A three-phase heuristic algorithm for fixed-charge capacitated material flow network design with input/output points location

In this paper, we consider the material flow network design problem in which locations of input and output points of departments and flow paths are determined concurrently on a given block layout. The objective of the problem is to minimize the sum of transportation cost, flow paths construction cost and penalty cost for non-smooth material flows, i.e., flows with turns. A mixed integer programming model is given for the problem and a three-phase heuristic algorithm is developed to solve the problem. In the suggested algorithm, we generate an initial flow network by determining locations of input/output points and flow paths sequentially in the first and second phases, respectively, and then improve it by changing locations of input/output points and flow paths iteratively in the third phase. To evaluate the performance of the suggested algorithms, a series of computational experiments are performed on well-known problem instances as well as randomly generated test problems. Results of computational experiments show that the suggested algorithm gives good solutions in a short computation time.     

A method for simulation based optimization using radial basis functions

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.     

Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems

We improve the job specific decomposition Lagrangian relaxation algorithm applied to industry size job shop scheduling problems with more than 10 000 resource constraints. We introduce two new features in the Lagrange multiplier updating procedure. First, the usual solution of all subproblems followed by dual cost estimation and update of multiplier values is replaced by the estimation of a surrogate dual cost function and a more frequent update of multipliers is implemented after each subproblem solution. Second, an adaptive step size in the subgradient based multiplier update is introduced. Asymptotic properties of the surrogate dual cost function are obtained and the proposed algorithmic improvements are evaluated in extensive numerical examples including published data used by other researchers, as well as extensive real industrial scheduling system data.     

A framework for design optimization using surrogates

Design optimization is a computationally expensive process as it requires the assessment of numerous designs and each of such assessments may be based on expensive analyses (e.g. computational fluid dynamics method or finite element based method). One way to contain the computational time within affordable limits is to use computationally cheaper approximations (surrogates) in lieu of the actual analyses during the course of optimization. This article introduces a framework for design optimization using surrogates. The framework is built upon a stochastic, zero-order, population-based optimization algorithm, which is embedded with a modified elitism scheme, to ensure convergence in the actual function space. The accuracy of the surrogate model is maintained via periodic retraining and the number of data points required to create the surrogate model is identified by a k-means clustering algorithm. A comparison is provided between different surrogate models (Kriging, radial basis functions (Exact and Fixed) and Cokriging) using a number of mathematical test functions and engineering design optimization problems. The results clearly indicate that for a given fixed number of actual function evaluations, the surrogate assisted optimization model consistently performs better than a pure optimization model using actual function evaluations.     

Metamodel Assisted Evolutionary Algorithm for Multi-objective Optimization of Non-steady Metal Forming Problems

Multiobjective optimization problems are considered in the field of nonsteady metal forming processes, such as forging or wire drawing. The Pareto optimal front of the problem solution set is calculated by a Genetic Algorithm. In order to reduce the inherent computational cost of such algorithms, a surrogate model is developed and replaces the exact the function simulations. It is based on the Meshless Finite Difference Method and is coupled to the NSGAII Evolutionary Multiobjective Optimization Algorithm, in a way that uses the merit function. This function offers the best way to select new evaluation points: it combines the exploitation of obtained results with the exploration of parameter space. The algorithm is evaluated on a wide range of analytical multiobjective optimization problems, showing the importance to update the metamodel along with the algorithm convergence. The application to metal forming multiobjective optimization problems show both the efficiency of the metamodel based algorithms and the type of practical information that can be derived from a multiobjective approach.     

基于Kriging代理模型的二维分数阶粘弹性问题的数值求解

为提高求解分数阶粘弹性正问题的计算效率,提出了一种基于Kriging代理模型的数值求解方法。利用拉丁超立方采样技术选取样本点,借助有限元和有限差分技术计算样本点的位移响应,从而建立Kriging代理模型。通过均质和区域非均质两个粘弹性算例,对所提方法的计算精度和计算效率进行了测试。测试分析表明:代理模型可提供合用的计算精度,当问题规模较大且正问题需要多次求解时,有望显著降低计算时间。     

带非凸二次约束的二次规划问题的全局优化方法

利用二次函数的线形下界函数对带有非凸二次约束的二次规划(QP)提出一种新的求其全局最优解的分支定界算法.为改进算法的收敛性,根据问题的最优性和可行性提出一新的区域剪枝准则以排除(QP)的可行域中不存在全局解的部分.数值算例表明该准则能有效地加速算法的收敛性.     

