Showing papers on "Minimum weight published in 2006"

Analysis, design and optimization of structures using force method and genetic algorithm

Abstract: In the first part of this paper, the energy formulation of the force method is presented and analysis is performed using genetic algorithm. Two simple examples are provided to show the accuracy of the approach. In the second part, an efficient method is developed for designing structures with prescribed stress ratios for its members. The genetic algorithm performed very well and designs with specified stress ratios were achieved with a good convergence rate. A unit value of ci for all the members of a structure corresponds to the well known fully stressed design. In the third part, minimum weight design is formulated by the additional conditions being imposed on the design process. Again, genetic algorithm showed to be a powerful means for optimization. Copyright © 2005 John Wiley & Sons, Ltd.

Some restrictions on weight enumerators of singly even self-dual codes

Abstract: In this correspondence, we give some restrictions on weight enumerators of singly even self-dual [n,n/2,d] codes whose shadows have minimum weight d/2. As a consequence, we determine the weight enumerators for which there is an extremal singly even self-dual [40,20,8] code and an optimal singly even self-dual [50,25,10] code

Optimal 3-terminal cuts and linear programming

Abstract: Given an undirected graph G=(V,E) and three specified terminal nodes t1,t2,t3, a 3-cut is a subset A of E such that no two terminals are in the same component of G\A. If a non-negative edge weight ce is specified for each e∈E, the optimal 3-cut problem is to find a 3-cut of minimum total weight. This problem is **-hard, and in fact, is max-** -hard. An approximation algorithm having performance guarantee ** has recently been given by Calinescu, Karloff, and Rabani. It is based on a certain linear-programming relaxation, for which it is shown that the optimal 3-cut has weight at most ** times the optimal LP value. It is proved here that ** can be improved to **, and that this is best possible. As a consequence, we obtain an approximation algorithm for the optimal 3-cut problem having performance guarantee **. In addition, we show that ** is best possible for this algorithm.

Genetic Algorithm Based Construction-Conscious Minimum Weight Design of Seismic Steel Moment-Resisting Frames

Abstract: The minimum weight criterion, which has been widely adopted in the literature for optimal design of steel structural systems, is inadequate to fully reflect the initial monetary investment due to lack of consideration of additional construction expenses resulting from varied degree of design complexity such as different member sections and splice/connection types. In this paper, design optimization of seismic steel moment-resisting frames involves simultaneous consideration of two competing objective functions: the steel material weight and an approximate measure of design complexity in terms of the number of different standard steel member section types. The code-compliant seismic structural design follows the equivalent lateral force procedure of the 2000 National Earthquake Hazards Reduction Program seismic provisions in conjunction with American Institute of Steel Construction load resistance factor design seismic steel design criteria. A genetic algorithm is used for the posed biobjective structural optimization problem to produce a set of alternative designs establishing optimized trade-off between the two merit objectives. Numerical examples show that a minimum weight design with a balanced degree of design complexity is expected to achieve an initial investment economy with more accuracy.

Minimum multicolored subgraph problem in multiplex PCR primer set selection and population haplotyping

Abstract: In this paper we consider the minimum weight multicolored subgraph problem (MWMCSP), which is a common generalization of minimum cost multiplex PCR primer set selection and maximum likelihood population haplotyping. In this problem one is given an undirected graph G with non-negative vertex weights and a color function that assigns to each edge one or more of n given colors, and the goal is to find a minimum weight set of vertices inducing edges of all n colors. We obtain improved approximation algorithms and hardness results for MWMCSP and its variant in which the goal is to find a minimum number of vertices inducing edges of at least k colors for a given integer k≤ n.

Optimum design criteria for elastic structures subject to random dynamic loads

Abstract: A new stochastic optimization method, which makes use of a constraint on structural reliability, is proposed for structures subject to dynamic random loads. A minimum weight problem is posed, in which a constraint condition imposes that the failure probability must be smaller than a given admissible level. The failure is determined by the first crossing outside the safe domain of a suitable structural response vector. The method is used to find the optimal shape of an elastic vertical column supporting a fixed mass positioned on the top, subject to a Gaussian filtered stationary stochastic horizontal acceleration process. The column, with variable annular cross-section, is described by a deterministic elastic multi-degree-of-freedom system. It is assumed that failure is reached when its lateral displacement exceeds an acceptable threshold value. Under this constraint, the structural weight is minimized and the optimal shape is determined for different structural conditions.

A hybrid heuristic for the minimum weight vertex cover problem

Abstract: Given an undirected graph with weights associated with its vertices, the minimum weight vertex cover problem seeks a subset of vertices with minimum sum of weights such that each edge of the graph has at least one endpoint belonging to the subset. In this paper, we propose a hybrid approach, combining a steady-state genetic algorithm and a greedy heuristic, for the minimum weight vertex cover problem. The genetic algorithm generates vertex cover, which is then reduced to minimal weight vertex cover by the heuristic. We have evaluated the performance of our algorithm on several test problems of varying sizes. Computational results show the effectiveness of our approach in solving the minimum weight vertex cover problem.

