Showing papers on "Minimum weight published in 2004"

Fast contour matching using approximate earth mover's distance

Abstract: Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost matching between two shapes' features often reveals how similar the shapes are. However due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the earth mover's distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search with locality-sensitive hashing (LSH). We demonstrate our shape matching method on a database of 136,500 images of human figures. Our method achieves a speedup of four orders of magnitude over the exact method, at the cost of only a 4% reduction in accuracy.

Truss Optimization on Shape and Sizing with Frequency Constraints

Abstract: An optimality criteria algorithm is presented for three-dimentional truss structure optimization with multiple constraints on its natural frequencies. Both nodal coordinates and element cross-sectional areas, which are quite different in their natures, are treated simultaneously in a unified design space for structural weight minimization. First the optimality criterion is developed for a single constraint based on differentiation of the Lagrangian function. It states that, at the optimum, all of the variables should have equal efficiencies. Then, the global sensitivity numbers are introduced to solve multiple constraints of frequencies, avoiding computation of the Lagrange multipliers. Finally, upon the sensitivity analysis, the most efficient variables are identified and modified in priority. The optimal solution is achieved gradually from the initial design with a minimum weight increment. Four typical trusses are used to demonstrate the feasibility and validity of the proposed method.

An ant colony optimization algorithm for the minimum weight vertex cover problem

Abstract: Given an undirected graph and a weighting function defined on the vertex set, the minimum weight vertex cover problem is to find a vertex subset whose total weight is minimum subject to the premise that the selected vertices cover all edges in the graph. In this paper, we introduce a meta-heuristic based upon the Ant Colony Optimization (ACO) approach, to find approximate solutions to the minimum weight vertex cover problem. In the literature, the ACO approach has been successfully applied to several well-known combinatorial optimization problems whose solutions might be in the form of paths on the associated graphs. A solution to the minimum weight vertex cover problem however needs not to constitute a path. The ACO algorithm proposed in this paper incorporates several new features so as to select vertices out of the vertex set whereas the total weight can be minimized as much as possible. Computational experiments are designed and conducted to study the performance of our proposed approach. Numerical results evince that the ACO algorithm demonstrates significant effectiveness and robustness in solving the minimum weight vertex cover problem.

Minimum weight of cold-formed steel sections under compression

Abstract: This paper presents a combined theoretical and experimental study on the minimum weight and the associated optimal geometric dimensions of an open-channel steel section with given length subjected to a prescribed axial compressive load. Sections both with and without lips are analyzed. The results obtained using a nonlinearly constrained optimization method are compared with those estimated from a simple-minded optimization procedure that assumes the simultaneous occurrence of all failure modes in a minimum weight structure. The types of failure mode considered include yielding, flexural buckling, torsional–flexural buckling, and local buckling. The failure criterion is based purely on compressive strength, with other possible design constraints (e.g. bending stiffness, minimum gauge and cost) ignored. The effects of end support conditions and restraint on torsional buckling are examined. The load capacity of a C-section calculated according to the 1998 British Standard Institution’s specifications on Structural Use of Steelwork in Building is used to check the validity of theoretical predictions. Finally, two new C-sections with lips were designed and manufactured based on the optimal results, and tested. Test results confirm the analytical predictions, with the optimal C-sections performing much better than the existing ones.

On Random Symmetric Travelling Salesman Problems

Abstract: Let the edges of the complete graphK nbe assigned independent uniform [0, 1] random edge weights. LetZTSP andZ2FAC be the weights of the minimum length travelling salesman tour and minimum weight 2-factor, respectively. We show thatwhp | ZTSP -Z2FAC| =o(1). The proof is obtained by the analysis of a polynomial time algorithm that finds a tour only a little longer thanZ2FAC.

A Lower Bound On The Integrality Gap For Minimum Multicut In Directed Networks

Abstract: Given a directed edge-weighted graph and k source-sink pairs, the Minimum Directed Multicut Problem is to find an edge subset with minimal weight, that separates each source-sink pair Determining the minimum multicut in directed or undirected graphs is NP-hard The fractional version of the minimum multicut problem is dual to the maximum multicommodity flow problem The integrality gap for an instance of this problem is the ratio of the minimum weight multicut to the minimum weight fractional multicut; trivially this gap is always at least 1 and it is easy to show that it is at most k In the analogous problem for undirected graphs this upper bound was improved to O(log k)In this paper, for each k an explicit family of examples is presented each with k source-sink pairs for which the integrality gap can be made arbitrarily close to k This shows that for directed graphs, the trivial upper bound of k can not be improved

Global optimization of minimum weight truss topology problems with stress, displacement, and local buckling constraints using branch‐and‐bound

Abstract: We present a convergent continuous branch-and-bound algorithm for global optimization of minimum weight truss topology problems with displacement, stress, and local buckling constraints. Valid inequalities which strengthen the problem formulation are derived. The inequalities are generated by solving well-defined convex optimization problems. Computational results are reported on a large collection of problems taken from the literature. Most of these problems are, for the first time, solved with a proof of global optimality. Copyright © 2004 John Wiley & Sons, Ltd.

