Showing papers on "Minimum weight published in 2005"

WFIM: Weighted Frequent Itemset Mining with a weight range and a minimum weight.

Abstract: Researchers have proposed weighted frequent itemset mining algorithms that reflect the importance of items. The main focus of weighted frequent itemset mining concerns satisfying the downward closure property. All weighted association rule mining algorithms suggested so far have been based on the Apriori algorithm. However, pattern growth algorithms are more efficient than Apriori based algorithms. Our main approach is to push the weight constraints into the pattern growth algorithm while maintaining the downward closure property. In this paper, a weight range and a minimum weight constraint are defined and items are given different weights within the weight range. The weight and support of each item are considered separately for pruning the search space. The number of weighted frequent itemsets can be reduced by setting a weight range and a minimum weight, allowing the user to balance support and weight of itemsets. WFIM generates more concise and important weighted frequent itemsets in large databases, particularly dense databases with low minimum support, by adjusting a minimum weight and a weight range.

Optimal design of compression corrugated panels

Abstract: Compression panels comprised of a corrugated core bonded to either one or two face sheets are optimally designed for minimum weight. Results obtained from two optimization procedures are compared: naive optimization where simultaneous occurrence of failure modes is assumed, and sequential quadratic programming (SQP) based optimization. A total of eight different panel geometries are considered, including hat- and blade-stiffened panels, and square, triangular and trapezoidal cores. From a weight standpoint, panels with hat-stiffeners are found to be the most efficient for the given boundary conditions, about 40% lighter at some load levels than the least efficient-sandwich panels with a square core.

Multi-fidelity optimization of laminated conical shells for buckling

Abstract: Optimum laminate configuration for minimum weight of filament-wound laminated conical shells is investigated subject to a buckling load constraint. In the case of a composite laminated conical shell, due to the manufacturing process, the thickness and the ply orientation are functions of the shell coordinates, which ultimately results in coordinate dependence of the stiffness matrices (A,B,D). These effects influence both the buckling load and the weight of the structure and complicate the optimization problem considerably. High computational cost is involved in calculating the buckling load by means of a high-fidelity analysis, e.g. using the computer code STAGS-A. In order to simplify the optimization procedure, a low-fidelity model based on the assumption of constant material properties throughout the shell is adopted, and buckling loads are calculated by means of a low-fidelity analysis, e.g. using the computer code BOCS. This work proposes combining the high-fidelity analysis model (based on exact material properties) with the low-fidelity model (based on nominal material properties) by using correction response surfaces, which approximate the discrepancy between buckling loads determined from different fidelity analyses. The results indicate that the proposed multi-fidelity approaches using correction response surfaces can be used to improve the computational efficiency of structural optimization problems.

A Matching Lower Bound on the Minimum Weight of SHA-1 Expansion Code.

Abstract: Recently, Wang, Yin, and Yu ([WYY05b]) have used a low weight codeword in the SHA-1 message expansion to show a better than brute force method to find collisions in SHA-1. The smallest minimum weight codeword they report has a (bit) weight of 25 in the last 60 of the 80 expanded words. In this paper we show, using a computer assisted method, that this is indeed the smallest weight codeword. In particular, we show that the minimum weight over F2 of any non-zero codeword in the SHA-1 (linear) message expansion code, projected on the last 60 words, is at least 25.

On some self-dual codes and unimodular lattices in dimension 48

Abstract: In this paper, binary extremal self-dual codes of length 48 and extremal unimodular lattices in dimension 48 are studied through their shadows and neighbors. We relate an extremal singly even self-dual [48, 24, 10] code whose shadow has minimum weight 4 to an extremal doubly even self-dual [48, 24, 12] code. It is also shown that an extremal odd unimodular lattice in dimension 48 whose shadow has minimum norm 2 relates to an extremal even unimodular lattice. Extremal singly even self-dual [48, 24, 10] codes with shadows of minimum weight 8 and extremal odd unimodular lattice in dimension 48 with shadows of minimum norm 4 are investigated.

Using bipartite and multidimensional matching to select the roots of a system of polynomial equations

Abstract: Assume that the system of two polynomial equations f(x,y) = 0 and g(x,y) = 0 has a finite number of solutions. Then the solution consists of pairs of an x-value and an y-value. In some cases conventional methods to calculate these solutions give incorrect results and are complicated to implement due to possible degeneracies and multiple roots in intermediate results. We propose and test a two-step method to avoid these complications. First all x-roots and all y-roots are calculated independently. Taking the multiplicity of the roots into account, the number of x-roots equals the number of y-roots. In the second step the x-roots and y-roots are matched by constructing a weighted bipartite graph, where the x-roots and the y-roots are the nodes of the graph, and the errors are the weights. Of this graph the minimum weight perfect matching is computed. By using a multidimensional matching method this principle may be generalized to more than two equations.

