Local Gradient Search Research Articles

A Quality Prediction and Parameter Optimization Approach for Turbine Blade Multistage Manufacturing

As core components of an aircraft engine, turbine blades are featured by complex curved surface with strict precision requirements in multistage manufacturing processes (MMPs). Hence, reliable quality prediction and parameter optimization strategy on MMPs have long been in great demand. However, most techniques focus on the precision improving of single-stage single-product manufacturing systems; these improvements are difficult to implement in MMPs with coordinate transformations among multiple machines. In this article, we propose a noninvasive feature-based quality prediction and parameter optimization framework for high-precision MMPs. In particular, rather than retrofitting sensors onto machinery after installation, this study presents an executable and noninvasive solution by using coordinate measuring machine (CMM) data as input features for prediction. Based on features of different stages of machining, a sequential multistep deep learning architecture is developed to predict the final product quality. A preheating optimization algorithm, modified from a local gradient search method, is used for the optimization of key initial machining features, which results are further improved by the L-BFGS method, thus increasing the final production quality. To estimate the effectiveness of the proposed framework, experiments are carried out on two series of aviation turbine blades with complex curved surfaces from the Wuxi Turbine Blade Company Ltd. China. CMM data at key stages (i.e., blade root milling and comprehensive accurate milling) are used as inputs to predict the final geometrical errors. Comparison results verify that the proposed framework achieves the smallest root mean square error at 0.030 mm and 0.032 mm for two blades, respectively.

Continuous-variable optimization with neural network quantum states

Inspired by proposals for continuous-variable quantum approximate optimization (CV-QAOA), we investigate the utility of continuous-variable neural network quantum states (CV-NQS) for performing continuous optimization, focusing on the ground state optimization of the classical antiferromagnetic rotor model. Numerical experiments conducted using variational Monte Carlo with CV-NQS indicate that although the non-local algorithm succeeds in finding ground states competitive with the local gradient search methods, the proposal suffers from unfavorable scaling. A number of proposed extensions are put forward which may help alleviate the scaling difficulty.

Universal effectiveness of high-depth circuits in variational eigenproblems

This paper shows that generic high-depth variational circuits can approximate the ground state of any given one-dimensional quantum many-body Hamiltonian by carrying out the local gradient search of the circuit parameters.

Gradient Immune-based Sparse Signal Reconstruction Algorithm for Compressive Sensing

The reconstruction aspect is the main core of the compressive sensing theory, in which the sparse signal is reconstructed from an incomplete set of random measurements. The constraint of spare signal reconstruction is the minimization of l0-norm, especially under noise condition. Thus, this paper proposes a new method called Gradient Immune-based Sparse Signal Reconstruction Algorithm for Compressive Sensing (GISSRA-CS) to optimize the trade-off between the reconstruction error and the sparsity requirements. The principle of the GISSRA-CS method is embedding the Gradient Local Search (GLS) method in the evolutionary process of the Immune Algorithm (IA) for solving the sparsity problem. Here, the sparsity problem is formulated as a multi-objective problem (MOP) by combining l0 and l1-norms of a solution and l2-norm of a residual error in the same criterion to optimize the trade-off between the sparsity requirements and the error. This MOP problem is solved in a several subproblems manner by assigning different weights for each subproblem to increase the population diversity. For a long-term sparse signal, the window method is used to divide it into multiple short signals to improve the performance and computational complexity of the proposed method. Mathematical analysis and simulation experiments are presented to validate the performance and complexity of the GISSRA-CS method. Results of different simulation scenarios based on the benchmark and simulated signals show that the GISSRA-CS method outperforms the other methods in recovering the sparse signals with a small reconstruction error from noiseless and noisy measurements. Furthermore, the convergence of GISSRA-CS is faster than the other evolutionary recovery methods, but it is slower than the traditional recovery methods.

Variable-Fidelity Methodology for the Aerodynamic Optimization of Helicopter Rotors

The design of helicopter rotor blades is a challenging task. On the one hand, there are the demanding simulations, which are a multidisciplinary endeavor. On the other hand, tools for parametric studies or optimizations require many simulations, making the design process even more costly. In the rotorcraft community, two routes for the numerical optimization task are observed. The first route is based upon local gradient search algorithms, which exploit low-fidelity tools or adjoint-based computational fluid dynamics (CFD) simulations. The second route is surrogate-based optimization in combination with high-fidelity CFD simulations. These surrogate-based optimizations can be further accelerated, when knowledge from low-fidelity models is used. This paper presents a framework that is developed for the multi-objective aerodynamic optimization of helicopter rotor blades including surrogate models based on different fidelities. The individual components necessary for performing a variable-fidelity, multi-objective optimization are reviewed before being applied. A novel technique to deal with unsuccessful simulations referred to as a failure map is additionally presented. The gain of the variable-fidelity optimizations in contrast to the single-fidelity optimizations is quantified, and a reduction in computational resources of up to 69% is observed. The failure map requires 78% less resources in contrast to the classical failure handling.