Weighted Bipartite Matching in Matrix Multiplication Time

Abstract: In this paper we consider the problem of finding maximum weighted matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problem work in 0(Wn ω ) 1 time, where ω is the matrix multiplication exponent, and W is the highest edge weight in the graph. As a consequence of this result we obtain O(Wn ω ) time algorithms for computing: minimum weight bipartite vertex cover, single source shortest paths and minimum weight vertex disjoint s-t paths.

Weighted bipartite matching in matrix multiplication time

Abstract: In this paper we consider the problem of finding maximum weighted matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problem work in $\tilde{O}(Wn^{\omega})$ time, where ω is the matrix multiplication exponent, and W is the highest edge weight in the graph. As a consequence of this result we obtain $\tilde{O}(Wn^{\omega})$ time algorithms for computing: minimum weight bipartite vertex cover, single source shortest paths and minimum weight vertex disjoint s-t paths.

A revised discrete Lagrangian-based search algorithm for the optimal design of skeletal structures using available sections

Abstract: Issues relating to the application of the discrete Lagrangian method (DLM) to the discrete sizing optimal design of skeletal structures are addressed. The resultant structure, whether truss or rigid frame, is subjected to stress and displacement constraints under multiple load cases. The members’ sections are selected from an available set of profiles. A table that contains sectional properties for all the available profiles is used directly in structural optimization. Each profile in the table is assigned by a unique profile number, which is used as the integer design variable for each of the structural members. It is proposed that we use a revised DLM search algorithm with static weighting to design trusses and rigid frames for minimum weight. Five examples are used to demonstrate the feasibility of the method. It is shown that, for monotonic as well as nonmonotonic constraint functions, the DLM is effective and robust for the discrete sizing design of skeletal structures.

Provably good codes for hash function design

Abstract: We develop a new technique to lower bound theminimum distance of quasi-cyclic codes with large dimension by reducing the problem to lower bounding the minimum distance of a few significantly smaller dimensional codes. Using this technique, we prove that a code which is similar to the SHA-1 message expansion code has minimum distance at least 82, and that too in just the last 64 of the 80 expanded words. Further the minimum weight in the last 60 words (last 48 words) is at least 75 (52 respectively). We expect our technique to be helpful in designing future practical collision-resistant hash functions. We also use the technique to find the minimum weight of the SHA-1 code (25 in the last 60 words), which was an open problem.

Optimum structural design of tankers using multi-objective optimization technique

Abstract: While designing a ship's structure, the material cost of hull's weight and the overall cost of construction processes should be minimized considering safety and reliability. In the past, the minimum weight design has focused mainly on reducing material cost and increasing dead weight, which reflects the interests of a ship's owner. But, in the past experience, the minimum weight design has inevitably led to increasing the construction cost, making it necessary for ships' structural designers to consider both structural weight and construction cost. From this point of view, this study proposes a multi-objective optimization technique for designing ships' structures. According to the proposed algorithm, the results of optimization were compared to the structural design of an existing very large crude oil carrier. Objective functions were weight cost and construction cost of the very large crude oil carrier, and evolution strategies, one of the stochastic search methods, was used as an optimization ...

A New Minimum Weight Algorithm for Additive Codes

Abstract: A new algorithm is presented for computing the minimum weight of additive codes. It is superior to the existing method, achieving performance similar to the Brouwer-Zimmermann algorithm applied to linear codes of the same cardinality.

Minimum weight design of framed structures using a genetic algorithm considering dynamic analiysis

Abstract: GENETIC ALGORITHMS CAN BE CONSIDERED AS A FAMILY OF COMPUTATIONAL MODELS INSPIRED ON THE PRINCIPALS OF EVOLUTION. THESE ALGORITHMS START FROM A SET OR POPULATION OF CHROMOSOMES IN WHICH EACH CHROMOSOME CONTAINS A POSSIBLE SOLUTION TO THE SPECIFIC PROBLEM. GENETIC OPERATORS, (SELECTION, CROSSOVER AND MUTATION) ARE APPLIED WHICH GENERATE A NEW POPULATION PRESERVING AND IMPROVING THE INFORMATION CONSIDERED IN THE ORIGINAL CHROMOSOMES. HERE THE OPTIMIZATION OF THE CROSS-SECTIONAL AREA OF FRAME STRUCTURES IS CONSIDERED IN ORDER TO OBTAIN THE MINIMUM WEIGHT FOR DYNAMIC ANALYSIS. THE OPTIMIZATION IS OBTAINED THROUGH THE MINIMIZATION OF AN OBJECTIVE FUNCTION, WHICH, FOR THE EXAMPLES CONSIDERED IS WRITTEN USING THE CROSS-SECTIONAL AREA AND THE LENGTH OF THE BARS AND THE SPECI¯C WEIGHT OF THE MATERIAL FROM WHICH THE TOTAL WEIGHT OF THE STRUCTURE CAN BE OBTAINED. THE CROSS-SECTIONAL AREAS ARE THE PROJECT VARIABLES WHICH SHOULD BE WITHIN CERTAIN LIMITS IN ORDER TO OBTAIN REALISTIC SOLUTIONS. RESTRICTIONS ARE APPLIED ON THE NATURAL FREQUENCIES. RESULTS ARE OBTAINED FOR SOME TEST PROBLEMS.

