Showing papers on "Minimum weight published in 1992"

Finding minimum areak-gons

Abstract: Given a setP ofn points in the plane and a numberk, we want to find a polygon[Figure not available: see fulltext.] with vertices inP of minimum area that satisfies one of the following properties: (1)[Figure not available: see fulltext.] is a convexk-gon, (2)[Figure not available: see fulltext.] is an empty convexk-gon, or (3)[Figure not available: see fulltext.] is the convex hull of exactlyk points ofP. We give algorithms for solving each of these three problems in timeO(kn3). The space complexity isO(n) fork=4 andO(kn2) fork?5. The algorithms are based on a dynamic programming approach. We generalize this approach to polygons with minimum perimeter, polygons with maximum perimeter or area, polygons containing the maximum or minimum number of points, polygons with minimum weight (for some weights added to vertices), etc., in similar time bounds.

Studying the locator polynomials of minimum weight codewords of BCH codes

Abstract: Primitive binary cyclic codes of length n=2/sup m/ are considered. A BCH code with designed distance delta is denoted B(n, delta ). A BCH code is always a narrow-sense BCH code. A codeword is identified with its locator polynomial, whose coefficients are the symmetric functions of the locators. The definition of the code by its zeros-set involves some properties for the power sums of the locators. Moreover, the symmetric functions and the power sums of the locators are related to Newton's identities. An algebraic point of view is presented in order to prove or disprove the existence of words of a given weight in a code. The principal result is the true minimum distance of some BCH codes of length 255 and 511. which were not known. The minimum weight codewords of the codes B(n2/sup h/-1) are studied. It is proved that the set of the minimum weight codewords of the BCH code B(n,2/sup m-2/-1) equals the set of the minimum weight codewords of the punctured Reed-Muller code of length n and order 2, for any m. >

Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract)

Abstract: We present (1) an algorithm that enumerates the cuts of a network by increasing weight with polynomial delay, and (2) an algorithm that computes the k-th minimum weight in polynomial time for fixed k We also show that in the case of undirected networks there are only polynomially many cuts that have the k-th minimum weight for any fixed k (whereas directed networks can have exponentially many different minimum cuts).

From sequential layers to distributed processes: deriving a distributed minimum weight spanning tree algorithm

Abstract: Analysis and design of distributed algorithms and protocols are difficult issues. An important cause for those difficulties is the fact that the logical structure of the solution is often invisible in the actual implementation. We introduce a framework that allows for a formal treatment of the design process, from an abstract initial design to an implementation tailored to specific architectures. A combination of algebraic and axiomatic techniques is used to verify correctness of the derivation steps. This is shown by deriving an implementation of a distributed minimum weight spanning tree algorithm in the style of [GHS].

Simulated annealing utilizing neural networks for discrete variable optimization problems in structural design

Abstract: R. A. Swift t and S. M. Batill tt Hessert Center for Aerospace Research Department of Aerospace and Mechanical Engineering University of Notre Dame Noue Dame, Indiana 46556 A simulated annealing application to the optimal design of structures involving discrete design variables is presented. Neural networks were used as approximate representations of the design spaces for candidate structural concepts. The simulated annealing algorithm was used to search these discrete design spaces. Design information obtained from finite element analysis and math-programming optimization was used to train the neural network representations. Three examples are presented. The first is a material system design of a 10 bar truss in which four isotropic materials were considered for each of the 10 axial force rods. Minimum weight was considered as the objective function. The second example is an ACOSS I1 space truss in which four materials were considered for each of the 113 rod elements, minimum weight being again the objective function. The final example is that of an Intermediate Complexity Wing (ICW), in which a discrete set of lamina orientations was considered for the composite skin, natural frequency being considered as the objective function. In each of the examples, the ability of the neural network to represent the desired information was achieved, and the simulated annealing procedure was able to extract improved designs (improved over the "best" designs in the training data).

Tight integral duality gap in the Chinese Postman problem

Abstract: LetG = (V, E) be a graph and letw be a weight functionw:E →Z+. Let\(T \subseteq V\) be an even subset of the vertices ofG. AT-cut is an edge-cutset of the graph which dividesT into two odd sets. AT-join is a minimal subset of edges that meets everyT-cut (a generalization of solutions to the Chinese Postman problem). The main theorem of this paper gives a tight upper bound on the difference between the minimum weightT-join and the maximum weight integral packing ofT-cuts. This difference is called the (T-join) integral duality gap. Letτw be the minimum weight of aT-join, and letvw be the maximum weight of an integral packing ofT-cuts. IfF is a non-empty minimum weightT-join, andnF is the number of components ofF, then we prove thatτw—vw≤nF−1.

On Generator Matrices of Codes

Abstract: The if class of the q-ary linear codes of given length, dimension and minimum weight is nonempty, it is shown to contain a code whose generator matrix consists of words of minimum weight.

