Multiple eigenvalue optimization of composite structures using discrete third order displacement models

This paper deals with the implementation and test of a non-smooth eigenfrequency based criterion to evaluate the directional derivatives applied to multilaminated plate structures, when non-differentiable multiple eigenfrequencies occur during the structural optimization process. The algorithm is applied to a family of C⁰ Lagrangian higher order shear deformation theory discrete models. Angle ply design variables and vectorial distances from the laminate middle surface to the upper surface of each ply are considered as design variables. The efficiency and accuracy of the algorithm developed is discussed with an illustrative case. The analytical single and/or directional derivatives are compared to forward finite difference derivatives for the developed discrete models.     

Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling

A new approach for data-based stochastic parametrization of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is implemented and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the cluster-weighted Markov chain scheme is investigated for long-term simulations as well as ensemble prediction. It clearly outperforms simple parametrization schemes and compares favourably with another recently proposed subgrid modelling scheme also based on conditional Markov chains.     

Adapting derivative free optimization methods to engineering models with discrete variables

In this paper we extend Continuous Derivative Free (CDF) algorithms that solve optimization models with continuous variables to the solution of optimization models with both continuous and discrete variables. The algorithm fits naturally to the solution of discretized models arising from continuous models. Roughly speaking, the finer the discretization, the closer the discretized solution is to its continuous counterpart. The algorithm also finds stationary points of real problems with continuous and discrete variables. Encouraging results are reported on an access point communication problem and on models solved with a Field Programmable Gate Array (FPGA) device, which generally forces a fixed point discretization of the problem.     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题.通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法.算例表明;这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率.     

离散变量结构优化设计的最优综合效能法

针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。     

A Study of Computerized Process Planning with Continuous and Discrete Data Base

This paper discusses methods for the computerized selection of machining variables to increase productivity and optimize economics of machining. An attempt has been made to use the computer for process planning in situations for which the relationships between the machining variables and the performance measures are complex and nonlinear functions with discrete values. An algorithm is presented which deals directly with the problem of a discrete data base. A comparison of continuous and discrete data base methods for process planning was made using the Electro Discharge Machining (EDM) process.     

An integrated simulation-based fuzzy regression-time series algorithm for electricity consumption estimation with non-stationary data

This study presents an integrated fuzzy regression, computer simulation, and time series algorithm to estimate and predict electricity demand for seasonal and monthly changes in electricity consumption especially in developing countries such as China and Iran with non-stationary data. Since, it is difficult to model the uncertain behavior of energy consumption with only conventional fuzzy regression or time series, the integrated algorithm could be an ideal method for such cases. Computer simulation is developed to generate random variables for monthly electricity consumption. The fuzzy regression is run with computer simulation output too. A Granger–Newbold test is used to select the optimum model, which could be a time series, a fuzzy regression (with or without pre-processed data, PD) or a simulation-based fuzzy regression (with or without PD). The preferred time series model is selected from linear or nonlinear models. At last, the preferred model from fuzzy regression and time series models is selected by Granger–Newbold. Monthly electricity consumption in Iran from 1995 to 2005 is considered as the basis of this study. The mean absolute percentage error estimates of a genetic algorithm, an artificial neural network, and a fuzzy inference system versus the proposed algorithm show the appropriateness of the proposed algorithm. This is the first study that introduces an integrated simulation-based fuzzy regression-time series for electricity consumption estimation with an imprecise set of data.     

Four approaches for groundwater development planning

Groundwater system development problems usually involve the placement and the operation of a set of wells. Finding the optimal solution for such problems, when all the corresponding costs are considered is a very difficult task since non-linear models that include discrete variables have to be solved. This is why such problems are often simplified either by ignoring fixed costs or by linearizing the cost functions. In this paper four different approaches are compared: a non-linear programming with polynomial penalty coefficient method; a non-linear programming with exponential penalty coefficient method; a mixed-integer-non-linear programming commercial solver, and a simulated annealing algorithm, in an attempt to solve this kind of problem while keeping a realistic model formulation not requiring simplifications.     