Multiobjective Sparse Non-Negative Matrix Factorization.

Non-negative matrix factorization (NMF) is becoming increasingly popular in many research fields due to its particular properties of semantic interpretability and part-based representation. Sparseness constraints are usually imposed on the NMF problems in order to achieve potential features and sparse representation. These constrained NMF problems are usually reformulated as regularization models to solve conveniently. However, the regularization parameters in the regularization model are difficult to tune and the frequently used sparse-inducing terms in the regularization model generally have bias effects on the induced matrix and need an extra restricted isometry property (RIP). This paper proposes a multiobjective sparse NMF paradigm which refrains from the regularization parameter issues, bias effects, and the RIP condition. A novel multiobjective memetic algorithm is also proposed to generate a set of solutions with diverse sparsity and high factorization accuracy. A masked projected gradient local search scheme is specially designed to accelerate the convergence rate. In addition, a priori knowledge is also integrated in the algorithm to reduce the computational time in discovering our interested region in the objective space. The experimental results show that the proposed paradigm has better performance than some regularization algorithms in producing solutions with different degrees of sparsity as well as high factorization accuracy, which are favorable for making the final decisions.

Application and Analysis of Bounded-Impulse Trajectory Models with Analytic Gradients

Bounded-impulse trajectory models are an important component of many spacecraft trajectory preliminary design workflows. This paper includes discussions on practical implementation considerations for establishing a numerically robust preliminary design optimization framework. Efficient computation of the mathematical components required to compute analytic gradients is discussed, and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cutoff events that result in nonsmooth derivatives. The challenges associated with incorporating the Spacecraft Planet Instrument C-Matrix Events high-fidelity ephemeris system into a trajectory optimization framework are discussed, and an alternative that results in smooth partial derivatives with respect to time is presented. Application problems that illustrate the benefits of employing analytic Jacobian calculations in favor of using the method of finite differences for both low- and high-thrust trajectory models are presented. The advantages of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored.

A global optimization algorithm for trajectory data based car-following model calibration

How to calibrate the parameters of car-following models based on observed traffic data is a vital problem in traffic simulation. Usually, the core of calibration is cast into an optimization problem, in which the decision variables are car-following model parameters and the objective function usually characterizes the difference between empirical vehicle movements and their simulated correspondences. Since the objective function is usually nonlinear and non-convex, various greedy or stochastic algorithms had been proposed during the last two decades. However, the performance of these algorithms remains to be further examined. In this paper, we revisit this important problem with a special focus on the geometric feature of the objective function. First, we prove that, from a global perspective, most existing objective functions are Lipschitz continuous. Second, we show that, from a local perspective, many of these objective functions are relatively flat around the global optimal solution. Based on these two features, we propose a new global optimization algorithm that integrates global direct search and local gradient search to find the optimal solution in an efficient manner. We compare this new algorithm with several existing algorithms, including Nelder–Mead (NM) algorithm, sequential quadratic programming (SQP) algorithm, genetic algorithm (GA), and simultaneous perturbation stochastic approximation (SPSA) algorithm, on NGSIM trajectory datasets. Results demonstrate that the proposed algorithm has a fast convergence speed and a high probability of finding the global optimal solution. Moreover, it has only two major configuration parameters that can be easily determined in practice.

Modified Social-Spider Optimization Algorithm Applied to Electromagnetic Optimization

Social-spider optimization (SSO) is a new nature-inspired algorithm of the swarm intelligence field to global optimization applications, which is based on the simulation of cooperative behavior of social spiders. To enhance the performance of the standard SSO, a modified SSO (MSSO) approach based on beta distribution and natural gradient local search was proposed in this paper. In order to verify the performance of the MSSO, tests using Loney’s solenoid benchmark and a brushless direct current motor benchmark are realized comparing the effectiveness of the SSO and the proposed MSSO. The results of this paper demonstrated that the MSSO performance is promising in electromagnetics optimization.

On Some Aspects of Genetic and Evolutionary Methods for Optimization Purposes

Abstract In this paper, the idea of applying some hybrid genetic algorithms with gradient local search and evolutionary optimization techniques is formulated. For two different test functions the proposed versions of the algorithms have been examined. Research results are presented and discussed to show potential efficiency in optimization purposes

Diversity-maintained differential evolution embedded with gradient-based local search

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.

