles, 2001) in order to achieve high search efficiency. In each iteration, POTS partitions the solution space into several subregions, evaluates the quality of each subregion and moves to promising subregions for more partitioning and sampling. To effectively assess the quality of a subregion, an extreme value type of inference in statistics is used to develop a new promising index which reflects the optimal objective value of a subregion and biases the search to regions that are likely to contain the optimal or near-optimal solutions. Under assumptions on the depth of partitioning and the probability of correct movement, POTS is shown to converge with probability one to the optimal region. The higher efficiency of the proposed method is illustrated by numerical examples. The application of POTS to beam angle selection, an important optimization problem in radiation treatment, is also presented in this paper.

CGRS — An advanced hybrid method for global optimization of continuous functions closely coupling extended random search and conjugate gradient method

A new hybrid method for global optimization of continuous functions is proposed. It is a combination of an extended random search method and a descent method. Random search is used as the global search strategy. A newly developed distribution-based region control makes use of already detected local minima to refine this search strategy. The approach resembles classical step size control in deterministic optimization. The descent method is embedded as a local search strategy for the detection of local minima. A special realization of this approach is presented in this paper and called CGRS. In CGRS the conjugate gradient method is utilized as descent method. The proof of global convergence in probability for CGRS is given and extended to other descent methods used in the hybrid optimization approach. In order to demonstrate the numerical properties of the approach test sets of multidimensional non-convex optimization problems are solved. The results are compared to well-established hybrid methods for global optimization. The new algorithm shows a high success rate with good and adjustable solution precision. Parameter tuning is not necessary, but of course possible. The new method proves to be efficient in terms of computational costs.

Коррекция исходной информации в балансовых уравнениях методом случайного поиска при наличии граничной функции

Коррекция исходной информации в балансовых уравнениях методом случайного поиска при наличии граничной функции

Optimizing the control process parameters for the induction soldering of aluminium alloy waveguide paths11The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research project № 16-48-242029

The paper describes the problem of selecting the optimal initial values of algorithm parameters for the process of the induction soldering of aluminium alloy waveguide paths. The authors consider some factors influencing the quality of waveguide soldered joint elements. These factors depend on the correct choice of initial values for control parameters. The problem of optimizing such parameters for further analytical and numerical studies is researched by authors. For solving the stated task, the random search method is selected, allowing for an acceptable field study within the stated time to solve the problem of control optimization with the level of accuracy required by the technological process. Therefore, optimal initial values of the induction soldering technological process were found for three sizes of waveguide tubes and flanges.

Optimal design of earth-moving machine elements with cusp catastrophe theory application

This paper deals with the optimal design problem solution for the operator of an earth-moving machine with a roll-over protective structure (ROPS) in terms of the catastrophe theory. A brief description of the catastrophe theory is presented, the cusp catastrophe is considered, control parameters are viewed as Gaussian stochastic quantities in the first part of the paper. The statement of optimal design problem is given in the second part of the paper. It includes the choice of the objective function and independent design variables, establishment of system limits. The objective function is determined as mean total cost that includes initial cost and cost of failure according to the cusp catastrophe probability. Algorithm of random search method with an interval reduction subject to side and functional constraints is given in the last part of the paper. The way of optimal design problem solution can be applied to choose rational ROPS parameters, which will increase safety and reduce production and exploitation expenses.

Simulation Optimization for Medical Staff Configuration at Emergency Department in Hong Kong

Medical staff configuration is a critical problem in the management of an emergency department (ED) in Hong Kong (HK). Given the service requirements by HK government, it is imperative for the hospital managers to develop medical staff configuration in a cost-and-time-effective way. In this paper, the medical staff configuration problem in ED is modeled as minimizing the total labor cost while satisfying the service quality requirements. To solve this issue, we propose a highly efficient search method, called random boundary generation with feasibility detection (RBG-FD). The random boundary generation (RBG) is applied to efficiently identify good-quality solutions based on the objective value. The feasibility detection (FD) procedure is used to retain the probability of correct feasibility detection of each sampled solution at the desired level, which intrinsically allocates a reasonable number of simulation replications. To estimate the performance measures of the ED, a discrete-event simulation model is developed to reflect the patient flow. Using these techniques, the efficiency of identifying the optimal staff configuration can be significantly improved. A case study is performed in a public hospital in HK. The numerical results indicate significantly higher practicability and efficiency of the proposed method with different patient arrival rates and service constraints. Note to Practitioners This paper seeks to solve the problem of minimizing the medical staff cost constrained by certain service requirements [i.e., patients’ waiting times for treatment] at an emergency department in Hong Kong. In our formulation, these service requirements are characterized by some stochastic constraints. Most of the existing random search methods concentrate on the computing efforts in the neighborhood of the best-so-far solutions in order to obtain good-quality solutions. Due to the special structure of this problem and ease of computing the objective values, we proposed an efficient random search approach that iteratively identifies a solution with a better objective value than that of the current best solution. Experimental studies demonstrate the significantly higher efficiency of this method. In order to obtain the same solution quality, it is able to reduce the computational time by 90% compared with some existing approaches in the literature.

NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION

This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented

Optimization of Horizontal Well Direction and Length Considering Geomechanics Properties and Drainage Area Using Genetic Algorithm in A Gas Field

To maximize a horizontal well production, we need to determine the optimum direction and horizontal well length that maximizes the gas field recovery for a certain constant flow rate called by plateau rate. This problem is conventionally solved by using a reservoir simulation model and trial and error procedure that consumes considerably a lot of time and efforts. This study uses a random search method, i.e., Genetic Algorithm (GA), to solve this optimization problem and it very much eases to find the best well location with less time and efforts consumed.Along the general technique in directing a horizontal well towards the least principal stress of rocks, this study considers the geomechanics effects that influence the gas production performance. And also, the drainage area of horizontal well will be considered in this study to obtain the optimum horizontal well direction and length. In order to do this, a new proposed objective function for the GA has been constructed based on basic reservoir properties (i.e., porosity, permeability and gas saturation) and geomechanics properties (i.e., Young’s modulus and Poisson’s ratio). The results of the proposed method are validated using a reservoir model and economics evaluation.It may be concluded that the applying GA, with the appropriate objective function, can give accurate and faster results compared with the trial and error method using reservoir simulator, technically and economically, and also the proposed method is able to reduce the amount of works considerably time.