The 2-path network problem

Abstract: Given a graph with nonnegative edge weights and a set D of node pairs, the 2-path network problem requires a minimum weight set of edges such that the induced subgraph contains a path with one or two edges connecting each pair in D. The problem is NP-hard. We present two integer programming models for the problem and study properties of associated polytopes, including cutting planes. Two approximation algorithms are suggested and analyzed. Some computational experience is reported. © 2004 Wiley Periodicals, Inc.

On the value of a random minimum weight

Abstract: Consider a complete graph on n vertices with edge weights chosen randomly and independently from an exponential distribution with parameter 1. Fix k vertices and consider the minimum weight Steiner tree which contains these vertices. We prove that with high probability the weight of this tree is (1+o(1))(k-1)(log n-log k)/n when k =o(n) and n→∞.

Construction of minimum-weight spanners

Abstract: Spanners are sparse subgraphs that preserve distances up to a given factor in the underlying graph. Recently spanners have found important practical applications in metric space searching and message distribution in networks. These applications use some variant of the so-called greedy algorithm for constructing the spanner — an algorithm that mimics Kruskal’s minimum spanning tree algorithm. Greedy spanners have nice theoretical properties, but their practical performance with respect to total weight is unknown. In this paper we give an exact algorithm for constructing minimum-weight spanners in arbitrary graphs. By using the solutions (and lower bounds) from this algorithm, we experimentally evaluate the performance of the greedy algorithm for a set of realistic problem instances.

Genetic algorithm based optimum design of non-linear steel frames with semi-rigid connections

Abstract: In this article, a genetic algorithm based optimum design method is presented for non-linear steel frames with semi-rigid connections. The design algorithm obtains the minimum weight frame by selecting suitable sections from a standard set of steel sections such as European wide flange beams (i.e., HE sections). A genetic algorithm is employed as optimization method which utilizes reproduction, crossover and mutation operators. Displacement and stress constraints of Turkish Building Code for Steel Structures (TS 648, 1980) are imposed on the frame. The algorithm requires a large number of non-linear analyses of frames. The analyses cover both the non-linear behaviour of beam-to-column connection and P-∆ effects of beam-column members. The Frye and Morris polynomial model is used for modelling of semi-rigid connections. Two design examples with various type of connections are presented to demonstrate the application of the algorithm. The semi-rigid connection modelling results in more economical solutions than rigid connection modelling, but it increases frame drift.

Topology Optimization with the Homogenization and the Level-Set Methods

Abstract: After a brief review of the homogenization and level-set methods for structural optimization we make some comparisons of their numerical results. The typical problem is to find the optimal shape of an elastic body which is both of minimum weight and maximal stiness under specified loadings. This problem is known to be “ill-posed”, namely there is generically no optimal shape and the solutions computed by classical numerical algorithms are highly sensitive to the initial guess and mesh-dependent. The homogenization method makes this problem well-posed by allowing microperforated composites as admissible designs. It induces new numerical algorithms which capture an optimal shape on a fixed mesh. The homogenization method is able to perform topology optimization since it places no explicit or implicit restriction on the topology of the optimal shape. The level-set method instead does not change the ill-posed nature of the problem. It is a combination of the level-set algorithm of Osher and Sethian with the classical shape gradient (or boundary sensitivity). Although this last method is not specifically designed for topology optimization, it can easily handle topology changes. Its cost is also moderate since the shape is captured on a fixed Eulerian mesh. We discuss their respective advantages and drawbacks.

Integrated Structural and Control Optimization

Abstract: This paper focuses on the integrated structural/control optimization of a large space structure with a robot arm subject to the gravity-gradient torque through a semi-analytical approach. It is well known that the computer effort to compute numerically derivatives of the constraints with respect to design variables makes the process expensive and time-consuming. In this sense, a semi-analytical approach may represent a good alternative when optimizing systems that require sensitivity calculations with respect to design parameters. In this study, constraints from the structure and control disciplines are imposed on the optimization process with the aim of obtaining the structure’s minimum weight and the optimum control performance. In the process optimization, the sensitivity of the constraints is computed by a semi-analytical approach. This approach combines the use of analytical derivatives of the mass and stiffness matrices with the numerical solution of the eigenvalue problem to obtain the eigenvalue d...

Degree-bounded minimum spanning trees.