Uniformly sampled genetic algorithm with gradient search for structural identification – Part II: Local search

This paper investigates several gradient local search methods as an enhancement to Part I, to further improve the computational efficiency while achieving the same identification accuracy. The present study is significant in several ways. First, this study reveals the characteristics of structural identification from the optimization perspective. Second, the ''switch point'' from global search to local search is determined with due consideration in convergence speed and avoidance of local optima. Finally, the combined strategy based on Part I and Part II with a particular local search (BFGS) is found to achieve substantial improvement in identification efficiency and accuracy.

A grid-based genetic algorithm combined with an adaptive simulated annealing for protein structure prediction

A hierarchical hybrid model of parallel metaheuristics is proposed, combining an evolutionary algorithm and an adaptive simulated annealing. The algorithms are executed inside a grid environment with different parallelization strategies: the synchronous multi-start model, parallel evaluation of different solutions and an insular model with asynchronous migrations. Furthermore, a conjugated gradient local search method is employed at different stages of the exploration process. The algorithms were evaluated using the protein structure prediction problem, having as benchmarks the tryptophan-cage protein (Brookhaven Protein Data Bank ID: 1L2Y), the tryptophan-zipper protein (PDB ID: 1LE1) and the ?-Cyclodextrin complex. Experimentations were performed on a nation-wide grid infrastructure, over six distinct administrative domains and gathering nearly 1,000 CPUs. The complexity of the protein structure prediction problem remains prohibitive as far as large proteins are concerned, making the use of parallel computing on the computational grid essential for its efficient resolution.

Multiuser Spectrum Optimization for Discrete Multitone Systems With Asynchronous Crosstalk

Finding computationally efficient spectrum optimization methods for a multiuser digital subscriber line (DSL) environment is a key objective of dynamic spectrum management for DSL systems. For synchronous discrete multitone (DMT) based DSL systems, the computational complexity issue can be partially addressed using a dual optimization approach that decomposes the problem in the frequency domain. However, the decomposition approach fails whenever the DMT system is asynchronous, in which case the power allocations in adjacent frequency tones interfere with each other. This paper provides a mathematical model for intercarrier interference due to symbol misalignment and proposes ways to modify the dual method for spectrum optimization of asynchronous DSL systems. The main ingredient of the algorithm is an efficient method to evaluate the minimum power required to support a given bit-allocation using a power series approximation, combined with a local gradient search.

New method for identifying finite degree Volterra series

In this paper, the identification of a class of nonlinear systems which admits input–output maps described by a finite degree Volterra series is considered. In actual fact, it appears that this class can model many important nonlinear multivariable processes not only in engineering, but also in biology, socio-economics, and ecology. To solve this identification problem, we propose a method based on local gradient search in a local parameterization of the state-space realization of finite degree Volterra series with infinite horizon. Using the local parameterization not only reduces the amount of the gradient calculations to the minimal value, but also overcomes the nonuniqueness problem of the optimal solution. Moreover, we propose a sequential projection method to provide an initial estimation of the parameters of finite degree Volterra series realization. This initial estimation is used to initialize the gradient search method.

Location of concentrators in a computer communication network: a stochastic automation search method

The following problem is considered. Given the locations of the Central Processing Unit (ar;the terminals which have to communicate with it, to determine the number and locations of the concentrators and to assign the terminals to the concentrators in such a way that the total cost is minimized. There is alao a fixed cost associated with each concentrator. There is ail upper limit to the number of terminals which can be connected to a concentrator. The terminals can be connected directly to the CPU also In this paper it is assumed that the concentrators can bo located anywhere in the area A containing the CPU and the terminals. Then this becomes a multimodal optimization problem. In the proposed algorithm a stochastic automaton is used as a search device to locate the minimum of the multimodal cost function The proposed algorithm involves the following. The area A containing the CPU and the terminals is divided into an arbitrary number of regions (say K). An approximate value for the number of concentrators is assumed (say m). The optimum number is determined by iteration later The m concentrators can be assigned to the K regions in ways (m > K) or ways (K>m).(All possible assignments are feasible, i.e. a region can contain 0,1,…, to concentrators). Each possible assignment is assumed to represent a state of the stochastic variable structure automaton. To start with, all the states are assigned equal probabilities. At each stage of the search the automaton visits a state according to the current probability distribution. At each visit the automaton selects a ‘point’ inside that state with uniform probability. The cost associated with that point is calculated and the average cost of that state is updated. Then the probabilities of all the states are updated. The probabilities are taken to bo inversely proportional to the average cost of the states After a certain number of searches the search probabilities become stationary and the automaton visits a particular state again and again. Then the automaton is said to have converged to that state Then by conducting a local gradient search within that state the exact locations of the concentrators are determined This algorithm was applied to a set of test problems and the results were compared with those given by Cooper's (1964, 1967) EAC algorithm and on the average it was found that the proposed algorithm performs better.