A technique for optimally designing fibre-reinforced laminated plates under in-plane loads for minimum weight with manufacturing uncertainties accounted for

Abstract: A procedure to design symmetrically laminated plates under buckling loads for minimum mass with manufacturing uncertainty in the ply angle, which is the design variable, is described. A minimum buckling load capacity is the design constraint implemented. The effects of bending–twisting coupling are neglected in implementing the procedure, and the golden section method is used as the search technique, but the methodology is flexible enough to allow any appropriate problem formulation and search algorithm to be substituted. Three different tolerance scenarios are used for the purposes of illustrating the methodology, and plates with varying aspect ratios and loading ratios are optimally designed and compared.

Biomimetics: Extending Nature’s Design OfThin-wall Shells With Cellular Cores

Abstract: Thin-walled, cylindrical structures are found extensively in both engineering and nature. Minimum weight design of such structures is essential in a variety of engineering applications, including space shuttle fuel tanks, aircraft fuselages, and offshore oil platforms. In nature, thin-walled cylindrical structures are often supported by a honeycombor foam-like cellular core, as for example, in plant stems, porcupine quills, or hedgehog spines. Previous studies have suggested that a compliant core increases the elastic buckling resistance of a cylindrical shell over that of a hollow cylinder of the same weight. We extend the linearelastic buckling theory by coupling basic plasticity theory to provide a more comprehensive analysis of isotropic, cylindrical shells with compliant cores. The minimum weight design of a thin-walled cylinder with a compliant core, of given radius and specified materials, subjected to a prescribed load in uniaxial compression or pure bending is examined. The analysis gives the values of the shell thickness, the core thickness, and the core density that minimize the weight of the structure for both loading scenarios. The weight optimization of the structure identifies the optimum ratio of the core modulus to the shell modulus. The design of natural, thin-walled structures with cellular cores is compared to the analytical optimal, and the deviation about the theoretical optimum is explored. The analysis also discusses the selection of materials in the design of the cylinders with compliant cores, identifying the most suitable material combinations. Finally, the challenges associated with achieving the optimal design in practice are discussed, and the potential for practical implementation is explored.

Membrane Analysis and Minimum Weight Design of Submerged Spherical Domes

Abstract: This paper is concerned with the membrane analysis and minimum weight design of submerged spherical domes. In addition to the hydrostatic pressure, loads acting on the dome include the self-weight and a skin cover load. By adopting a uniform strength design as governed by the Tresca yield condition, the variation of the shell thickness of spherical domes can be accurately defined by a power series. Based on a family of uniform strength designs associated with a given depth of water and the dome’s base radius, we determine the optimal subtended angle 2α (and the optimal dome height) for the minimum weight design of submerged spherical domes.

Cost minimization of 2D continuum structures under stress constraints by increasing commonality in their skeletal equivalents

Abstract: It is well known that, for real-life engineering problems, minimum weight does not necessarily mean minimum cost, thus it is of practical value to simultaneously achieve both layout optimization and cost minimization of a structure. Towards this direction, the present paper discusses a procedure of four steps concerning 2D continuum structures under stress constraints only. The continuum is first substituted by an equivalent skeletal structure, which is then optimized using the Sequential Quadratic Programming (SQP) technique. In the sequel the optimized structural members of equal or near-equal cross-sections are appropriately grouped and finally all optimized structural members of imposed critical minimum or near-minimum cross-section are eliminated. Both grouping and elimination procedures were based on a simple statistical manipulation. The proposed procedure was applied to four test cases, namely the short and long cantilever, the MBB beam and the L-shape beam. The conclusion of the present work was that, for 2D continuum structures under stress constraints only, the proposed procedure provided the means for both layout optimization and structural cost minimization.

