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.     

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

In this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.     

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.     

A lower-bound formulation for the geometry and topology optimization of truss structures under multiple loading

In this contribution, we propose an effective formulation to address the stress-based minimum volume problem of truss structures. Starting from the lower-bound formulation in topology optimization, the problem is further expanded to geometry optimization and multiple loading scenarios, and systematically reformulated to alleviate numerical difficulties related to the melting node effect and stress singularities. The subsequent simultaneous analysis and design (SAND) formulation is well suited for a direct treatment by introducing a barrier function. Using exact second derivatives, this difficult class of problem is solved by sequential quadratic programming with trust regions. These building blocks result into an integrated design process. Two examples–including a large-scale application–illustrate the robustness of the proposed formulation.     

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 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.     

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.     

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。     

计及多元不确定性的综合能源系统优化配置

综合能源系统的优化配置关键在于设备选型与数量配置,而能源负荷负荷和可再生能源出力预测误差以及故障发生的不确定性将直接影响配置方案的合理性以及经济性.为此,本文提出一种考虑源–网–荷多元不确定性的综合能源系统多目标–机会约束规划方法.考虑可再生能源出力与负荷需求预测误差引起的不确定性,本文构建了满足置信概率的能量供需平衡约束;针对供能网络中设备N-1故障引起的不确定性,提出调整裕度模型,进而构建了调整裕度与N-1设备能量缺额的机会约束.对于获得的帕累托解集,采用信息熵与逼近理想排序法构建多准则评价模型,以确定最优的系统配置.将本文方法应用于某区域综合能源系统的最优结构设计,实验结果表明,本文方法的有效性与可靠性.     

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 for size and shape with frequency constraints using a collaborative optimization strategy

A new metaheuristic strategy is proposed for size and shape optimization problems with frequency constraints. These optimization problems are considered to be highly non-linear and non-convex. The proposed strategy extends the idea of using a single optimization process to a series of collaborative optimization processes. In this study, a modified teaching-learning-based optimization (TLBO), which is a relatively simple algorithm with no intrinsic parameters controlling its performance, is utilized in a collaborative framework and introduced as a higher-level TLBO algorithm called school-based optimization (SBO). SBO considers a school with multiple independent classrooms and multiple teachers with inter-classroom collaboration where teachers are reassigned to classrooms based on their fitness. SBO significantly improves the both exploration and exploitation capabilities of TLBO without increasing the algorithm's complexity. In addition, since the SBO algorithm uses multiple independent classrooms with interchanging teachers, the algorithm is less likely to be influenced by local optima. A parametric study is conducted to investigate the effects of the number of classes and the class size, which are the only parameters of SBO. The SBO algorithm is applied to five benchmark truss optimization problems with frequency constraints and the statistical results are compared to other optimization techniques in the literature. The quality and robustness of the results indicate the efficiency of the proposed SBO algorithm.