Abstract: Given n points in the Euclidean plane, the degree-@d minimum spanning tree (MST) problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most @d. The problem is NP-hard for 2@?@d@?3, while the NP-hardness of the problem is open for @d=4. The problem is polynomial-time solvable when @d=5. By presenting an improved approximation analysis for Chan's degree-4 MST algorithm [T. Chan, Euclidean bounded-degree spanning tree ratios, Discrete & Computational Geometry 32 (2004) 177-194], we show that, for any arbitrary collection of points in the Euclidean plane, there always exists a degree-4 spanning tree of weight at most (2+2)/3<1.1381 times the weight of an MST.

A study on lower bound of direct proportional length-based DNA computing for shortest path problem

Abstract: Previously, we proposed a direct proportional length-based DNA computing approach for weighted graph problem. The approach has been proposed essentially to overcome the shortcoming of constant proportional length-based DNA computing approach. However, by using this approach, the minimum weight of edges that can be encoded is limited. Hence, in this paper, the lower bound, in term of minimum weight that can be encoded by direct proportional length-based DNA computing is analyzed. Also, the parameters contribute to the lower bound are investigated in order to identify the relation between those parameters and the lower bound of the direct proportional length-based DNA computing approach.

Wing structural weight evolution with the cruise mach number of a commercial transport aircraft

Abstract: The present work performs a detailed analysis of the impact of the cruise speed of a commercial twinjet transport aircraft on its wing structural weight. The results will provide designers some guidelines for conceptual studies, when a cruise speed must be then specified. Some assumptions were made in order to conduct the proposed analysis: the fuel shall be store d in the wings only; the same fuselage was considered for all configurations, regardless of their cruise speed; and a maximum range of 3,695 nm (6,843 km). An algorithm named Asa Turbo was developed for the estimation of the initial wing configuration. By fulfilling design requirements and employing a performance calculation code, the procedure is able to calculate the corresponding lift coefficient and wing geometry parameters such as sweep angle, area, and airfoil maximum thickness, additionally providing an initial estimation for the wing structural weight according to the Torenbeek’s method. In order to better calculate the wing structural weight, a framework for wing structure preliminary design was employed. A code developed as PDWSW, which stands for Pre-Design Wing Structural Weight, was conceived to satisfy structural constraints as well as design requirements, based on load envelops and stress analyses under a Knowledge Based Engineering (KBE) environment. PDWSW outputs a minimum-weight structural configuration for a given wing planform. In order to start the weight estimation procedure, the wing conceptual -design Asa Turbo generated ten wing geometries for different cruise Mach numbers, ranging from Mach 0.75 to 0.90. All these wings were then modeled with CATIA ® and their structural design was considerably refined with the PDWSW framework. In order to utilize PDWSW, the user must define the position of the spars, ribs, and stringers and provide all preliminary dimensions of wings structure elements to obtain the minimum weight, within the required boundary safety. The numerical procedure implemented obtains the optimal number of ribs per wing box (main and trailing), the optimal number of stringers per rib bay, and optimal sizing of all structural components (skin, spars, ribs and stringers). This procedure guarantees that acceptable margins of safety and functionality requirements are fulfilled. The automation of the process is important in this particular application considering the enormous amount of data to be handled in a short period of time.

Local zooming genetic algorithm and its application to radial gate support problems

Abstract: On the basis of a structural analysis of radial gate (i.e. Tainter gate), the current paper focuses on weight minimization according to the location of the arms on a radial gate. In spite of its economical significance, there are hardly any previous studies on the optimum design of radial gate. Accordingly, the present study identifies the optimum position of the support point for a radial gate that guarantees the minimum weight satisfying the strength constraint conditions. This study also identifies the optimum position for 2 or 3 radial arms with a convex cylindrical skin plate relative to a given radius of the skin plate curvature, pivot point, water depth, ice pressure, etc. These optimum designs are then compared with previously constructed radial gates. Local genetic and hybrid-type genetic algorithms are used as the optimum tools to reduce the computing time and enhance the accuracy. The results indicate that the weights of the optimized radial gates are appreciably lower than those of previously constructed gates.

A Comparision Between ANSYS Optimizationand GA in the Truss Structure

Abstract: For a ten-bar truss optimization problem of seeking the minimum weight, both ANSYS and genetic algorithms(GA)are used for camparing.The result shows that GA is more effective in the optimization of the truss structure.

On the Minimum Weight of Codes over F 5 Constructed from Certain Conference Matrices

Abstract: In this paper, codes over F5 with parameters [36, 18, 12], [48, 24, 15], [60, 30, 18], [64, 32, 18] and [76, 38, 21] which improve the previously known bounds on the minimum weight for linear codes over F5 are constructed from conference matrices. Through shortening and truncating, the above codes give numerous new codes over F5 which improve the previously known bounds on minimum weights.

