Multidimensional Optimization Problem Research Articles

Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem

Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem

Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application

The multi-dimensional optimization of mechanisms is a typical optimization problem encountered in mechanical design. Herein, the Hybrid strategy improved Beetle Antennae Search (HSBAS) algorithm is proposed to solve the multi-dimensional optimization problems encountered in structural design. To solve the problems of local optimization and low accuracy of the high-dimensional solution of the Beetle Antennae Search (BAS) algorithm, the algorithm adopts the adaptive step strategy, multi-directional exploration strategy, and Lens Opposition-Based Learning strategy, significantly reducing the probability of the algorithm falling into the local optimum and improving its global search capability. Comparative experiments of the improved algorithm are carried out by selecting eleven benchmark test functions. HSBAS can reach 1 × 10−22 accuracy from the optimal value when dealing with low-dimensional functions. It can also obtain 1 × 10−2 accuracy when dealing with high-dimensional functions, significantly improving the algorithm’s capability. According to Friedman’s ranking test result, HSBAS ranks first, which proves that HSBAS is superior to the other three algorithms. The HSBAS algorithm is further used to optimize the design of the altitude compensation module of the gravity compensation device for solar wings, controlling the fluctuation of bearing capacity within 0.25%, which shows that the algorithm can be used as an effective tool for engineering structural optimization problems.

Optimal allocation of solar PV and wind energy power for radial distribution system using spider monkey optimization

The integration of renewable energy sources, relatable as Solar Photovoltaic (PV) and Wind Power, into the radial distribution system has gained significant attention due to their eco-friendly and sustainable attributes. This article presents a narrative advent for achieving the finest share of Solar PV and Wind force power through a radial distribution system using the innovative Spider Monkey Optimization (SMO) algorithm. Multi-objective function for the minimization of distribution loss and voltage deviation with the constraints of power balance equation and boundary limits of voltage and power is considered. The Spider Monkey Optimization algorithm, stimulated via the community activities of spider monkeys, be employed to effectively search for the finest allotment of Solar PV and Wind Energy Power within the distribution network. The SMO algorithm exhibits robustness in handling non-linear and multi-dimensional optimization problems, making it suitable for this complex task. To authorize the usefulness and efficiency of the planned approach, it is functional to standard 33-bus radial division coordination. Comparative analyses of optimization techniques are reported and SMO reduces the losses to 104 KW and the voltage deviation is minimized to 0.0458 pu. The valuable perception is that incorporating Solar PV and Wind Energy sources into radial distribution systems improves the quality.

რისკების რაოდენობრივი შეფასების მაჩვენებელთა სისტემა და მათი ეკონომიკური ეფექტიანობის შეფასების მეთოდები

The mathematical models of the company's optimal risk management mechanism ensure the maximum efficiency of the activity at the level of risk acceptable to the enterprise. Classification of risks into operational risk and interest risk is given. One of the possible options for determining the tasks of optimal planning of the enterprise is presented, which includes restrictions on the values of operational effect (OE) (OR). The OE (two) indicator is considered as a limitation, the normative value of which can be considered as a given value during planning. It is a multidimensional linear optimal planning problem with linear constraints. Its size is determined by the number of product types in the enterprise. We have formulated original economic-mathematical models of the distribution type, which are used to create the optimal production plan of the enterprise. In order to minimize the interest risk, we have used the duration indicator analysis method. Duration represents the elasticity of the price of a financial instrument (in this case the present value of a stream of payments) with respect to the interest rate (discount rate) and is therefore a measure of the risk of the price of the instrument changing when the interest rate changes.

A simulation framework to determine optimal strength training and musculoskeletal geometry for sprinting and distance running.

