Optimal design of a truss configuration under multiloading conditions

The paper deals with the optimum structural design of a truss for which coordinates of structural nodes as well as member sizes constitute a set of design variables. The truss may be loaded by as many loading conditions as needed and is subjected to constraints imposed on stress displacements and complementary energy. An important relation between the cost function, Lagrange multipliers and limit values of constraints is derived. The paper presents the outline of an algorithm for the solution of a system of equations and inequality arising from the Kuhn-Tucker necessary condition for an optimum problem. Five numerical examples of 2D trusses are presented.Presented at the International Conference Structural Optimization '93, Rio de Janeiro, August 2–4, 1993.     

Optimization of geometry in truss design

In this paper a method is presented which attempts to minimize the weight of a 3-dimensional truss structure subject to displacement-, stress- and buckling constraints under multiple load conditions. Both the cross section areas of the bars and the geometry (but not the topology) of the structure are permitted to vary during the optimization.The method generates a sequence of subproblems which are solved by a dual method of convex programming. The convergence of the overall algorithm is in evidence on some test problems.     

Optimization methods for truss geometry and topology design

Truss topology design for minimum external work (compliance) can be expressed in a number of equivalent potential or complementary energy problem formulations in terms of member forces, displacements and bar areas. Using duality principles and non-smooth analysis we show how displacements only as well as stresses only formulations can be obtained and discuss the implications these formulations have for the construction and implementation of efficient algorithms for large-scale truss topology design. The analysis covers min-max and weighted average multiple load designs with external as well as self-weight loads and extends to the topology design of reinforcement and the topology design of variable thickness sheets and sandwich plates. On the basis of topology design as an inner problem in a hierarchical procedure, the combined geometry and topology design of truss structures is also considered. Numerical results and illustrative examples are presented.     

Automated design of truss and frame geometry

It is shown that the optimization of truss and frame structures where layout geometry variables are included as design variables is inherently poorly scaled and that a two-step procedure can be used to overcome this problem. Using a standard optimization package this procedure is used to find the optimal geometry and sizing of a two-dimensional and a three-dimensional frame structure.     

On simultaneous optimization of truss geometry and topology

The paper addresses the classical problem of optimal truss design where cross-sectional areas and the positions of joints are simultaneously optimized. Se-veral approaches are discussed from a general point of view. In particular, we focus on the difference between simultaneous and alternating optimization of geometry and topology. We recall a rigorously mathematical approach based on the implicit programming technique which considers the classical single load minimum compliance problem subject to a volume constraint. This approach is refined leading to three new problem formulations which can be treated by methods of Mathematical Programming. In particular, these formulations cover the effect of melting end nodes, i.e., vanishing potential bars due to changes in the geometry. In one of these new problem formulations, the objective function is a polynomial of degree three and the constraints are bilinear or just sign constraints. Because heuristics is avoided, certain optimality properties can be proven for resulting structures. The paper closes with two numerical test examples.     

A new mixed convex approximation method with applications for truss configuration optimization

A mixed approximation method called DQA-GMMA is presented in this paper. This approximation uses the combination of Diagonal Quadratic Approximation (DQA) and the Generalized Method of the Moving Asymptotes (GMMA). It has the flexibility to deal with both monotonic and non-monotonic design functions. The convexity and the separable form of this approximation ensures the efficient solution of constructed optimization problem by dual approach. Truss geometry and configuration problems are solved by this method.     

Optimal randomized parallel algorithms for computational geometry

We present parallel algorithms for some fundamental problems in computational geometry which have a running time ofO(logn) usingn processors, with very high probability (approaching 1 asn → ∞). These include planar-point location, triangulation, and trapezoidal decomposition. We also present optimal algorithms for three-dimensional maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on a CREW PRAM model and have optimal processor-time product which improve on the previously best-known algorithms of Atallah and Goodrich [5] for these problems. The crux of these algorithms is a useful data structure which emulates the plane-sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [26] and Reif and Valiant [25] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach.     

