An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

Optimization Algorithms for Sidelobes SSL Reduction: A Comparative Study

The development of new technologies in smart cities is often hailed as it becomes a necessity to solve many problems like energy consumption and transportation. Wireless networks are part of these technologies but implementation of several antennas, using different frequency bandwidths for many applications might introduce a negative effect on human health security. In wireless networks, most antennas generate sidelobes SSL. SSL causes interference and can be an additional resource for RF power that can affect human being health. This paper aims to study algorithms that can reduce SSL. The study concerns typical uniform linear antenna arrays. Different optimum side lobe level reduction algorithms are presented. Genetic algorithm GA, Chebyshev, and Particle Swarm Optimization algorithm are used in the optimization process. A comparative study between the indicated algorithms in terms of stability, precision, and running time is shown. Results show that using these algorithms in optimizing antenna parameters can reduce SSL. A comparison of these algorithms is carried out and results show the difference between them in terms of running time and SSL reduction Level.

Fully asynchronous distributed optimization with linear convergence over directed networks

We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.

Global optimization over linear constraint non-convex programming problem

A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.

Quantum-Inspired Equilibrium Optimizer for Linear Antenna Array

With the rapid development of communication technology,the problem of antenna array optimization plays a crucial role.Among many types of antennas,line antenna arrays(LAA)are the most commonly applied,but the side lobe level(SLL)reduction is still a challenging problem.In the radiation process of the linear antenna array,the high side lobe level will interfere with the intensity of the antenna target radiation direction.Many conventional methods are ineffective in obtaining the maximumside lobe level in synthesis,and this paper proposed a quantum equilibrium optimizer(QEO)algorithm for line antenna arrays.Firstly,the linear antenna array model consists of an array element arrangement.Array factor(AF)can be expressed as the combination of array excitation amplitude and position in array space.Then,inspired by the powerful computing power of quantum computing,an improved quantum equilibrium optimizer combining quantum coding and quantum rotation gate strategy is proposed.Finally,the proposed quantum equilibrium optimizer is used to optimize the excitation amplitude of the array elements in the linear antenna array model by numerical simulation to minimize the interference of the side lobe level to the main lobe radiation.Six differentmetaheuristic algorithms are used to optimize the excitation amplitude in three different arrays of line antenna arrays,the experimental results indicated that the quantum equilibrium optimizer is more advantageous in obtaining the maximum side lobe level reduction.Compared with other metaheuristic optimization algorithms,the quantum equilibrium optimizer has advantages in terms of convergence speed and accuracy.

An Intelligent Optimization Method of Reinforcing Bar Cutting for Construction Site

To meet the requirements of specifications,intelligent optimization of steel bar blanking can improve resource utilization and promote the intelligent development of sustainable construction.As one of the most important building materials in construction engineering,reinforcing bars(rebar)account for more than 30%of the cost in civil engineering.A significant amount of cutting waste is generated during the construction phase.Excessive cutting waste increases construction costs and generates a considerable amount of CO_(2)emission.This study aimed to develop an optimization algorithm for steel bar blanking that can be used in the intelligent optimization of steel bar engineering to realize sustainable construction.In the proposed algorithm,the integer linear programming algorithm was applied to solve the problem.It was combined with the statistical method,a greedy strategy was introduced,and a method for determining the dynamic critical threshold was developed to ensure the accuracy of large-scale data calculation.The proposed algorithm was verified through a case study;the results confirmed that the rebar loss rate of the proposed method was reduced by 9.124%compared with that of traditional distributed processing of steel bars,reducing CO_(2)emissions and saving construction costs.As the scale of a project increases,the calculation quality of the optimization algorithmfor steel bar blanking proposed also increases,while maintaining high calculation efficiency.When the results of this study are applied in practice,they can be used as a sustainable foundation for building informatization and intelligent development.

System-L evel Efficiency Optimization of a Linear Induction Motor Drive System

Linear induction motors are superior to rotary induction motors in direct drive systems because they can generate direct forward thrust force independent of mechanical transmission.However,due to the large air gap and cut-open magnetic circuit,their efficiency and power factor are quite low,which limit their application in high power drive systems.To attempt this challenge,this work presents a system-level optimization method for a single-sided linear induction motor drive system.Not only the motor but also the control system is included in the analysis.A system-level optimization method is employed to gain optimal steady-state and dynamic performances.To validate the effectiveness of the proposed optimization method,experimental results on a linear induction motor drive are presented and discussed.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

A LINEAR PRECODING STRATEGY BASED ON PARTICLE SWARM OPTIMIZATION IN MULTICELL COOPERATIVE TRANSMISSION

An optimal linear precoding scheme based on Particle Swarm Optimization(PSO),which aims to maximize the system capacity of the cooperative transmission in the downlink channel,is proposed for a multicell multiuser single input single output system.With such a scheme,the optimal precoding vector could be easily searched for each user according to a simplified objective function.Simulation results show that the proposed scheme can obtain larger average spectrum efficiency and a better Bit Error Rate(BER) performance than Zero Forcing(ZF) and Minimum Mean Square Error(MMSE) algorithm.

Prediction of Wind Speed Using a Hybrid Regression-Optimization Approach

Predicting wind speed is a complex task that involves analyzing various meteorological factors such as temperature, humidity, atmospheric pressure, and topography. There are different approaches that can be used to predict wind speed, and a hybrid optimization approach is one of them. In this paper, the hybrid optimization approach combines a multiple linear regression approach with an optimization technique to achieve better results. In the context of wind speed prediction, this hybrid optimization approach can be used to improve the accuracy of existing prediction models. Here, a Grey Wolf Optimizer based Wind Speed Prediction (GWO-WSP) method is proposed. This approach is tested on the 2016, 2017, 2018, and 2019 Raw Data files from the Great Lakes Environmental Research Laboratories and the National Oceanic and Atmospheric Administration’s (GLERL-NOAA) Chicago Metadata Archive. The test results show that the implementation is successful and the approach yields accurate and feasible results. The computation time for execution of the algorithm is also superior compared to the existing methods in literature.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Global Optimization of Nonlinear Blend-Scheduling Problems

The scheduling of gasoline-blending operations is an important problem in the oil refining industry. Thisproblem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but alsonon-convex nonlinear behavior, due to the blending of various materials with different quality properties.In this work, a global optimization algorithm is proposed to solve a previously published continuous-timemixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimi-zation, the distribution problem, and several important operational features and constraints. The algorithmemploys piecewise McCormick relaxation （PMCR） and normalized multiparametric disaggregation tech-nique （NMDT） to compute estimates of the global optimum. These techniques partition the domain of oneof the variables in a bilinear term and generate convex relaxations for each partition. By increasing the num-ber of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates ofthe global solution. The algorithm is compared to two commercial global solvers and two heuristic methodsby solving four examples from the literature. Results show that the proposed global optimization algorithmperforms on par with commercial solvers but is not as fast as heuristic approaches.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS:I.ALGORITHM AND GLOBAL CONVERGENCEXIU NAIHUA

A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ．LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.

Control of Neural Network Feedback Linearization Based on Chaotic Particle Swarm Optimization

A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.