Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local functions.Since nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training times.To address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective functions.Nevertheless,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex functions.In this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex objectives.We derive a sufficient condition,which limits the fidelity of compression,to guarantee convergence.Moreover,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression equivalent.Numerical experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order simultaneously.And experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying topologies.Overall,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex objectives.Additionally,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

SELECTION OF OBJECTIVE FUNCTIONS AND APPLICATION OF GENETIC ALGORITHMS IN DAMPING DESIGN OF PIPE SYSTEM

The vibration failure of pipe system of aeroengine seriously influences the safety of aircraft.Its damping design is determined by the selection of the design target,method and their feasibility.Five objective functions for the vibration design of a pipeline or pipe system are introduced,namely,the frequency,amplitude,transfer ratio,curvature and deformation energy as options for the optimization process.The genetic algorithms(GA)are adopted as the opti- mization method,in which the selection of the adaptive genetic operators and the method of implementation of the GA process are crucial.The optimization procedure for all the above ob- jective functions is carried out using GA on the basis of finite element software-MSC/NASTRAN. The optimal solutions of these functions and the stress distribution on the structure are calculated and compared through an example,and their characteristics are analyzed.Finally we put forward two new objective functions,curvature and deformation energy for pipe system optimization.The calculations show that using the curvature as the objective function can reflect the case of minimal stress,and the optimization results using the deformation energy represent lesser and more uni- form stress distribution.The calculation results and process showed that the genetic algorithms can effectively implement damping design of engine pipelines and satisfy the efficient engineering design requirement.

Well production optimization using streamline features-based objective function and Bayesian adaptive direct search algorithm

Well production optimization is a complex and time-consuming task in the oilfield development.The combination of reservoir numerical simulator with optimization algorithms is usually used to optimize well production.This method spends most of computing time in objective function evaluation by reservoir numerical simulator which limits its optimization efficiency.To improve optimization efficiency,a well production optimization method using streamline features-based objective function and Bayesian adaptive direct search optimization(BADS)algorithm is established.This new objective function,which represents the water flooding potential,is extracted from streamline features.It only needs to call the streamline simulator to run one time step,instead of calling the simulator to calculate the target value at the end of development,which greatly reduces the running time of the simulator.Then the well production optimization model is established and solved by the BADS algorithm.The feasibility of the new objective function and the efficiency of this optimization method are verified by three examples.Results demonstrate that the new objective function is positively correlated with the cumulative oil production.And the BADS algorithm is superior to other common algorithms in convergence speed,solution stability and optimization accuracy.Besides,this method can significantly accelerate the speed of well production optimization process compared with the objective function calculated by other conventional methods.It can provide a more effective basis for determining the optimal well production for actual oilfield development.

Reactor Network Synthesis Based on Instantaneous Objective Function Characteristic Curves

It is believed that whether the instantaneous objective function curves of plug-flow-reactor (PFR) and continuous-stirred-tank-reactor (CSTR) overlap or not, they have a consistent changing trend for complex reactions(steady state, isothermal and constant volume). As a result of the relation of the objective functions (selectivity or yield) to the instantaneous objective functions (instantaneous selectivity or instantaneous reaction rate), the optimal reactor network configuration can be determined according to the changing trend of the instantaneous objective function curves. Further, a recent partition strategy for the reactor network synthesis based on the instantaneous objective function characteristic curves is proposed by extending the attainable region partition strategy from the concentration space to the instantaneous objective function-unreacted fraction of key reactant space. In this paper,the instantaneous objective function is closed to be the instantaneous selectivity and several samples axe examined to illustrate the proposed method. The comparison with the previous work indicates it is a very convenient and practical systematic tool of the reactor network synthesis and seems also promising for overcoming the dimension limit of the attainable region partition strategy in the concentration space.

FUZZY IDENTIFICATION METHOD BASED ON A NEW OBJECTIVE FUNCTION

A method of fuzzy identification based on a new objective function is proposed. The method could deal with the issue that input variables of a system have an effect on the input space while output variables of the system do not exert an influence on the input space in the proposed objective functions of fuzzy clustering. The method could simultaneously solve the problems about structure identification and parameter estimation; thus it makes the fuzzy model become optimal. Simulation example demonstrates that the method could identify non linear systems and obviously improve modeling accuracy.