Musculoskeletal geometry and muscle volumes vary widely in the population and are intricately linked to the performance of tasks ranging from walking and running to jumping and sprinting. As an alternative to experimental approaches, where it is difficult to isolate factors and establish causal relationships, simulations can be used to independently vary musculoskeletal geometry and muscle volumes, and develop a fundamental understanding. However, our ability to understand how these parameters affect task performance has been limited due to the high computational cost of modelling the necessary complexity of the musculoskeletal system and solving the requisite multi-dimensional optimization problem. For example, sprinting and running are fundamental to many forms of sport, but past research on the relationships between musculoskeletal geometry, muscle volumes, and running performance has been limited to observational studies, which have not established cause-effect relationships, and simulation studies with simplified representations of musculoskeletal geometry. In this study, we developed a novel musculoskeletal simulator that is differentiable with respect to musculoskeletal geometry and muscle volumes. This simulator enabled us to find the optimal body segment dimensions and optimal distribution of added muscle volume for sprinting and marathon running. Our simulation results replicate experimental observations, such as increased muscle mass in sprinters, as well as a mass in the lower end of the healthy BMI range and a higher leg-length-to-height ratio in marathon runners. The simulations also reveal new relationships, for example showing that hip musculature is vital to both sprinting and marathon running. We found hip flexor and extensor moment arms were maximized to optimize sprint and marathon running performance, and hip muscles the main target when we simulated strength training for sprinters. Our simulation results provide insight to inspire future studies to examine optimal strength training. Our simulator can be extended to other athletic tasks, such as jumping, or to non-athletic applications, such as designing interventions to improve mobility in older adults or individuals with movement disorders.

Identification of High and Low Voltage Ride-Through Control Parameters for Electromechanical Transient Modeling of Photovoltaic Inverter

The electromechanical transient model of a photovoltaic (PV) inverter’s high and low voltage ride-through has complex operating circumstances and a large number of control parameters, which makes parameter adjustment difficult. Furthermore, it is frequently challenging to identify a single set of control parameters that can successfully handle a variety of operating conditions. The Improved Differential Evolution Particle Swarm Optimization (IDEPSO) algorithm is proposed in this paper to provide a control parameter identification technique for high and low voltage ride-through that addresses these problems. Taking a 320kW PV inverter of a certain company as the research object, based on the specified current control strategy of high and low voltage ride-though, the parameters to be identified were determined by analyzing the influence of model parameters. Secondly, To enhance the algorithm’s capability to solve multidimensional optimization problems, convergence speed, and global search ability, the Differential Evolution (DE) algorithm’s search mechanism is incorporated into the Particle Swarm Optimization (PSO) algorithm, along with a non-fixed gradient inertia weight strategy for the algorithm’s inertia weight and the elite retention idea for the cross factor. Then, the objective function of the IDEPSO algorithm was built based on the concept of minimum deviation between simulation data and various groups of test data, and the significance of various working conditions was distinguished by weight division to improve the robustness of identification parameters. Finally, the identification parameters are imported into the PSASP program type 2 photovoltaic power station model, and the interval division and deviation calculation of the test data and simulation data are carried out. It is confirmed that the identification parameters meet the standards of the maximum variation permitted in GB/T 32892-2016 and are appropriate for a variety of working scenarios.

SABO algorithm for optimum design of truss structures with multiple frequency constraints

In this study, a very recently developed intelligent algorithm called the self-adaptive bonomo optimizer (SABO) algorithm is implemented for the size and shape optimizations of the truss structures with the multiple frequency constraints. The bonomo optimizer (BO) algorithm is a recently developed metaheuristic optimization algorithm that imitates the social behavior and reproductive schemes of the bonobos and this algorithm is successfully applied to solve some challenging and highly nonlinear optimization problems. On the other hand, the BO algorithm suffers from the poor exploration and prematurely converges to the non-optimal solutions, especially when dealing with the multi-dimensional optimization problems. In order to overcome these shortcomings, an improved version of this algorithm, the so-called self-adaptive bonomo optimizer (SABO) algorithm, is utilized to optimize the truss structures subjected to the design constraints. The objective of this study is to minimize the weight of the truss structures with the multiple frequency constraints. Five well-known benchmark problems are considered to verify the robustness and reliability of the SABO algorithm. The design results obtained by the SABO algorithm are compared with those previously reported in the literature.

