An equivalent linear method for structural system reliability with nonlinear safety margins

In Ref. [1 (Comput. Struct.42, 255–262, 1992)], the authors presented the numerical integration method in M space for computing structural system reliability with linear safety margins of the structural system failure modes. It has two advantages over the integration method in the space constructed by the basic variables of the structural system in that: (1) the integral domain is very simple and the integral grid can easily be generated; (2) the computer run time is short. In this paper, an equivalent linear method of the nonlinear safety margins is presented and the integration method in M space is employed in solving the equivalent linear system. Furthermore, for decreasing the computer run time or increasing the computational accuracy, the Gaussian numerical integration method is used for computing the two- and three-order joint failure probabilities of structural failure modes. Several examples illustrate the effectiveness of the method.     

Applications of linear programming in structural layout and optimization

Various computer methods have been developed for the optimal design of indeterminate structures, but it is not possible to guarantee that the result of any method will be a global optimum, rather than merely a local optimum. By temporarily neglecting the conditions of elastic compatibility and formulating a mathematical optimization problem based on the equilibrium conditions and the stress constraints, it is possible to obtain an approximate design which avoids merely local optima. In the cases examined, this design is close to the exact global optimum obtained by enforcing the compatibility conditions and is therefore a good starting point for an optimizing procedure. Examples include a graphical solution of a simple grillage known to have multiple local optima, and a sequence of planar trusses under alternate loading conditions. Linear programming is used to find the minimum weight truss designs satisfying equilibrium; this method eliminates extraneous members and leads to better indeterminate truss configurations than does a stress-ratio type algorithm.     

Application of fuzzy multi-objective linear programming to aggregate production planning

This study develops a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-product aggregate production planning (APP) decision problem in a fuzzy environment. The proposed model attempts to minimize total production costs, carrying and backordering costs and rates of changes in labor levels considering inventory level, labor levels, capacity, warehouse space and the time value of money. A numerical example demonstrates the feasibility of applying the proposed model to APP problem. Its advantages are also discussed. The proposed model yields a compromise solution and the decision maker's overall levels of satisfaction. In particular, in contrast to other APP models, several significant characteristics of the proposed model are presented.     

遗传算法在系统可靠性优化中的应用

研究性等价、体积和重量约束条件下，多级串联系统和桥式网络系统可靠性优化问题.使用遗传算法对该问题进行求解，利用基于排名的选择方法和最优保存策略，改善了遗传算法的收敛性能。计算机仿真实验结果表明，用遗传算法求解该问题是有效的。     

Application of fuzzy goal programming approach to multi-objective linear fractional inventory model

In this paper, we propose a model and solution approach for a multi-item inventory problem without shortages. The proposed model is formulated as a fractional multi-objective optimisation problem along with three constraints: budget constraint, space constraint and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision-making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. A numerical example is given to illustrate the proposed model.     

Robust controller design by linear programming with application to a double-axis positioning system

A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A lower bound on the crossover frequency and a new linear stability margin which guarantees lower bounds for the classical robustness margins are defined. Two optimization problems are proposed and solved by linear programming. In the first one the robustness margin is maximized for a given lower bound on the crossover frequency, whereas in the second one the closed-loop performance in terms of the load disturbance rejection is optimized with constraints on the new stability margin. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach.     

Bicriterion linear programming

Basically leaning on the concept of “best” compromise, the technique seeks the optimal solution by fair relaxations of the objectives commensurate with their degrees of importance until the optimum feasible compromise is reached. The concept is made operational by deriving a linear constraint (referred to as the compromise constraint) to be added into the original set. An offspring of both objective functions, the compromise constraint cuts the original feasible region and forces both objectives to settle on a common point along this added restriction. The resulting singular equivalent of the bicriterion problem optimizes any one of the two objective functions and their equivalent sum (referred to as the supergoal) subject to the new set of constraints. Post optimality analysis is employed to minimize the computational effort usually done by a computer. A very attractive feature of this new practical technique is its ability to search for the optimum in any point in the feasible region, even other than the vertices of the convex set.     

Rule-based intelligence to support linear programming analysis

Increased size and complexity of linear programs make it difficult to understand results and manage the model. This difficulty is overcome, at least partially, with new advances in computing environments and techniques from artificial intelligence and operations research. A software system, called ANALYZE, is presented within the larger context of developing an artificially intelligent environment for mathematical programming modeling and analysis. With heuristics governed by rule-based reasoning and with syntax-driven translations into English, the ANALYZE system enables a form of intelligence to support analysis. Particular problems that illustrate this capability are explanations of dual prices, diagnoses of infeasibilities, and reasoning about redundancy.     

A sequential linear programming approach to solve mixed integer programming problems

The optimal operation of pumps in a large water supply system under time-of-use electricity rates is formulated as a mixed integer programming (MIP) problem. The problem is solved using an iterative linear programming (LP) scheme. The scheme is applied to an actual world problem, the City of Inglewood Water Supply System. Computational results are presented and termination criteria for the solution scheme are discussed.     

