Application of sequential quadratic programming based on active set method in cleaner production

Clean Technologies and Environmental Policy - On the platform of general chemical process simulation software (it was named Optimization Engineer, OPEN), a general optimization algorithm for...     

A new hybrid method for optimal circuit design using semi-definite programming

In this article a new method for yield optimization (design centring) is introduced. The method has a statistical-geometrical nature, hence it is called hybrid. The method exploits the semi-definite programming applications in approximating the feasible region with two bounding ellipsoids. These ellipsoids are obtained using a two phase algorithm. In the first phase, the minimum volume ellipsoid enclosing the feasible region is obtained. The largest ellipsoid that can be inscribed inside the feasible region is obtained in the second phase. The centres of these bounding ellipsoids are used as design centres. In the second phase, an additional polytopic region approximation is constructed. A comparison between the obtained region approximations is given. Saving in the number of circuit simulations needed for yield optimization is also considered. Practical examples are given to show the effectiveness of the new method.     

Moving asymptotes and active set strategy for constrained optimization design in magnetostatic problems

In this paper, we present an improvement of the optimization technique of the moving asymptotes applied to a class of magnetostatic design problem. Our approach includes, among other aspects, an active set strategy which turns possible to find feasible points during the iterative process. We present some numerical results obtained on real-life case studies where the functions are computed by a complex finite-element routine.     

A general strategy for the optimal design of composite laminates by the polar-genetic method

The object of the present work is the development and application of a totally general approach to optimal design of composite laminates where all the required properties for the laminate are explicitly expressed as criteria of the optimisation process. Our formulation is in the form of a highly non-linear and non-convex single- or multi-objective optimisation problem subject to equality and inequality constraints. We show here applications to the design of maximum stiffness, maximum buckling load, maximum eigenfrequencies, maximum strength as well as combinations of the afore mentioned criteria; all types of elastic symmetries can also be taken into account. In order to keep the same greatest generality in solving our optimisation problem, we developed an evolved version of the genetic algorithm BIANCA for the design of composite laminates. We show here a number of numerical solutions found using BIANCA.     

A steepest edge active set algorithm for solving sparse linear programming problems

A steepest edge active set algorithm is described which is suitable for solving linear programming problems where the constraint matrix is sparse and has more rows than columns. The algorithm uses a steepest edge criterion for selecting the search direction at each iteration and recurrence relations are derived which enable it to execute efficiently. The canonical form for the active set method is convenient for many applications and may be exploited to devise a simple crash procedure which is employed prior to phase one. A complete two-phase algorithm which incorporates the crash procedure is outlined. Only one artificial variable is needed to determine if the linear programming problem has a feasible solution in phase one. Some computational results are given to illustrate the effectiveness of the algorithm for a range of sparse linear programming problems. Comparisons between the steepest edge criterion and the traditional Dantzig criterion suggest that the former usually requires fewer iterations and often leads to substantial savings for large problems.     

Robust design with dynamic characteristics using stochastic sequential quadratic programming

Robust design with dynamic characteristics is an important off-line quality engineering technique for improving product quality over a range of input conditions by reducing variations caused by uncontrolled factors. Since several studies have indicated that there are important limitations to Taguchi's S/N ratio analysis, the solution procedure for dynamic systems deserves further investigation. This paper proposes a stochastic optimization modeling procedure to overcome the difficulty in Taguchi's method to accommodate dynamic characteristics. The main idea underlying the proposed method is to minimize the total variations on quality characteristics while attaining the target performance over a range of input conditions. Due to the nonlinear nature of the stochastic optimization model, two stochastic versions of sequential quadratic programming respectively embedded with a Monte Carlo simulation and numerical approximations are devised to solve the problem. In the robust design of a temperature control circuit often discussed in dynamic problems, the proposed method performs efficiently and effectively. Compared with the Taguchi method, the design solved in this paper has smaller variations, indicating that the proposed method is a promising technique for dynamic-characteristic robust design.     