Multi-Compression Scale DNN Inference Acceleration based on Cloud-Edge-End Collaboration

Edge intelligence has emerged as a promising paradigm to accelerate DNN inference by model partitioning, which is particularly useful for intelligent scenarios that demand high accuracy and low latency. However, the dynamic nature of the edge environment and the diversity of end devices pose a significant challenge for DNN model partitioning strategies. Meanwhile, limited resources of the edge server make it difficult to manage resource allocation efficiently among multiple devices. In addition, most of the existing studies disregard the different service requirements of the DNN inference tasks, such as its high accuracy-sensitive or high latency-sensitive. To address these challenges, we propose a Multi-Compression Scale DNN Inference Acceleration (MCIA) based on cloud-edge-end collaboration. We model this problem as a mixed-integer multi-dimensional optimization problem, jointly optimizing the DNN model version choice, the partitioning choice, and the allocation of computational and bandwidth resources to maximize the tradeoff between inference accuracy and latency depending on the property of the tasks. Initially, we train multiple versions of DNN inference models with different compression scales in the cloud, and deploy them to end devices and edge server. Next, a deep reinforcement learning-based algorithm is developed for joint decision making of adaptive collaborative inference and resource allocation based on the current multi-compression scale models and the task property. Experimental results show that MCIA can adapt to heterogeneous devices and dynamic networks, and has superior performance compared with other methods.

A New Integral Function Algorithm for Global Optimization and Its Application to the Data Clustering Problem

The filled function method is an approach to finding global minimum points of multidimensional unconstrained global optimization problems. The conventional parametric filled functions have computational weaknesses when they are employed in some benchmark optimization functions. This paper proposes a new integral function algorithm based on the auxiliary function approach. The proposed method can successfully be used to find the global minimum point of a function of several variables. Some testing global optimization problems have been used to show the ability of this recommended method. The integral function algorithm is then implemented to solve the center-based data clustering problem. The results show that the proposed algorithm can solve the problem successfully.

Результати проектування надзвукового сопла з подвійним розширенням для рідинного ракетного двигуна першого ступеня методами обчислювального аналізу

The subject of this study is dual-bell supersonic nozzles of liquid rocket engines. The goal is to design a dual-bell supersonic nozzle that will provide maximum thrust for a liquid rocket engine in the first stage of a launch vehicle by solving an optimization problem using numerical simulation methods. The goal of the study is to choose the exit pressures of each part of the dual-bell nozzle based on the known flight trajectory of the launch vehicle, set and solve the problem of optimizing the dual-bell nozzle contour, and assess the impact of the use of a dual-bell nozzle on the efficiency of a liquid-propellant rocket engine. The methods used are: numerical methods for solving the hyperbolic system of unsteady equations of gas dynamics and multidimensional minimization problems. The following results were obtained. The formulation and solution of the optimization problem of the contour of a dual-bell supersonic nozzle, considering the design limitations in the form of a fixed length of the nozzle, is carried out. By analyzing the flight path of the first stage of the launch vehicle, a first approximation of the nozzle contour was obtained. For further calculations, both sections were approximated by parabolas, the coefficients of which, together with the lengths of the sections, formed a vector of optimized parameters. An expression for the axial component of thrust with the opposite sign was used as the objective function to solve the minimization problem. Because of solving the optimization problem, a dual-bell nozzle contour was designed to provide maximum thrust. An assessment of the effectiveness of his work was also conducted. The calculated value of the average along the trajectory of the specific impulse when using a dual-bell nozzle was higher by 1.6% than when using a standard nozzle. Conclusions. The scientific novelty of the obtained results is as follows: the design of the dual-bell nozzle contour was performed by solving the problem of multidimensional optimization, taking into account the design constraints, and using computational analysis methods

Models and methods of learning neural networks with differentiated activation functions

Analysis of the literature made it clear that the problem associated with improving the performance and acceleration of ANN learning is quite actual, as ANNs are used every day in more and more industries. The concepts of finding more profitable activation functions have been outlined a lot, but changing their behavior as a result of learning is a fresh look at the problem. The aim of the study is to find new models of optimization tasks for the formulated prob-lem and effective methods for their implementation, which would improve the quality of ANN training, in particular by overcoming the problem of local minima. A studied of models and methods for training neural networks using an extended vector of varying parameters is conducted. The training problem is formulated as a continuous mul-tidimensional unconditional optimization problem. The extended vector of varying parameters implies that it includes some parameters of activation functions in addition to weight coeffi-cients. The introduction of additional varying parameters does not change the architecture of a neural network, but makes it impossible to use the back propagation method. A number of gradient methods have been used to solve optimization problems. Different formulations of optimization problems and methods for their solution have been investigated according to ac-curacy and efficiency criteria. The analysis of the results of numerical experiments allowed us to conclude that it is expedient to expand the vector of varying parameters in the tasks of training ANNs with con-tinuous and differentiated activation functions. Despite the increase in the dimensionality of the optimization problem, the efficiency of the new formulation is higher than the generalized one. According to the authors, this is due to the fact that a significant share of computational costs in the generalized formulation falls on attempts to leave the neighborhood of local min-ima, while increasing the dimensionality of the solution space allows this to be done with much lower costs.