Simple distributed algorithms for approximating minimum steiner trees

Abstract: Given a network G=(V,E), edge weights w(.), and a set of terminals S⊆V, the minimum-weight Steiner tree problem is to find a tree in G that spans S with minimum weight. Most provable heuristics treat the network G is a metric; This assumption, in a distributed setting, cannot be easily achieved without a subtle overhead. We give a simple distributed algorithm based on a minimum spanning tree heuristic that returns a solution whose cost is within a factor of two of the optimal. The algorithm runs in time O(|V|log|V|) on a synchronous network. We also show that another heuristic based on iteratively finding shortest paths gives a Θ(log |V|)-approximation using a novel charging scheme based on low-congestion routing on trees. Both algorithms work for unit-cost and general cost cases. The algorithms also have applications in finding multicast trees in wireless ad hoc networks.

A Simple and Provably Good Code for SHA Message Expansion.

Abstract: We develop a new computer assisted technique for lower bounding the minimum distance of linear codes similar to those used in SHA-1 message expansion. Using this technique, we prove that a modified SHA-1 like 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 propose a new compression function which is identical to SHA-1 except for the modified message expansion code. We argue that the high minimum weight of the message expansion code makes the new compression function resistant to recent differential attacks.

Optimum Shape Design of Composite Structures Using Boundary-Element Method

Abstract: The boundary-element method, combined with a numerical optimization algorithm, has been employed for the shape optimization of two-dimensional anisotropic structures. To find the optimum shape of a structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses, weight, and geometry. The optimum shapes of a series of anisotropic structures are obtained for maximum stiffness and minimum weight and stress, for specified loading conditions. The results are compared with the optimum shapes, that were already created by the minimization of the structural weight while satisfying certain constraints upon stresses and geometry. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. Because of the nonlinear nature of the mean compliance, weight, and stresses, the numerical optimization algorithm used is the feasible direction method, together with the golden section method for the one-dimensional search. Hermitian cubic spline functions are used to represent boundary shapes that offer considerable advantages in fitting a wide range of curves and in the automatic remeshing process. Five example problems with anisotropic material properties are presented to demonstrate the applications of this general-purpose program.

On two doubly even self-dual binary codes of length 160 and minimum weight 24

Abstract: This correspondence revisits the idea of constructing a binary [mn,mk] code from an [n,k] code over F/sub 2//sup m/ by concatenating the code with a suitable basis representation of F/sub 2//sup m/ over F/sub 2/. We construct two nonequivalent examples of doubly even self-dual binary codes of length 160 which turn out to be of minimum distance 24. This improves the lower bound for this class of codes, whereas the upper bound is given by 28. The construction at hand seems to be of interest beyond this particular example.

An Investigaton of Minimum-Weight Dual-Material Symmetrically Loaded Wheels and Torsion Arms

Abstract: A cylindrically symmetric layout of two opposite families of logarithmic spirals is shown to define the layout of minimum-weight, symmetrically loaded wheel structures, where different materials are used for the tension and compression members, respectively; referred to here as dual-material structures. Analytical solutions are obtained for both structure weight and deflection. The symmetric solutions are shown to form the basis for torsion arm structures, which when designed to accept the same total load, have identical weight and are subjected to identical deflections. The theoretical predictions of structure weight, deflection, and support reactions are shown to be in close agreement to the values obtained with truss designs, whose nodes are spaced along the theoretical spiral layout lines. The original Michell solution based on 45 deg equiangular spirals is shown to be in very close agreement with layout solutions designed to be kinematically compatible with the strain field required for an optimal dual-material design.

On the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets

Abstract: Let P and Q be disjoint point sets with 2r and 2s elements respectively, and M1 and M2 be their minimum weight perfect matchings (with respect to edge lengths). We prove that the edges of M1 and M2 intersect at most |M1|+|M2|−1 times. This bound is tight. We also prove that P and Q have perfect matchings (not necessarily of minimum weight) such that their edges intersect at most min{r,s} times. This bound is also sharp.

A minimum weight FEM formulation for Structural TopologicalOptimization with local stress constraints

Abstract: 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May - 03 June 2005, Brazil

Design of Functionally Graded Structures for Enhanced Thermal Behavior

Abstract: Multi-material structures take advantage of beneficial properties of different materials to achieve an increased level of functionality. In an effort to reduce the weight of vehicle components such as brake disk rotors, which are generally made of cast iron, light materials such as aluminum alloys may be used. These materials, however, may lead to unacceptable temperature levels. Alternatively, functionally graded structures may offer a significant decrease in weight without altering thermal performance. The design of such structures is not trivial and is the focus of this paper. The optimization combines a transient heat transfer finite element code with a genetic algorithm. This approach offers the possibility of finding a global optimum in a discrete design space, although this advantage is balanced by high computational expenses due to many finite element analyses. The goal is to design a brake disk rotor for minimum weight and optimal thermal behavior using two different materials. Knowing that computational time can quickly become prohibitively high, strategies, such as finite element grouping to reduce the number of design variables and local mesh refinement, must be employed to efficiently solve the design problem. This paper discussed the strengths and weaknesses of the proposed design method.© 2005 ASME

Multiobjective shape optimization using estimation distribution algorithms and correlated information

Abstract: We propose a new approach for multiobjective shape optimization based on the estimation of probability distributions. The algorithm improves search space exploration by capturing landscape information into the probability distribution of the population. Correlation among design variables is also used for the computation of probability distributions. The algorithm uses finite element method to evaluate objective functions and constraints. We provide several design problems and we show Pareto front examples. The design goals are: minimum weight and minimum nodal displacement, without holes or unconnected elements in the structure.