Optimal randomized parallel algorithms for computational geometry

We present parallel algorithms for some fundamental problems in computational geometry which have a running time ofO(logn) usingn processors, with very high probability (approaching 1 asn ). These include planar-point location, triangulation, and trapezoidal decomposition. We also present optimal algorithms for three-dimensional maxima and two-set dominance counting by an application of integer sorting. Most of these algorithms run on a CREW PRAM model and have optimal processor-time product which improve on the previously best-known algorithms of Atallah and Goodrich [5] for these problems. The crux of these algorithms is a useful data structure which emulates the plane-sweeping paradigm used for sequential algorithms. We extend some of the techniques used by Reischuk [26] and Reif and Valiant [25] for flashsort algorithm to perform divide and conquer in a plane very efficiently leading to the improved performance by our approach.This is a substantially revised version of the paper that appeared as Optimal Randomized Parallel Algorithms for Computational Geometry in theProceedings of the 16th International Conference on Parallel Processing, St. Charles, Illinois, August 1987.This research was supported by DARPA/ARO Contract DAAL03-88-K-0195, Air Force Contract AFOSR-87-0386, DARPA/ISTO Contracts N00014-88-K-0458 and N00014-91-J-1985, and by NASA Subcontract 550-63 of Primecontract NAS5-30428.     

Growth method for size,topology, and geometry optimization of truss structures

The problem of optimally designing the topology of plane trusses has, in most cases, been dealt with as a size problem in which members are eliminated when their size tends to zero. This article presents a novel growth method for the optimal design in a sequential manner of size, geometry, and topology of plane trusses without the need of a ground structure. The method has been applied to single load case problems with stress and size constraints. It works sequentially by adding new joints and members optimally, requiring five basic steps: (1) domain specification, (2) topology and size optimization, (3) geometry optimization, (4) optimality verification, and (5) topology growth. To demonstrate the proposed growth method, three examples were carried out: Michell cantilever, Messerschmidt–Bölkow–Blohm beam, and Michell cantilever with fixed circular boundary. The results obtained with the proposed growth method agree perfectly with the analytical solutions. A Windows XP program, which demonstrates the method, can be downloaded from http://www.upct.es/~deyc/software/tto/.     

Optimal configuration of Energy-Efficient Ethernet

The IEEE 802.3az standard provides a new low power mode that Ethernet network interfaces can use to save energy when there is no traffic to transmit. Simultaneously with the final standard approval, several algorithms were proposed to govern the physical interface state transition between the normal active mode and the new low power mode. In fact, the standard leaves this sleeping algorithm unspecified to spur competition among different vendors and achieve the greatest energy savings. In this paper, we try to bring some light to the most well known sleeping algorithms, providing mathematical models for the expected energy savings and the average packet delay inflicted on outgoing traffic. We will then use the models to derive optimum configuration parameters for them under given efficiency constraints.     

Optimal design of truss structures using parallel computing

Parallel design optimization of large structural systems calls for a multilevel approach to the optimization problem. The general optimization problem is decomposed into a number of non-interacting suboptimization problems on the first level. They are controlled from the second level through coordination variables. Thus, the solutions of the independent first-level subsystems are directed towards the overall system optimum. In the present paper, optimal design of truss structures using parallel computing technique is described. In this method, optimization of a large truss structure has been carried out by decomposing the structure into sub-domains and suboptimization tasks. Each sub-domain has independent design variables and a small number of behaviour constraints. The two-level sub-domain optimum design approach is summarized by several numerical examples with speedups and efficiencies of algorithms on message passing systems. It has been noticed that the efficiency of the algorithm for design optimization increases with the size of the structure.     