Time-division based integrated sensing, communication, and computing in integrated satellite-terrestrial networks

In this paper, we investigate time-division based framework for integrated sensing, communication, and computing in integrated satellite-terrestrial networks. We consider a scenario, where Internet-of-Things devices on the ground operate with sensing and communication in a time-division manner, and can process the sensing results locally, at the edge, or in the cloud via the satellite communication link. Based on the proposed framework, we formulate a multi-dimensional optimization problem to maximize the utility performance of sensing, communication, and computing abilities. After decomposing the original optimization problem into two subproblems, we first derive the closed-form solution of the optimal task partitioning strategy for terrestrial users and satellite users. Then, we develop the joint subframe allocation and task partitioning strategy to optimize the overall performance, by means of which the Pareto optimal solutions can be obtained along the Pareto frontier. Extensive simulations are provided to demonstrate the effectiveness of the proposed strategy, which is 10% to 60% superior compared with the benchmarks. Also, the trade-off between the multidimensional resource and multi-functional performance is analyzed from the perspective of network design.

SPECIAL FEATURES OF OPTIMIZATION DESIGN AND EVALUATION OF TECHNICAL RESOURCE FOR TRACTION GEAR TRANSMISSIONS OF RAILWAY ROLLING STOCK

The article highlights the peculiarities of optimization design for traction gear transmissions of railway rolling stock, aimed at determining the main structural parameters of corresponding paired gears and toothed wheels to increase their technical resource. The recommendations provide a formalized description of such investigations in the form of multidimensional optimization problems with constraints. Significant attention is given to the selection peculiarities of main variable parameters, primary criteria (related to reducing wear on tooth contact surfaces), and secondary numerical criteria (corresponding to functional constraints). The displacement coefficients of the gear and toothed wheel are considered as the main variable parameters, with a decisive impact on engagement parameters and characteristics. The main criterion, taking into account the focus on increasing the technical resource, is the minimization of the difference between the maximum coefficients of specific sliding on the feet of the lateral profiles of contacting teeth. Numerical functional constraints correspond to general design conditions for manufacturing and meshing of gear elements. The article elucidates the peculiarities of searching for optimal solutions using available generalized mathematical models that describe changes in the main criterion and existing functional constraints based on selected main variable parameters. It is also recommended to use constructed blocking contours based on these models to define the region of admissible solutions and find the corresponding optimization solution. For each variant of structural parameters of the paired gear and toothed wheel found during optimization design, the article suggests evaluating the respective changes in the technical resource according to the provided recommendations. The article presents the results of a comprehensive study of traction gear transmissions in various series of locomotives and electric trains, including assessments of increased technical resource achieved by using paired gears and toothed wheels with specified design parameters obtained through optimization design.

A Gaussian random walk salp swarm algorithm for optimal dynamic charging of electric vehicles