Approximating the minimum weight triangulation

Abstract: In O(n log n) time we compute a triangulation with O(n) new points, and no obtuse triangles, that has length within a constant factor of the minimum possible. We also approximate the minimum weight Steiner triangulation using triangulations with no sharp angles. No previous polyonomial time triangulation achieved an approximation factor better than O(log n).

Optimization of Ship Structural Design by Genetic Algorithm

Abstract: In general, ship basic design is based on design-spiral approach where variable design parameters are defined through repetition of trial and error. This kind of approach is a process of satisfying a lot of complicated design criteria empirically, rather than optimizing some object function. However, in order to realize optimum or rational design for a new type of structural concept with complicated design criteria, it is necessary to model the design problem as strictly as possible and accomplish more highly numerical optimization.As for ship structural optimization, the object function (hull steel weight or total cost including material, fabrication and paint cost) is closely related to principal dimensions and general arrangement. Therefore, in order to obtain better design in the optimization process, it is desirable to search broader design space with many design variables such as principal dimensions, arrangement, frame spaces, stiffener spaces, scantlings and material.This type of optimization is considered as a combinatorial optimization problem, and such optimization method that is robust and quickly converging to global optimum is required. In this paper the authors apply the genetic algorithm which simulates the law of the survival of the fittest to structural optimization problems.At first, the authors apply the genetic algorithm to minimum weight problem of a hatch cover with 6 independent variables, and compare several approaches to the genetic algorithm through numerical experiments. As a result of the examination the authors propose the genetic algorithm which attaches importance to vicinity search as the method appropriate for structural optimization problems.Then, the authors apply the genetic algorithm to the optimum design problem of a double hull tanker with 40 independent variables. It is shown that the proposed method is effective for the optimization with a variety of independent variables of different types. Using this method it is possible to obtain more accurate optimum design of ship structure by enhancing the accuracy of the estimation of object functions and many appropriate constraints.

Integrating aerodynamics and structures in the minimum weight design of a supersonic transport wing

Abstract: An approach is presented for determining the minimum weight design of aircraft wing models which takes into consideration aerodynamics-structure coupling when calculating both zeroth order information needed for analysis and first order information needed for optimization When performing sensitivity analysis, coupling is accounted for by using a generalized sensitivity formulation The results presented show that the aeroelastic effects are calculated properly and noticeably reduce constraint approximation errors However, for the particular example selected, the error introduced by ignoring aeroelastic effects are not sufficient to significantly affect the convergence of the optimization process Trade studies are reported that consider different structural materials, internal spar layouts, and panel buckling lengths For the formulation, model and materials used in this study, an advanced aluminum material produced the lightest design while satisfying the problem constraints Also, shorter panel buckling lengths resulted in lower weights by permitting smaller panel thicknesses and generally, by unloading the wing skins and loading the spar caps Finally, straight spars required slightly lower wing weights than angled spars

Minimum weight spanning trees with bounded diameter

Abstract: MINIMUM WEIGHT SPANNING TREES WITH BOUNDED DIAMETER N.R. Achuthan and L. Caccetta School of Mathematics and Statistics Curtin University of Technology GPO Box U1987 Perth, 6001 Western Australia. Let G be a simple graph with non-negative edge weights. Determining a minimum weight spanning tree is a fundamental problem that arises in network design and as a subproblem in many combinatorial optimization problems such as vehicle routing. In some applications, it is necessary to restrict the diameter of the spanning tree and thus one is interested in the problem : Find, in a given weighted graph G, a minimum weight spanning tree of diameter at most D. This problem is known to be NP-complete for D 2:: 4. In this paper we present a mixed integer linear programming formulation and discuss some solution procedures.

Minimum weight design of structural topologies

Abstract: A design procedure for optimizing structural topologies is presented. The member sizes are the design variables and the constraints are related to stresses, displacements, and bounds on the variables. The proposed procedure is intended to overcome some basic difficulties involved in the solution process. A near optimal solution is achieved by solving sequentially several simple subproblems. A main feature of this approach is that the exact analysis of the structure need not be repeated many times during the solution process. The effectiveness of the proposed solution procedure is demonstrated by several examples. It is shown that optimal topologies are significantly better than nonoptimal ones.

When Wrestlers Slim to Win: What's a Safe Minimum Weight?

Abstract: In brief High school wrestlers often select a weight class below their normal weight without considering how much weight they can safely lose. Body composition assessments provide objective estimates of minimum weight for competition. However, even if athletes follow medically accepted guidelines for minimum weight, losing weight may still affect their health and performance. Using a variety of techniques, primary care physicians can determine and interpret minimum weight estimates for young wrestlers and offer advice on safe weight loss.