Experimental Evaluation of Objective Functions for Well-balanced Mapping

High performance of parallel computing on a message-passing multicomputer System relies on the balance of the workloads located on the processing elements of the System and the minimum communication ovcrheads among them. Mapping is the technology to partition the problem domain wellbalanced into multiple distinct execution tasks based on some measures. In mapping, a good objective function is the criterion to guarantce the distinct execution tasks equitable. In this paper, we evaluate five categories of those existed objective functions with three different problem subjects using experiments and find an objective function is much suitable for all kinds of problems.

Searching for an Optimized Single-objective Function Matching Multiple Objectives with Automatic Calibration of Hydrological Models

In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single-or multi-objective functions when utilizing automatic calibration approaches.In most previous studies, there is a general opinion that no single-objective function can represent all important characteristics of even one specific hydrological variable(e.g., streamflow).Thus hydrologists must turn to multi-objective calibration.In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes(i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds.The new objective function was applied to 196 model parameter estimation experiment(MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model.The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively.Results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration.The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed.

Randomized Objective Function Linear Programming in Risk Management

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.

Adaptive Learning Rate Optimization BP Algorithm with Logarithmic Objective Function

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Multi-objective optimization of rolling schedule based on cost function for tandem cold mill

In terms of tandem cold mill productivity and product quality,a multi-objective optimization model of rolling schedule based on cost function was proposed to determine the stand reductions,inter-stand tensions and rolling speeds for a specified product.The proposed schedule optimization model consists of several single cost functions,which take rolling force,motor power,inter-stand tension and stand reduction into consideration.The cost function,which can evaluate how far the rolling parameters are from the ideal values,was minimized using the Nelder-Mead simplex method.The proposed rolling schedule optimization method has been applied successfully to the 5-stand tandem cold mill in Tangsteel,and the results from a case study show that the proposed method is superior to those based on empirical formulae.

A New Augmented Lagrangian Objective Penalty Function for Constrained Optimization Problems

In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.

A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.

An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem

By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains;and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an interactive algorithm of MP is designed accordingly. Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker.

VECTOR WAVE FUNCTION EXPANSION FOR SOLVING ELECTROMAGNETIC SCATTERING BY BURIED OBJECTS

An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.

Object-Oriented Modeling of the Variation of Acceleration and Deceleration Characteristics in Relation to Speed Bands for Railway Vehicles

Automated operation and artificial intelligence technology have become essential for ensuring the safety, efficiency, and punctuality of railways, with applications such as ATO (Automatic Train Operation). In this study, the authors propose a method to efficiently simulate the kinematic characteristics of railroad vehicles depending on their speed zone. They utilized the function overloading function supported by a programming language and applied the fourth-order Lunge-Kutta method for dynamic simulation. By constructing an object model, the authors calculated vehicle characteristics and TPS and compared them with actual values, verifying that the developed model represents the real-life vehicle characteristics accurately. The study highlights potential improvements in automated driving and energy consumption optimization in the railway industry.

基于改进YOLOv5s的小目标检测算法

针对当前主流目标检测算法对图像中远距离小目标产生的漏检、误检等问题,提出一种改进YOLOv5s的小目标检测算法。在模型训练过程中,通过引入Focal-EIOU定位损失函数,加强边界框的定位精度;在骨干网络中,通过添加小目标检测层,提高小目标的检测精度;在Neck结构中,通过优化上采样算子和添加注意力机制,加强小目标的特征信息。实验结果表明,改进后的算法在VisDrone数据集上与YOLOv5s算法相比,mAP@small提高了3.2%,且检测速度满足实时性的要求,能够很好地应用于小目标检测任务中。

结合Cokriging模型和单目标函数的随机模型修正

将Cokriging代理模型技术和单目标函数进行结合,提出了一种随机模型修正方法。该方法将不确定性模型修正问题转化为较简单的待修正参数统计特征的修正问题,能够在保证模型修正精度的同时,有效缓解模型修正中由于分步修正和多目标修正造成的计算成本高的问题。首先,假设待修正参数和响应均服从高斯分布,采用拉丁超立方抽样获取训练集样本,构造满足精度要求的Cokriging模型替代复杂的有限元模型参与迭代计算。然后,建立有限元模型计算响应统计特征与试验响应统计特征的加权残差目标函数,引入土狼优化算法最小化该单目标函数来得到待修正参数的统计特征。最后,通过二维和三维桁架结构验证了所提方法的可行性。