Sequential quadratic programming and the ASTROS structural optimization system

The NLPQL sequential quadratic programming algorithm of Schittkowski is integrated with the Automated Structural Optimization System (ASTROS) and tested on three largescale optimization problems, including one with constraints from multiple disciplines. Furthermore, the traditional solution approach, which involves the formulation and solution of an explicitly defined approximate problem during each iteration, is replaced by a simpler approach, in which the approximate problem is eliminated, and each finite element analysis is followed by one iteration of the optimizer. To compensate for the cost of additional analyses, a much more restrictive active set strategy is used. Although not much computational efficiency is gained, the alternative approach gives accurate solutions. The largest test problem, which had 1527 design variables and 6124 constraints was solved with ASTROS for the first time using a direct method. The resulting design represents the lowest weight feasible design recorded to date.Research done while a graduate student at the Air Force Institute of Technology, Dayton, Ohio. The views expressed in this article are those of the authors, and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government     

Multi-media instructional approach to teaching linear programming

This paper describes different strategies employed in converting a lecture-oriented mathematical programming course to a Personalized Self-Paced Instructional (PSI) format. This is an elective course for students in science, engineering and management. A multi media instructional approach is used in the PSI system which combines traditional lectures, self-paced and individualized learning assisted by interactive computer programs and video taped instructional materials. This unique PSI system for mathematical programming provides maximum learning opportunity and flexibility to students. The author's experiences with the PSI system and the students' evaluation of the self-paced system are also discussed.     

Introduction: New approaches to linear programming

This issue ofAlgorithmica present papers on various aspects of nonlinear methods for solving linear programming problems, inspired by the work of Karmarkar. This introduction describes some of these aspects and briefly mentions other recent developments in the field. A bibliography of recent articles is included.     

Introduction: New approaches to linear programming

This issue ofAlgorithmica present papers on various aspects of nonlinear methods for solving linear programming problems, inspired by the work of Karmarkar. This introduction describes some of these aspects and briefly mentions other recent developments in the field. A bibliography of recent articles is included.     

Application of dynamic programming to control khuzestan water resources system

An approximate optimization technique based on discrete dynamic programming called discrete differential dynamic programming (DDDP), is employed to obtain the near optimal operation policies of a water resources system in the Khuzestan Province of Iran. The technique makes use of an initial nominal state trajectory for each state variable, and forms corridors around the trajectories. These corridors represent a set of subdomains of the entire feasible domain. Starting with such a set of nominal state trajectories, improvements in objective function are sought within the corridors formed around them. This leads to a set of new nominal trajectories upon which more improvements may be sought. Since optimization is confined to a set of subdomains, considerable savings in memory and computer time are achieved over that of conventional dynamic programming. The Kuzestan water resources system considered in this study is located in southwest Iran, and consists of two rivers, three reservoirs, three hydropower plants, and three irrigable areas. Data and cost benefit functions for the analysis were obtained either from the historical records or from similar studies.     

Computational efficiency of improved move limit method of sequential linear programming for structural optimization

The imporved move limit method of sequential linear programming is briefly explained. Comparison of computing efficiencies is made between the improved method and the conventional move limit method with six test problems. The usefulness of the method in the context of structural optimization is shown with the help of four examples.     

Application of linear programming to the optimal plastic design of circular plates subject to technological constraints

This paper is concerned with plastic minimum-volume design of circular or annular plates under axially symmetric loading. Accordingly, all characteristics of the plate depend only on the radial coordinate r. The plate is divided into rings of constant yield moment. Other technological constraints may be added, for instance bounds on the yield moments of the rings. Linear programming is used to obtain an approximate solution of the problem, and the optimality criteria are derived from the duality relations. The method is illustrated by examples which show that it is quite accurate.     

Interactive multiple objective linear programming system implemented on a microcomputer

Linear programming is one of the most widely used Operations Research/Management Science techniques. Recently, multiple objective decision making has been well established as a practical approach to seek a satisfactory solution to a decision making problem. Much attention has been focused on a microcomputer as an economical management tool.

In this paper we propose an interactive goal attainment method using the eigenvector algorithm for solving a multiple objective linear programming problem interactively on microcomputers. In the software package Micro-LPS based on the method proposed, we design a conversational and user-friendly system in which the user commands are involved.     

Application of radial basis functions to linear and nonlinear structural analysis problems

The basic characteristic of the techniques generally known as meshless methods is the attempt to reduce or even to eliminate the need for a discretization (at least, not in the way normally associated with traditional finite element techniques) in the context of numerical solutions for boundary and/or initial value problems.The interest in meshless methods is relatively new and this is why, despite the existence of various applications of meshless techniques to several problems of mechanics (as well as to other fields), these techniques are still relatively unknown to engineers. Furthermore, and compared to traditional finite elements, it may be difficult to understand the physical meaning of the variables involved in the formulations.As an attempt to clarify some aspects of the meshless techniques, and simultaneously to highlight the ease of use and the ease of implementation of the algorithms, applications are made, in this work, to structural analysis problems.The technique used here consists of the definition of a global approximation for a given variable of interest (in this case, components of the displacement field) by means of a superposition of a set of conveniently placed (in the domain and on the boundary) radial basis functions (RBFs).In this work various types of one-dimensional problems are analyzed, ranging from the static linear elastic case, free vibration and linear stability analysis (for a beam on elastic foundation), to physically nonlinear (damage models) problems. To further complement the range of problems analysed, the static analysis of a plate on elastic foundation was also addressed. Several error measures are used to numerically establish the performance of both symmetric and nonsymmetric approaches for several global RBFs. The results obtained show that RBF collocation leads to good approximations and very high convergence rates.