Parametric quadratic programming method for elastic contact fracture analysis

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the parametric variational principle and FEM, a linear complementary method is extended to analyze contact fracture mechanics. The near-tip fields are properly modeled in the analysis using special crack tip elements with quarter-point nodes. Stress intensity factor solutions are presented for some frictional contact fracture problems and are compared with known results where available.     

A numerical method for the optimal blank shape design

This paper describes a numerical procedure for the blank shape design of thin metallic parts obtained by stamping. The objective is to determine the initial blank shape knowing the geometry of the desired 3D CAD part. The numerical procedure consists of two stages: At first, an estimation of the initial blank shape is given using the one step inverse approach (IA). Then, update of the blank shape is continued by iterations combining optimization algorithms and finite element analysis (FEA). The numerical procedure for the blank shape design is tested in the case of an industrial stamping process where the part is formed using a manual press without blank-holder. The proposed numerical procedure can provide very quickly the optimal blank shape in a few iterations.     

A finite element method for elasto-plastic structures and contact problems by parametric quadratic programming

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto-plastic structures is constructed. A series of PQP formulae for contact problems and elastic-plastic structures is derived in the text, and some numerical examples are illustrated as well.     

The quadratic programming approach to the finite element method

A finite element approximation technique is described in which the potential energy function is minimized subject to liner constraints. The constraints require satisfaction of all kinematic boundary conditions and interelement continuity conditions. An example, indicating the efficiency of the proposed method, is presented.     

Dynamic programming approach to optimal feedback-feed-forward controller design

Summary A new derivation of the parametric expansion of the dynamic programming algorithm for optimal feedback-feed-forward controller design is presented. Matrix methods are employed to give clarity to the results first offered by Merriam. The advantages of the optimal design technique for multivariable problems are readily apparent. A unique technique is given for easily solving the design equations for the case of time invariant systems with gaussian load disturbance.     

A reduced SAND method for optimal design of non-linear structures

An SQP-based reduced Hessian method for simultaneous analysis and design (SAND) of non-linearly behaving structures is presented and compared with conventional nested analysis and design (NAND) methods. It is shown that it is possible to decompose the SAND formulation to take advantage of the particular structure of the problem at hand. The resulting reduced SAND method is of the same size as the conventional NAND method but it is computationally more efficient. The presentation here builds on previous research on SAND methods generalizing the solution approach to cases with both equality and inequality constraints. The new version of the reduced SAND method is tested in the context of weight minimization of 3-D truss structures with geometrically non-linear behaviour. © 1997 John Wiley & Sons, Ltd.     

Tabu search method with random moves for globally optimal design

Optimum engineering design problems are usually formulated as non-convex optimization problems of continuous variables. Because of the absence of convexity structure, they can have multiple minima, and global optimization becomes difficult. Traditional methods of optimization, such as penalty methods, can often be trapped at a local optimum. The tabu search method with random moves to solve approximately these problems is introduced. Its reliability and efficiency are examined with the help of standard test functions. By the analysis of the implementations, it is seen that this method is easy to use, and no derivative information is necessary. It outperforms the random search method and composite genetic algorithm. In particular, it is applied to minimum weight design examples of a three-bar truss, coil springs, a Z-section and a channel section. For the channel section, the optimal design using the tabu search method with random moves saved 26.14 per cent over the weight of the SUMT method.     

A quadratic programming approach to image labelling

Image labelling tasks are usually formulated within the framework of discrete Markov random fields where the optimal labels are recovered by extremising a discrete energy function. The authors present an alternative continuous relaxation approach to image labelling, which makes use of a quadratic cost function over the class labels. The cost function to be minimised is convex and its discrete version is equivalent up to a constant additive factor to the target function used in discrete MRF approaches. Moreover, its corresponding Hessian matrix is given by the graph Laplacian of the adjacency matrix. Therefore the optimisation of the cost function is governed by the pairwise interactions between pixels in the local neighbourhood. This leads to a sparse Hessian matrix for which the global minimum of the continuous relaxation problem can be efficiently found by solving a system of linear equations using the Cholesky factorisation. The authors elaborate on the links between the method and other techniques elsewhere in the literature and provide results on synthetic and real-world imagery. The authors also provide a comparison with competing approaches.     