Automated accessibility analysis and measurement clustering for CMMs

The aim of inspection planning tasks is to ensure the generation of efficient operation for coordinate measurement machines (CMMs). This paper presents a methodology to automatically define the accessibility domain of measurement points and then group them into a set of clusters. The methodology uses the computer-aided design (CAD) model of the workpiece and tolerance information as input to an algorithm for defining points accessibility. For each measurement point, the algorithm determines all feasible inspection probe orientations, as a subset of the total set of available orientations for a given CMM probe. A heuristic algorithm then groups the measurement points into a set of clusters which provide the maximum number of probe orientations. This methodology was applied to three examples which contain solid model and free-form surface representations.     

A univariate Chebyshev polynomials method for structural systems with interval uncertainty

This paper presents an effective univariate Chebyshev polynomials method (UCM) for interval bounds estimation of uncertain structures with unknown-but-bounded parameters. The interpolation points required by the conventional collocation methods to generate the surrogate model are the tensor product of each one-dimensional (1D) interpolating point. Therefore, the computational cost is expensive for uncertain structures containing more interval parameters. To deal with this issue, the univariate decomposition is derived through the higher-order Taylor expansion. The structural system is decomposed into a sum of several univariate subsystems, where each subsystem only involves one uncertain parameter and replaces the other parameters with their midpoint value. Then the Chebyshev polynomials are utilized to fit the subsystems, in which the coefficients of these subsystems are confirmed only using the linear combination of 1D interpolation points. Next, a surrogate model of the actual structural system composed of explicit univariate Chebyshev functions is established. Finally, the extremum of each univariate function that is obtained by the scanning method is substituted into the surrogate model to determine the interval ranges of the uncertain structures. Numerical analysis is conducted to validate the accuracy and effectiveness of the proposed method.     

基于代理模型的通风盘式制动器制动盘结构优化设计

该文提出一种基于代理模型的复杂结构优化设计方法,并用于通风盘式制动器制动盘结构优化设计。提出的优化设计方法集成了CAE分析、实验设计、代理模型构造及非线性优化几部分,实验设计采用拉丁超立方抽样策略,代理模型选用改进的响应面模型,非线性优化算法采用序列二次规划算法。为了解决传统的响应面模型部分预测值与实验值误差较大问题,改进方法认为只有能够确保在每一个抽样点处的预测值与试验值的相对误差均在一定范围内的响应面模型才是一个可行的模型。在保证制动盘质量不变情况下,以寿命最大化为目标,应用设计的集成优化方法对制动盘进行优化设计,优化设计结果较好,其中制动盘疲劳寿命根据Coffin-Manson方法预测,制动过程中制动盘表面最大热应力及最高温度通过热机耦合的有限元模拟紧急制动过程获得。优化结果表明该文提出的方法是一种有效的复杂结构的优化设计方法。     

Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems

We present a model reduction approach to the solution of large‐scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non‐linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we compute an approximation of the non‐linear term using a select subset of interpolation points. Further, through this formulation we show similarities among the existing techniques of gappy proper orthogonal decomposition, missing point estimation, and empirical interpolation via coefficient‐function approximation. The resulting model reduction methodology is applied to a highly non‐linear combustion problem governed by an advection–diffusion‐reaction partial differential equation (PDE). Our reduced model is used as a surrogate for a finite element discretization of the non‐linear PDE within the Markov chain Monte Carlo sampling employed by the Bayesian inference approach. In two spatial dimensions, we show that this approach yields accurate results while reducing the computational cost by several orders of magnitude. For the full three‐dimensional problem, a forward solve using a reduced model that has high fidelity over the input parameter space is more than two million times faster than the full‐order finite element model, making tractable the solution of the statistical inverse problem that would otherwise require many years of CPU time. Copyright © 2009 John Wiley & Sons, Ltd.     