基于梯度优化方法的钢结构标准截面选型优化设计

实际的工程应用中,钢框架的基本构件大多是根据钢结构设计规范要求,从标准型钢库中选取,所组成的框架结构的截面尺寸非连续变化。因此,钢结构截面优化设计是典型的离散设计变量优化问题。若采用基于启发式的算法(如遗传算法等)进行求解,当可选截面类型较多时,其计算量巨大,求解效率低下。该文通过引入高维拉格朗日插值函数对该离散设计问题进行连续化,建立了可采用梯度优化方法进行求解的钢结构标准截面选型设计模型,并且使得连续化以后的设计变量个数大幅度减少。对给定截面类型种数为2n个的可选截面集合,其设计变量只需n个即可。具体算例表明：与基于遗传算法的优化方法相比,该方法的计算效率提高1~2个数量级,并且在结构性能基本相当的情况下,得到的型钢种类更少,便于工程应用。     

A discrete stress–strength interference model based on universal generating function

Continuous stress–strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data.     

An optimization technique using the characteristics of genetic algorithm

Optimization problems could happen often in discrete or discontinuous search space. Therefore, the traditional gradient‐based methods are not able to apply to this kind of problems. The discrete design variables are considered reasonably and the heuristic techniques are generally adopted to solve this problem, and the genetic algorithm based on stochastic search technique is one of these. The genetic algorithm method with discrete variables can be applied to structural optimization problems, such as composite laminated structures or trusses. However, the discrete optimization adopted in genetic algorithm gives rise to a troublesome task that is a mapping between each strings and discrete variables. And also, its solution quality could be restricted in some cases. In this study, a technique using the genetic algorithm characteristics is developed to utilize continuous design variables instead of discrete design variables in discontinuous solution spaces. Additionally, the proposed algorithm, which is manipulating a fitness function artificially, is applied to example problems and its results are compared with the general discrete genetic algorithm. The example problems are to optimize support positions of an unstable structure with discontinuous solution spaces.     

A nested modelling approach to infrastructure performance characterisation

Reliable and accurate predictions of infrastructure condition can save significant amounts of money for infrastructure management agencies through better planned maintenance and rehabilitation activities. Infrastructure deterioration is a complicated, dynamic and stochastic process affected by various factors such as design, environmental conditions, material properties, structural capacities and some unobserved variables. Previous researchers have explored different types of modelling techniques, ranging from simple deterministic models to sophisticated probabilistic models, to characterise the deterioration process of infrastructure systems; however, these models have limitations in various aspects. Traditional deterministic models are inadequate to capture the uncertainties associated with infrastructure deterioration processes. State-based probabilistic models can only predict conditions at fixed time points. Time-based probabilistic models require frequent observations that, in practice, are not easy to perform. The goal of this research is to develop a new probabilistic model that is capable of capturing the stochastic nature of infrastructure deterioration, while at the same time avoiding the limitations of previous modelling efforts. The proposed nested model is based on discrete choice model theory. It can be used to predict the probability of an infrastructure system staying at defined condition states by relating an index representing the performance of the infrastructure to a number of explanatory variables that characterise the structural adequacy, traffic loading and environmental conditions of the infrastructure. The proposed model includes different possible implementation paths (sequential versus multinomial) depending on the considered explanatory variables and the available data. In the case study, the proposed probabilistic model is implemented with pavement performance data collected in Texas, yielding promising preliminary results.     

Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System

In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization variables are categorical if the objective function or the constraints can not be evaluated unless the variables take one of a prescribed enumerable set of values. The key issue is that categorical variables can not be treated as ordinary discrete variables are treated by relaxing them to continuous variables with a side constraint that they be discrete at the solution.A new mixed variable programming (MVP) algorithm makes it possible to optimize directly with respect to mixtures of discrete, continuous, and categorical decision variables. The result of applying MVP is shown here to give a 65% reduction in the objective function over the previously published result for a thermal insulation model from the engineering literature. This reduction is largely because MVP optimizes simultaneously with respect to the number of heat intercepts and the choices from a list of insulator types as well as intercept locations and temperatures. The main purpose of this paper is to show that the mixed variable optimization algorithm can be applied effectively to a broad class of optimization problems in engineering that could not be easily solved with earlier methods.     