Optimal design of truss structures using ant algorithm

An ant algorithm, consisting of the Ant System and API (after “apicalis” in Pachycondyla apicalis) algorithms, was proposed in this study to find optimal truss structures to achieve minimum weight objective under stress, deflection, and kinematic stability constraints. A two-stage approach was adopted in this study; first, the topology of the truss structure was optimized from a given ground structure employing the Ant System algorithm due to its discrete characteristic, and then the size and/or shape of member was optimized utilizing the API algorithm. The effectiveness of the proposed ant algorithm was evaluated through numerous different 2-D and 3-D truss-structure problems. The proposed algorithm was observed to find truss structures better than those reported in the literature. Moreover, multiple different truss topologies with almost equal overall weights can be found simultaneously.     

Optimal configuration of a multicore server processor for managing the power and performance tradeoff

We consider the problem of power and performance management for a multicore server processor in a cloud computing environment by optimal server configuration for a specific application environment. The motivation of the study is that such optimal virtual server configuration is important for dynamic resource provision in a cloud computing environment to optimize the power and performance tradeoff for certain specific type of applications. Our strategy is to treat a multicore server processor as an M/M/m queueing system with multiple servers. The system performance measures are the average task response time and the average power consumption. Two core speed and power consumption models are considered, namely, the idle-speed model and the constant-speed model. Our investigation includes justification of centralized management of computing resources, server speed constrained optimization, power constrained performance optimization, and performance constrained power optimization. Our main results are (1) cores should be managed in a centralized way to provide the highest performance without consumption of more energy in cloud computing; (2) for a given server speed constraint, fewer high-speed cores perform better than more low-speed cores; furthermore, there is an optimal selection of server size and core speed which can be obtained analytically, such that a multicore server processor consumes the minimum power; (3) for a given power consumption constraint, there is an optimal selection of server size and core speed which can be obtained numerically, such that the best performance can be achieved, i.e., the average task response time is minimized; (4) for a given task response time constraint, there is an optimal selection of server size and core speed which can be obtained numerically, such that minimum power consumption can be achieved while the given performance guarantee is maintained.     

圆形平面麦克风阵列构型的优化设计方法

提出利用遗传算法来优化设计圆形麦克风阵列构型。构造了兼顾主瓣宽度和最大旁瓣增益的目标函数,使得两者之间有着较好折中。考虑到实用性,将圆形面板划分为1 cm×1 cm的方格,坐标只能在方格中心取值,确保优化阵列构型是可实现的。设计了选择、交叉和变异等操作的解决方案,保证整个算法可行。仿真结果表明:优化算法可以得到合适的阵列构型,相对于规则型阵列,这种优化阵列构型在主瓣宽度和最大旁瓣增益控制方面有着明显优势。     

Optimal multiway search trees for variable size keys

Summary This paper considers the construction of optimal search trees for a sequence of n keys of varying sizes, under various cost measures. Constructing optimal search cost multiway trees is NP-hard, although it can be done in pseudo-polynomial time O ³ and space O ², where L is the page size limit. An optimal space multiway search tree is obtained in O ³ time and O ² space, while an optimal height tree in O(n ² log² n) time and O(n) space both having additionally minimal root sizes. The monotonicity principle does not hold for the above cases. Finding optimal search cost weak B-trees is NP-hard, but a weak B-tree of height 2 and minimal root size can be constructed in O(n log n) time. In addition, if its root is restricted to contain M keys then a different algorithm is applied, having time complexity O(nM log n). The latter solves a problem posed by McCreight.     

Optimal design of truss structures using weighted superposition attraction algorithm

Engineering with Computers - In this paper, a recently developed swarm based metaheuristic algorithm called weighted superposition attraction (WSA) is implemented for sizing optimization of truss...     

Optimal discrete sizing of truss structures subject to buckling constraints

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with conservative regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.     

General response formula for two-dimensional linear systems with variable coefficients

A new definition of the transition matrix for a general 2-D system model with variable coefficients is presented. The general response formula for the general 2-D system model with variable coefficients is derived. Solution to the first and the second Fornasini-Marchesini models with variable coefficients are also given.