Salp swarm algorithm (SSA) is one of the recently developed meta-heuristic optimization algorithms. Since SSA outperforms other swarm-based algorithms, it has recently been employed in various applications, including feature selection, neural network training and renewable energy systems. In this paper, an improved salp swarm algorithm based on a Gaussian random walk is proposed, which enhances the algorithm’s performance particularly for multidimensional constrained global optimization problems. The integration of a Gaussian random walk into the algorithm balances between its exploration and exploitation capabilities. Furthermore, the proposed algorithm introduces a new re-dispersion strategy in the case of stagnation at local optimum points, which considerably enhances exploration. The performance of the proposed algorithm is evaluated using a set of twenty-three benchmark test functions and is compared to the performance of prevalent metaheuristic algorithms. Statistical analysis is performed using Wilcoxon signed-rank test, and the results reveal considerable improvement over the competing algorithms. Then, 21 real-world optimization problems are used to further evaluate the efficacy of the proposed algorithm. The winners of the CEC2020 Competition on Real-World Single Objective Constrained Optimization, SASS, sCMAgES, EnMODE, and COLSHADE algorithms, are used as four comparable algorithms in the real-world optimization problems. The convergence curves and simulations provide very competitive performance compared to the comparative algorithms. The proposed algorithm is used to address one of the most challenging real-world constrained problems in power system applications, namely, determining the optimal charging schedule for electric vehicles at charging stations. The results reveal that the proposed algorithm outperforms other existing algorithms in terms of increasing the charging revenues and achieving maximum power grid stability.

A novel hybrid particle swarm optimization with marine predators

Particle swarm optimization algorithms are often applied to solve optimization problems. However, the traditional particle swarm optimization algorithm has a single search method and is less capable of exploration and exploitation when solving high-dimensional and complex problems. In this paper, a hybrid particle swarm optimization algorithm for marine predators (HMPPSO) is proposed by combining the multi-stage search strategy of marine predators algorithm (MPA). We divide the search process of HMPPSO into three stages: the first stage uses Brownian motion for exploration; the middle stage divides the population into two parts, the first half remains responsible for exploration through Brownian motion. Besides, in the second half of the population, a random wandering strategy is proposed to randomly select five particles so that it can control the update of particles to prevent falling into the local optimal solution; the learning strategy is improved in the later stage. The control parameters are used to adjust the strategy, while making the single case learning method and the example averaging method alternate. This strategy accelerates the convergence of the algorithm while enhancing the diversity of the algorithm in the later stage and improving the development ability of the algorithm. In addition, the population diversity is enhanced using chaotic initialization and opposition-based learning strategies. The algorithm in this paper is applied to different types of CEC2017 benchmark test functions and four multi-dimensional non-linear structural design optimization problems. Compared with other recent algorithms, the results show that the performance of HMPPSO is significantly better than other algorithms.

Joint dynamic pricing and marketing‐mix strategies for revenue management applications with stochastic demand

AbstractTo attract potential customers and to effectively sell their inventories over time, retailers often invest in different marketing levers and apply dynamic pricing strategies. However, composing a profitable marketing mix in dynamic settings is challenging. The high problem complexity increases further if one seeks to account for stochastic and inventory‐dependent demand, which is essential for various practical applications. In this paper, we examine such stochastic dynamic pricing and marketing models under a finite as well as an infinite time horizon. We assume that marketing dimensions, such as information advertising, design quality, and the like, are substitutes only if they are all positive; otherwise, the demand vanishes. For a reasonably general demand formulation with asymmetric multidimensions marketing, we show how to transform the multidimensional optimal control problem into a two‐dimensional one, simplifying the analytical complexity. Further, for well‐established cases with isoelastic and exponential demand, we present optimal closed‐form solutions allowing detailed sensitivity analyses. Using numerical examples, we illustrate and analyze how optimally controlled sales processes are influenced by different model parameters and infer managerial insights. Our results provide general qualitative and quantitative insights into the complex interplay of marketing‐mix controls over time.

A New Pelican Optimization Algorithm for the Parameter Identification of Memristive Chaotic System

A memristor is a kind of nonlinear electronic component. Parameter identification for memristive chaotic systems is a multi-dimensional variable optimization problem. It is one of the key issues in chaotic control and synchronization. To identify the unknown parameters accurately and quickly, we introduce, in this paper, a modified Pelican Optimization Algorithm (POA) called the fractional-order chaotic Pareto Pelican Optimization Algorithm (FPPOA). First, the pelican population’s diversity is augmented with the integration of a fractional chaotic sequence. Next, the utilization of the Pareto distribution is incorporated to alter the hunting strategy of pelicans in the POA. These measures are effective in hastening the speed of finding an optimal solution and circumventing local optimization issues. Thirdly, the FPPOA is used to determine the values of the parameters of the simplest memristive chaotic system, which has a property of conditional symmetry. The proposed algorithm was evaluated during simulations, where it was utilized to solve six objective functions of varying unimodal and multimodal types. The performance of the FPPOA exceeds three traditional swarm intelligence optimization algorithms. In the parameter identification experiment, the results for the parameters with the FPPOA had error rates all within a 1% range. Extensive testing shows that our new strategy has a faster rate of convergence and better optimization performance than some other traditional swarm algorithms.