An exact penalty function method for optimising QAP formulation in facility layout problem

A quadratic assignment problem (QAP), which is a combinatorial optimisation problem, is developed to model the problem of locating facilities with material flows between them. The aim of solving the QAP formulation for a facility layout problem (FLP) is to increase a system’s operating efficiency by reducing material handling costs, which can be measured by interdepartmental distances and flows. The QAP-formulated FLP can be viewed as a discrete optimisation problem, where the quadratic objective function is optimised with respect to discrete decision variables subject to linear equality constraints. The conventional approach for solving this discrete optimisation problem is to use the linearisation of the quadratic objective function whereby additional discrete variables and constraints are introduced. The adoption of the linearisation process can result in a significantly increased number of variables and constraints; solving the resulting problem can therefore be challenging. In this paper, a new approach is introduced to solve this discrete optimisation problem. First, the discrete optimisation problem is transformed into an equivalent nonlinear optimisation problem involving only continuous decision variables by introducing quadratic inequality constraints. The number of variables, however, remains the same as the original problem. Then, an exact penalty function method is applied to convert this transformed continuous optimisation problem into an unconstrained continuous optimisation problem. An improved backtracking search algorithm is then developed to solve the unconstrained optimisation problem. Numerical computation results demonstrate the effectiveness of the proposed new approach.     

遗传算法在桁架结构优化设计中的应用

本文提出桁架结构系统优化设计的新方法—遗传算法。它与常规化算法的不同之处在于从多个初始点开始寻优，并采用交迭和变异算子避免过早地收敛到局部最优解，可获得全局最优解，且不受初始值影响。该算法不必求导计算，编程简单、快捷，尤其适用于具有离散变量的结构优化设计问题。     

具有协变量的高斯图模型的结构学习

图模型是一种研究变量之间相依关系的重要工具．除了节点变量外,数据常常包括协变量而且可能影响网络结构．然而现有关于图模型的工作大多仅考虑节点变量．本文基于图模型研究具有协变量的网络结构特征学习问题,在稀疏正则化的框架下,通过假设变量之间的条件独立为线性关系,建立具有协变量信息的稀疏高斯图模型,估计网络结构特征．所得结果具有实际解释性且易于求解,我们利用坐标下降法求解模型,通过实验说明含协变量比无协变量的效果更好,从而说明本文模型的高效性和实用性．     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

A sequential approximation method using neural networks for engineering design optimization problems

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often ‘pass–fail’, ‘0–1’ type binary constraints. This paper presents a sequential approximation method specifically for engineering optimization problems with the three characteristics. In this method a back-propagation neural network is trained to simulate a rough map of the feasible domain formed by the constraints using a few representative training data. A training data point consists of a discrete design point and whether this design point is feasible or infeasible. Function values of the constraints are not required. A search algorithm then searches for the optimal point in the feasible domain simulated by the neural network. This new design point is checked against the true constraints to see whether it is feasible, and is then added to the training set. The neural network is trained again with this added information, in the hope that the network will better simulate the boundary of the feasible domain of the true optimization problem. Then a further search is made for the optimal point in this new approximated feasible domain. This process continues in an iterative manner until the approximate model locates the same optimal point in consecutive iterations. A restart strategy is also employed so that the method may have a better chance to reach a global optimum. Design examples with large discrete design spaces and implicit constraints are solved to demonstrate the practicality of this method.     

An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.     

An alternating optimization approach for mixed discrete non-linear programming

This article contributes to the development of the field of alternating optimization (AO) and general mixed discrete non-linear programming (MDNLP) by introducing a new decomposition algorithm (AO-MDNLP) based on the augmented Lagrangian multipliers method. In the proposed algorithm, an iterative solution strategy is proposed by transforming the constrained MDNLP problem into two unconstrained components or units; one solving for the discrete variables, and another for the continuous ones. Each unit focuses on minimizing a different set of variables while the other type is frozen. During optimizing each unit, the penalty parameters and multipliers are consecutively updated until the solution moves towards the feasible region. The two units take turns in evolving independently for a small number of cycles. The validity, robustness and effectiveness of the proposed algorithm are exemplified through some well known benchmark mixed discrete optimization problems.