Solving minimum weight exact satisfiability in time O (2 0.2441 n )

Abstract: We show that the NP-hard optimization problem minimum weight exact satisfiability for a CNF formula over n propositional variables equipped with arbitrary real-valued weights can be solved in time O(20.2441n). To the best of our knowledge, the algorithm presented here is the first handling the weighted XSAT optimization version in non-trivial worst case time.

Minimum Weight Shape Design For The NaturalVibration Problem Of Plate And Shell Structures

Abstract: In this paper we present a solution to a shape optimization problem involving plate and shell structures subject to natural vibration. The volume is chosen as the response to be minimized under a specified eigenvalue constraint with mode tracking. The designed boundaries are assumed to be movable in the in-plane direction so as to maintain the initial curvatures. The surfaces are discretized by plane elements based on the Mindlin-Reissner plate theory. A non-parametric or a distributed shape optimization problem is formulated and the shape gradient function is theoretically derived using the material derivative method and the Lagrange multiplier method. The traction method, a shape optimization method developed by the authors, is applied to obtain the optimal shape in this problem. The validity of the numerical solution for minimizing the weight of the plate and shell structures is verified through application to fundamental design problems and an actual automotive suspension component.

Optimizations of Stiffened Composite Panel Using Fractal Branch and Bound Method

Abstract: This paper describes the development of a new low-cost optimization method for the optimal design of the laminated composite structures and a result of the application of this method in the minimum weight design of a hat-stiffened composite panel subject to a buckling constraint. This new method is based on two main works. First, the fractal branch and bound method, which is a stacking sequence optimization method we have proposed, is integrated with the particle swarm optimization technique. Second, the Kriging-based response surface is used to find out the global optimum, not just to approximate an objective function value. The criterion ‘expected improvement (EI)’ based on the Kriging model is adopted for this purpose. The validity of the proposed method is examined. The result indicates that the method provides valuable solutions with good precision and a low computational cost.

Structural optimization with member dimensional imperfections

Abstract: The paper deals with the effect of dimensional imperfections of truss members on the minimum weight design of a structure. It is assumed that for each element its imperfections cannot exceed given a priori maximum values, called tolerances. The incorporation of the considered imperfections into the design is achieved by diminishing the limit values of state functions by the product of assumed imperfections and appropriate sensitivities. Therefore, the given method allows the introduction of tolerances into the design in a relatively simple way. In the submitted paper both members’ cross-section and length imperfections are discussed. The paper is illustrated with several design examples, considering cases with multiple loading conditions and buckling analysis. The achieved optimum solutions for designs with admissible tolerances show significant differences in structural weight and material distribution compared to ideal structures (i.e. having nominal dimensions). The calculations for designs with buckling analysis also reveal changes in material distribution compared to the designs without buckling constraints.

Multiobjective shape optimization using estimation distribution algorithms and correlated information

Abstract: We propose a new approach for multiobjective shape optimization based on the estimation of probability distributions. The algorithm improves search space exploration by capturing landscape information into the probability distribution of the population. Correlation among design variables is also used for the computation of probability distributions. The algorithm uses finite element method to evaluate objective functions and constraints. We provide several design problems and we show Pareto front examples. The design goals are: minimum weight and minimum nodal displacement, without holes or unconnected elements in the structure.

A tool for the simulation and optimization of the damping material treatment of a car body

Abstract: The cost and weight reduction requirements in automotive applications are very important targets in the design of a new car. For this reason all the components of the vehicle should be optimized and the design of the damping material layout needs thoroughly analyzing, in order to have a good NVH performance with the minimum weight and cost. A tool for optimizing the damping material layout has been implemented and tested here - the need to explore the entire design space with a large number of variables suggested the use of a multi-objective genetic algorithm. These algorithms require a large number of calculations, and so the solution of the complete NVH model would be too expensive in terms of computational time. For this reason a new software tool has been developed, based on simulation of the damping material treatments by means of auxiliary mass and stiffness matrices added to the baseline modal base. Using this procedure, the required simulation time for each damping material layout configuration is reduced to a few minutes, by exploiting the capability of the genetic algorithm to efficiently explore the design space. As a result, some configurations with a significant weight reduction or a much better acoustic performance have been found. Once the most effective damping areas have been identified, a second developed optimization tool is able to further refine the shape of the previously found damping patches, in order to improve the performance/cost ratio. This second procedure uses the superelement approach for the car body surrounding the panel in question, and the acoustic response is calculated by a simplified approach based on a unilateral fluid-structure coupling.

Remark on a 5-Design Related to a Putative Extremal Doubly-Even Self-Dual [96, 48, 20] Code

Abstract: In this note, it is shown that if there is a self-orthogonal 5-(96,20,816) design, then the rows of its block-point incidence matrix generate an extremal doubly-even self-dual code of length 96. In other words, a putative extremal doubly-even self-dual code of length 96 is generated by the codewords of minimum weight.