Error modeling for surrogates of dynamical systems using machine learning

A machine learning–based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high‐dimensional regression techniques (eg, random forests, and LASSO) to map a large set of inexpensively computed “error indicators” (ie, features) produced by the surrogate model at a given time instance to a prediction of the surrogate‐model error in a quantity of interest (QoI). This eliminates the need for the user to hand‐select a small number of informative features. The methodology requires a training set of parameter instances at which the time‐dependent surrogate‐model error is computed by simulating both the high‐fidelity and surrogate models. Using these training data, the method first determines regression‐model locality (via classification or clustering) and subsequently constructs a “local” regression model to predict the time‐instantaneous error within each identified region of feature space. We consider 2 uses for the resulting error model: (1) as a correction to the surrogate‐model QoI prediction at each time instance and (2) as a way to statistically model arbitrary functions of the time‐dependent surrogate‐model error (eg, time‐integrated errors). We apply the proposed framework to model errors in reduced‐order models of nonlinear oil‐water subsurface flow simulations, with time‐varying well‐control (bottom‐hole pressure) parameters. The reduced‐order models used in this work entail application of trajectory piecewise linearization in conjunction with proper orthogonal decomposition. When the first use of the method is considered, numerical experiments demonstrate consistent improvement in accuracy in the time‐instantaneous QoI prediction relative to the original surrogate model, across a large number of test cases. When the second use is considered, results show that the proposed method provides accurate statistical predictions of the time‐ and well‐averaged errors.     

Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework

Shape optimization is applied to time-dependent trailing-edge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a non-gradient based pattern search method chosen for its efficiency and rigorous convergence properties. Using SMF, design space exploration is performed not with the expensive actual function but with an inexpensive surrogate function. The use of a polling step in the SMF guarantees that the algorithm generates a convergent subsequence of mesh points in the parameter space. Each term of this subsequence is a weak local minimizer of the cost function on the mesh in a sense to be made precise later. We will discuss necessary optimality conditions for the design problem that are satisfied by the limit of this subsequence. Results are presented for an unsteady laminar flow past an acoustically compact airfoil. Constraints on lift and drag are handled within SMF by applying the filter pattern search method of Audet and Dennis, within which a penalty function is used to form and optimize a surrogate function. Optimal shapes that minimize noise have been identified for the trailing-edge problem in constrained and unconstrained cases. Results show a significant reduction (as much as 80%) in acoustic power with reasonable computational cost using several shape parameters. Physical mechanisms for noise reduction are discussed.     

基于线性基函数模型的虹膜定位

针对非圆虹膜定位困难的问题,本文提出了一种基于线性基函数模型的虹膜定位算法.该算法将虹膜定位问题看作从虹膜边缘点求虹膜边缘曲线的机器学习问题,先粗定位找到边缘点,再建立线性基函数模型从边缘点求得边缘曲线,从而实现了虹膜的精确定位.与传统的虹膜定位算法相比,所提算法能很好的定位非圆虹膜,而且花费时间只有极少的增加.在CA...     

带软时间窗的同时取送货车辆路径问题研究

考虑软时间窗下的车辆路径问题,客户点常伴有同时取送货的双重需求。针对此类问题,通过对软时间窗、车辆在途前后时间关系及二者融合问题进行刻画,同时将车辆行驶距离、车辆使用数、违反软时间窗总时间、客户满意度等纳入综合考量,构建相应混合整数非线性规划(mixed integer nonlinear programming, MINLP)模型。设计相应多目标优化求解算法,运用理想点法对目标函数进行转化,将多目标优化问题转化为单目标优化问题。结合相应算例集,运用LINGO 17.0全局求解程序求得每组算例的全局最优解。结果表明,针对带软时间窗的同时取送货车辆路径问题(vehicle routing problem with simultaneous pick-up and delivery and soft time windows, VRPSPDSTW),所建模型及算法是有效且可行的。     

An adaptive metamodel-based global optimization algorithm for black-box type problems

In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.     