On the convergence quality of minimum-weight design of large space frames under multiple dynamic constraints*

Abstract: Weight optimization of large space frames under dynamic constraints requires adaptable design search techniques because of the enormous number of sizing variables, the highly nonlinear frequency constraint surfaces, and the multiple points of local minima. With modern OC procedures, based on alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing), the convergence to weight minima is oftentimes oscillatory. Even though the convergence rate for OC methods is initially fast, it gradually slows near local extrema, mainly because the selection of appropriate step sizes (or move limits) in the redesign phase becomes increasingly difficult. The focus here is to create specific criteria based on past scaled designs to “damp out” the oscillatory convergence propensity of OC recursive methods. Several OC recursive strategies, which are frequently worked to resize and to evaluate the Lagrange multipliers, are steered by the present approach to design large space frames under multiple dynamic constraints. Besides this, the design iteration histories obtained by the various recursive strategies are compared graphically. On the whole, the present OC approach achieves a smooth upper-bound convergence to weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the method eliminates the need for adjustments of internal parameters during the redesign phase.

Truss topology optimization with simultaneous analysis and design

Abstract: Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.

Design optimization with static and dynamic displacement constraints

Abstract: A design optimization procedure using a sequential linear programming technique is proposed in this paper to design minimum weight structures subjected to frequency response and static displacement constraints. The merit of the proposed approach is that the reanalyses of the static and dynamic responses, as well as the computations of the static and dynamic sensitivity data, are performed in a reduced approximate model. A significant saving of computer time for large scale structures is expected. Two numerical examples show good results of this method.

Preliminary wing design of a high speed civil transport aircraft by multilevel decomposition techniques

Abstract: A multilevel decomposition approach for the preliminary design of a High Speed Civil Transport (HSCT) aircraft wing structure is described. The wing design is decomposed into three levels. The top level uses the ACSYNT aircraft synthesis program to generate preliminary weight, mission and performance information needed for the calculations. The optimization criterion is productivity as expressed by a productivity index for a specified mission. The second level of the system performs a basic finite element structural analysis of the wing box. The wing structure is sized for minimum weight subject to structural and aeroelastic constraints. Sensitivity derivatives are computed with respect to the top level design variables. Level 3 performs a detailed stress and buckling analysis of the wing skin panels and thus creates an updated wing weight that is passed to the top level together with the sensitivity information. The methodology will be verified using a baseline HSCT configuration derived from the NASA HiSAIR studies. Currently data acquisition and computer program installation are in progress.

Optimal Design of Structures with Kinematic Nonlinear Behavior

Abstract: This paper suggests an optimization-based methodology for the design of minimum weight structures with kinematic nonlinear behavior. Attention is focused on three-dimensional reticulated structures idealized with beam elements under proportional static loadings. The algorithm used for optimization is based on a classical optimality criterion approach using an active-set strategy for extreme limit constraints on the design variables. A first-order necessary condition is derived and used as the basis of a fixed-point iteration method to search for the optimal design. A fixed-point iteration algorithm is used based on the criterion that at optimum design the nonlinear strain energy is equal in all members. A nonlinear analysis procedure for three-dimensional structures is discussed and used in developing the optimization algorithm. Several examples are given to evaluate the validity of the underlying assumptions and to demonstrate some of the characteristics of the proposed procedures. The procedure is verified using two well-known examples.

Optimum design of laminated composite structures via a multilevel substructuring approach

Abstract: This paper presents a multilevel substructuring and optimization approach to the minimum weight design of laminated composite structures. The optimization process is carried out in a double scheme which consists of optimizations at system and subsystem levels. At the system level of optimization, an optimality criterion method is used to design component thicknesses which minimize structural weight subject to structural behavioral constraints as well as side constraints. At the subsystem level, the structure being divided into several substructures, fiber directions and layer thicknesses of each substructure are determined to minimize its weight subject to component behavioral constraints as well as side constraints. The objective at the subsystem level is accomplished by carrying out the minimization process again in a double scheme where the quasi-Newton method is used at the first sub-level of optimization for the optimal design of fiber directions and an optimality criterion method at the second sub-l...

Experimental validation of the utility of structural optimization

Abstract: This paper addresses the topic of validating structural optimization methods by use of experimental results. The paper describes the need for validating the methods as a way of effecting a greater and an accelerated acceptance of formal optimization methods by practicing engineering designers. The range of validation strategies is defined which includes comparison of optimization results with more traditional design approaches, establishing the accuracy of analyses used, and finally experimental validation of the optimization results. The remainder of the paper describes examples of the use of experimental results to validate optimization techniques. The examples include experimental validation of the following: optimum design of a trussed beam; combined control-structure design of a cable-supported beam simulating an actively controlled space structure; minimum weight design of a beam with frequency constraints; minimization of the vibration response of helicopter rotor blade; minimum weight design of a turbine blade disk; aeroelastic optimization of an aircraft vertical fin; airfoil shape optimization for drag minimization; optimization of the shape of a hole in a plate for stress minimization; optimization to minimize beam dynamic response; and structural optimization of a low vibration helicopter rotor.