The Stacking Sequence Optimization of Stiffened Laminated Curved Panels with Different Loading and Stiffener Spacing

Abstract: An efficient procedure to obtain the optimal stacking sequence and the minimum weight of stiffened laminated composite curved panels under several loading conditions and stiffener layouts has been developed based on the finite element method and the genetic algorithm that is powerful for the problem with integer variables. Often, designing composite laminates ends up with a stacking sequence optimization that may be formulated as an integer programming problem. This procedure is applied for a problem to find the stacking sequence having a maximum critical buckling load factor and the minimum weight. The object function in this case is the weight of a stiffened laminated composite shell. Three different types of stiffener layouts with different loading conditions are investigated to see how these parameters influence on the stacking sequence optimization of the panel and the stiffeners. It is noticed from the results that the optimal stacking sequence and lay-up angles vary depending on the types of loading and stiffener spacing.

Minimum Weight Design of Composite Structures with Local Postbuckling and Blending Constraints

Abstract: In this paper, we formulate the minimum weight design of large composite structure with local postbuckling and blending constraint with stacking sequence of laminates as design variable chosen from a discrete set of 0, ±45, and 90 degrees. In design of complex structure, it is customary to decompose the problem into several independent or semi-independent local design problems via a global/local design methodology. At the global level, the model used to predict load distribution or load paths is very coarse because of computational cost. This works if the structure is loaded such that no panel buckles. However, the above approach fails if some or all structural components are allowed to go beyond buckling load. A full scale nonlinear analysis to predict the load paths is beyond scope. In this paper, we used an efficient iterative approach with the same coarse global model ∗Research Assistant,Dept. of Aerospace and Ocean Engineering, oseresta@vt.edu, Student Member, AIAA. †Assistant Professor, Aerospace Structures, Delft University of Technology, M.M.Abdalla@lr.tudelft.nl, Member, AIAA. ‡Professor, Aerospace Structures, Delft University of Technology,, Z.Gurdal@lr.tudelft.nl, Member, AIAA.

Counting all solutions of minimum weight exact satisfiability

Abstract: We show that the number of all solutions of minimum weight exact satisfiability can be found in O(n2.||C||+20.40567 n) time, for a CNF formula C containing n propositional variables equipped with arbitrary real-valued weights. In recent years merely the unweighted counterpart of this problem has been studied [2, 3, 7].

Design of a recurve actuator for maximum energy efficiency

Abstract: In this paper we study the optimal design of recurve arrays. An analytic model of the static response of the recurve actuator with energy flow in the system is derived. Two optimization problems for the recurve array are formulated with material, packaging, and performance constraints. One formulation is based on minimum weight. The second formulation is based on energy efficiency. A genetic algorithm is used to find the optimum designs. Recurve arrays designed for maximum energy conversion efficiency are compared to those designed for minimum weight. Parametric studies are conducted to investigate the effect of the stiffness of the driven structure and the maximum deliverable voltage on the optimized designs. These optimization formulations are effective design tools for a relatively complex actuator.

Fixed-Parameter Algorithms for Optimal Convex Partitions and Other Results

Abstract: In this thesis I study two-dimensional geometric optimization problems for which it is difficult to find efficient, exact, deterministic algorithms. All known solutions to these problems require time that is exponential in the total size of the input. The work done in this thesis is a contribution to the research directed at attacking and coping with such NP hard problems in computational geometry. A promising way to attack and cope with such problems is to find an algorithm that is exponential in the size of only one input parameter and polynomial in the size of all other input parameters. Such an algorithm is called a fixed parameter algorithm, because if we fix the single troublesome input at any one value, the problem can be solved efficiently (i.e.in polynomial time). In this thesis, I give algorithms based on this idea. Generally, the input I work with has n vertices and I choose the number k of vertices lying in the interior of the boundary of the input as the fixed parameter. Based on this idea the results in this thesis include algorithms for the minimum weight triangulation problem, the minimum weight convex partition problem, and the minimum number convex partition problem: I present four fixed parameter algorithms for finding the minimum weight triangulation of a simple polygon with n-k vertices on the perimeter and k vertices in the interior (hole vertices), that is, or a total of n vertices. All four algorithms have been implemented in Java and I report results of experiments carried out with these implementations. For the minimum weight and minimum number convex partition problem I present fixed parameter algorithms for a convex polygon with n k vertices on the perimeter and k vertices in the interior (hole vertices). However, the results for these two problems also hold for the more general case where the input is an n-vertex planar straight line graph and k is the total number of holes and/or reflex vertices inside the convex hull. For the special case of the minimum weight convex partition problem of a convex polygon with a single hole vertex (the so-called local minimum weight convex partition problem), I present an optimal algorithm and an approximation algorithm. In addition to the above closely connected results, this thesis presents results on the following related subjects: I show bounds on optimally triangulating connected subsets of the minimum weight convex partition of simple polygons and points in the plane. I consider the minimum line covering problem, which is also known to be NP-hard. I give exact and approximate algorithms and a lower time bound for restricted variants of this problem. Finally, I discuss minimum spanning trees with bi chromatic vertices. I present tight upper bounds on the maximum degree of a node in the color conforming minimum weight spanning tree and discuss bounds on the total length of the edges.