QPSchur: A dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming

We describe an active-set, dual-feasible Schur-complement method for quadratic programming (QP) with positive definite Hessians. The formulation of the QP being solved is general and flexible, and is appropriate for many different application areas. Moreover, the specialized structure of the QP is abstracted away behind a fixed KKT matrix called K_o and other problem matrices, which naturally leads to an object-oriented software implementation. Updates to the working set of active inequality constraints are facilitated using a dense Schur complement, which we expect to remain small. Here, the dual Schur complement method requires the projected Hessian to be positive definite for every working set considered by the algorithm. Therefore, this method is not appropriate for all QPs. While the Schur complement approach to linear algebra is very flexible with respect to allowing exploitation of problem structure, it is not as numerically stable as approaches using a QR factorization. However, we show that the use of fixed-precision iterative refinement helps to dramatically improve the numerical stability of this Schur complement algorithm. The use of the object-oriented QP solver implementation is demonstrated on two different application areas with specializations in each area; large-scale model predictive control (MPC) and reduced-space successive quadratic programming (with several different representations for the reduced Hessian). These results demonstrate that the QP solver can exploit application-specific structure in a computationally efficient and fairly robust manner as compared to other QP solver implementations.     

A method of vehicle active suspension design

This paper contributes to the design of active suspension systems, by the use of spatial vehicle model, without filtered feedback of the control system. A method of “stochastic parameters optimisation” has been utilized for the optimisation of the parameters of active suspension. The optimisation objective was simultaneous minimization of sprung mass vibration and standard deviation of forces in tire-to-ground contact area and vehicle handling.     

A method for optimal design of steel fiber reinforced concrete composition

Existing design approaches for steel fiber reinforced concrete composition practically do not consider the interaction between the concrete components. It decreases the design efficiency and accuracy. The paper deals with methodology for design of optimal steel fibered fine-grained concrete composition based on stiff mixtures. Such concrete is used for production of thin walled precise elements. The current investigation enables to find the influence of the main factors (water–cement ratio, fiber content, fineness and quantity of sand) on the concrete mixture stiffness, compressive and flexural strength of concrete. The study has also enabled to obtain corresponding mathematical models of concrete properties. Based on the models a methodology for design of steel fibered concrete was developed and appropriate nomograms were prepared. The proposed methodology allows obtaining of optimal steel fibered fine-grained concrete composition, taking into account the required flexural strength of concrete, sand fineness and concrete mixture workability.     

A computational method for optimal structural design II: Continuous problems

A method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary-value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.     

基于GA优化控制规则的汽车主动悬架模糊PID控制

主动悬架是未来汽车悬架的主要发展方向,它能够根据车身的振动情况主动调整悬架控制力,使悬架处于最优减振状态,关键问题是如何设计控制规则,从而施加最优控制力,达到进一步改善汽车行驶平顺性的目的。针对该问题,以车身垂直振动加速度为控制目标,将遗传算法与模糊PID控制策略相融合,优化了模糊PID控制器的控制规则,采用基于GA优化后的模糊PID控制方法对汽车主动悬架进行控制并建立了Matlab文本与Simulink相结合的联合仿真模型。仿真结果表明,经GA优化后的模糊PID控制下的主动悬架能够很好的减小车身垂直振动加速度,可以进一步提高乘坐舒适性。     

球约束凸二次规划的一个算法

针对球约束凸二次规划问题，利用Lagrange对偶将其转化为无约束优化问题，然后运用单纯形法对其求解，获得原问题的最优解。最后，对文中给出的算法给出了论证。