СОВРЕМЕННОЕ СОСТОЯНИЕ БИОЭВРИСТИК: КЛАССИФИКАЦИЯ, БЕНЧМАРКИНГ, ОБЛАСТИ ПРИМЕНЕНИЯ

The purpose of this article is to analyze the current state of research in the field of developmentof algorithms inspired by nature, including categorization, classification, testing, citation,and application areas. A new multi-level classification system based on the following features ispresented: the criterion of conformity to a natural metaphor, structural, behavioral, search, component,and evaluation criteria. The classification of bio heuristics involves the systematic assignmentof each bio heuristics to one and only one class within a system of mutually exclusive andnon-overlapping classes. Categorization allows an objective approach to the choice of bio heuristics.For each bio heuristics there are specific tasks with which it copes well. Knowing these relationshipsis important for the purposeful application of bio heuristics. An example of classificationis considered. It is noted that the most informative classification criterion is the behavioral criterion,the most cited class of bio heuristics are swarm intelligence algorithms, and the most cited bioheuristics is the PSO particle swarm algorithm. Modern approaches to benchmarking of bio heuristicsare presented: discrete and continuous optimization problems, as well as optimization engineeringproblems. There is a tendency to compare the performance of bio heuristics using statisticalhypothesis testing on benchmarks. The tasks successfully solved by bio heuristics in such areasas engineering design, image processing and computer vision, computer networks and communications,energy and energy management, data analysis and machine learning, robotics, medicaldiagnostics are systematized. There is a tendency to hybridize bio heuristics in one optimizer.However, convincing evidence is required that the results compensate for the increase in complexitycompared to individual algorithms. Optimization problems requiring further research are noted:dynamic and stochastic optimization problems; multicriteria optimization problems; multimodaloptimization problems; multidimensional optimization problems; memetic optimizationproblems in which a variety of search algorithms are combined; optimization problems and adaptationof bio heuristics parameter settings to achieve a balance between the convergence rate andthe diversification of the solution search space.

Metaheuristic methods to identify parameters and orders of fractional-order chaotic systems

For the synchronization and control of fractional-order chaotic systems, knowing parameters and orders is essential as well as being a hot topic. In this paper, the problem of parameters and orders identification is transformed into a multidimensional optimization problem. Five of the latest metaheuristic methods are employed to solve the parameter identification problem for six fractional-order chaotic systems. These metaheuristic methods involve Ali Baba and the Forty Thieves (AFT), Chameleon Swarm (CS) method, Artificial Gorilla Troops (AGT) Optimizer, Coot Bird (CB), and Harris Hawks (HH) optimization. Three novel fractional-order chaotic systems, in addition to Borah, Chen, and financial systems, are investigated. The Mean Square Error is used as an objective function to find the optimal parameters and orders of fractional-order chaotic systems. Numerical simulations demonstrate that the Ali Baba and the Forty Thieves (AFT) method achieves greater accuracy with a higher convergence rate for parameter identification problem for four selected fractional-order chaotic systems, while the Artificial Gorilla Troops (AGT) optimizer obtains better numerical and graphical results for two fractional-order chaotic systems compared to other metaheuristic methods.

A Family of Multi-Step Subgradient Minimization Methods

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with a built-in algorithm for finding the descent direction that forms an acute angle with all subgradients in the neighborhood of the current minimum. Minimizing the function along the opposite direction (with a minus sign) enables the algorithm to go beyond the neighborhood of the current minimum. The family of algorithms for finding the descent direction is based on solving systems of inequalities. The finite convergence of the algorithms on separable bounded sets is proved. Algorithms for solving systems of inequalities are used to organize the RSM family. On quadratic functions, the methods of the RSM family are equivalent to the conjugate gradient method (CGM). The methods are intended for solving high-dimensional problems and are studied theoretically and numerically. Examples of solving convex and non-convex smooth and non-smooth problems of large dimensions are given.