稠密采样点模型的快速隐式曲面重建

算法以稠密采样点模型表面局部区域内的双边滤波函数值为依据,模型表面附近任意一点的函数值通过与该点最近的模型表面的K个采样点数据直接计算得到。与已有的隐式曲面重建方法相比,该方法既不用曲面内部或外部的支撑点,也不用求解线性和非线性方程,其重建速度快。此外,由于采用双边滤波函数作为其重建的隐式曲面的函数值,因此还能对带有噪声的采样点模型进行特征保持的表面重建。实验结果表明,对于稠密采样点模型,该方法可以快速重建出逼近程度高,效果好的曲面。     

Optimization procedures for simultaneous road rehabilitation and bridge replacement decisions in highway networks

A road-bridge rehabilitation model is formulated as a mixed non-linear programming problem with linear constraints. The purpose of the model is to minimize user travel costs under limited availability of funds. Two constraints are related to budget availability for road rehabilitation and bridge replacement (or rehabilitation). For a given set of replaced bridges, the problem is reduced to a continuous non-linear programming problem that can be further decomposed into a traffic assignment problem (TAP) and a road rehabilitation budget allocation problem (RBAP). The solution to the non-linear problem is found by iteratively solving the TAP and the RBAP. Since the TAP has a non-convex objective function, its solution is only guaranteed to be a local optimum. Several local optima are obtained at each branch of the search tree to estimate a lower confidence limit on the user cost of a global solution.     

Electric vehicle scheduling and optimal charging problem: complexity,exact and heuristic approaches

This paper deals with the Electric Vehicle (EV) Scheduling and Optimal Charging Problem. More precisely, given a fleet of EVs and Combustion Engine Vehicles (CVs), a set of tours to be processed by vehicles and a charging infrastructure, the problem aims to optimise the assignment of vehicles to tours and minimise the charging cost of EVs while considering several operational constraints mainly related to chargers, electricity grid and EVs driving range. We prove that the Electric Vehicle Scheduling and Charging Problem (EVSCP) is NP-hard in the ordinary sense. We provide a mixed-integer linear programming formulation to model the EVSCP and use CPLEX to solve small and medium instances. To solve large instances, we propose two heuristics: a Sequential Heuristic (SH) and a Global Heuristic (GH). The SH considers the EVs sequentially. To each EV, it assigns a set of tours and guarantees the feasibility of a charging schedule. Then, it generates an optimal charging schedule for this EV. However, the GH computes, in the first step, a feasible assignment of tours to all EVs. In the second step, it applies a global Min-Cost-Flow-based charging algorithm to minimise the charging cost of the EVs fleet. To evaluate the efficiency of our solving approaches, computational results on a large set of real and randomly generated test instances are reported and compared.     

Practical solution approaches to solve a hierarchical stochastic production planning problem in a flexible automated workshop in China

This paper deals with a Hierarchical Stochastic Production Planning (HSPP) problem of Flexible Automated Workshops (FAWs), each with a number of Flexible Manufacturing Systems (FMSs). The problem includes not only the standard (demand, capacity and material supply) uncertainties but also uncertainties in processing times, necessity for rework and scrap. In contrast to most work that only considers either single period or infinite horizons, we also considers multiple time periods and multiple products. One objective of this paper is to determine a cost minimizing production plan for each FMS taking into consideration work-inprocess inventory, work centers overload and underload, cumulative over- and under-production of finished products over a finite time horizon. The HSPP problem is formulated as a stochastic nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. To facilitate the solution procedure, the model is first transformed into a deterministic nonlinear programming model and then into a linear programming model. For medium- or small-scale problems, Karmarkar's algorithm is applied to obtain the solution. For large-scale problem, an interaction/prediction algorithm is used. The effectiveness of these approaches is benchmarked against the linear programming method in Matlab 5.0 in various HSPP settings.