Structural Design Of A Composite Aileron Using AMulti-step Integrated Procedure

Abstract: This work describes the structural design of a composite material aileron of a business aircraft with the target of weight reduction with respect to the metallic reference baseline. It proposes a multi-step procedure for the design and analysis of a composite material structure. A carbon-epoxy material is used for the structural item. An integrated procedure (FEM/analytical and computational formulations) for the design and analysis is developed. In the first level the structural item is considered as concentrated elements. The internal loads are evaluated by elementary theory and a preliminary layup configuration for the structural components (skin, spar, etc.) is chosen by means of a stand-alone approach using a structural sizing software. In the next step a finite element model of the structural item is developed with the preliminary layups, and a general-purpose finite element software is used to evaluate the internal FEA loads acting on the different structural components. Finally the finite element model (geometry and internal loads) is imported into the structural sizing software, which chooses, for the different structural parts, the best layup satisfying the minimum weight requirement. The iterative procedure FEM/structural sizing software is defined and it runs until a convergent solution is obtained. The aileron is designed at ultimate loads and a weight reduction of about 14% respect to the metallic baseline is achieved. The skin and the spar are made of solid laminate and a foam material is used at the trailing edge for shape stability according to RTM technology constraints.

Pseudo-Topology and Sizing Optimization of a Composite Advanced Sail Structure with Buckling Constraints

Abstract: Through linear and nonlinear design variable-to-sizing relationships, low- and highcomplexity finite element models of a composite advanced sail (CAS) structure are developed and optimized to determine the optimal placement of internal stiffeners in presence of stringent stability constraints associated with many closely clustered local buckling modes. The pseudo-topology optimization problem is formulated and solved as a constrained sizing optimization problem for minimum strain energy. To improve the computational efficiency of the high-complexity model, the contribution of the geometric stiffness matrix to the buckling sensitivities are ignored with no significant loss of accuracy. Based on the results of the pseudo-topology optimization for the low- and high-complexity models, a detailed finite-element model of the new CAS design with optimal stiffener layout is developed and optimized for minimum weight. Depending upon the degree of variability in skin thickness, the results show a weight saving of up to 19% over the baseline model while satisfying all structural requirements.

Sequence clustering alignment method by fragment

Abstract: PROBLEM TO BE SOLVED: To perform a clustering process which classifies sequences for every group having sequences with many common parts and an alignment process for clarifying a correspondence of each part of the sequences in the group, when information on a partial sequence, that is common in a plurality of sequences and is a result of comparison of the plurality of sequences, and on partial sequences which only exist in specific base sequences is given. SOLUTION: A directive graph having their fragments as nodes is built based on the given fragment information. After deleting closed way from this directive graph, the minimum weight route is identified by using a known method for searching for the minimum weight route. The sequence having many common parts is identified based on the fragment sequence corresponding to this route. Further, each sequence is multiple-aligned at a fragment unit by utilizing the minimum weight route. COPYRIGHT: (C)2006,JPO&NCIPI

A Constraint Handling Strategy for Bit-Array Representation GA in Structural Topology Optimization

Abstract: In this study, an improved bit-array representation method for structural topology optimization using the Genetic Algorithm (GA) is proposed. The issue of representation degeneracy is fully addressed and the importance of structural connectivity in a design is further emphasized. To evaluate the constrained objective function, Deb’s constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the GA. A hierarchical violation penalty method is proposed to drive the GA search towards the topologies with higher structural performance, less unusable material and fewer separate objects in the design domain in a hierarchical manner. Numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this novel bit-array representation method and suggest that the GA performance can be significantly improved by handling the design connectivity properly.

Structural Optimization in Aircraft Engineering using Support Vector Machines

Abstract: The minimum weight design of structures made of fiber reinforced composite materials leads to a class of discrete optimization problems for which evolutionary algorithms (EAs) are well suited. Based on these algorithms the optimization tool package GEOPS has been developed at TU Dresden.

Minimum weight design of a high authority flexural actuator based on electro-elastomers

Abstract: A flexural actuator based on the operating principles of electro-elastomers has been proposed. The actuating element comprises multilayers of the electro-elastomer and a helical spring. The variables are the geometrical dimensions and the failure modes. A design that integrates this basic unit into a high authority flexural system has been analyzed. An optimization procedure has been devised and used to determine preferred designs. The analysis establishes the authority (product of end displacement and load to be lifted), at a specified electric field by determining the minimum weight as a function of the actuation strain and the number of electro-elastomer layers, nfilm. The dimensions of the constituents at the minimum weight emerge from the analysis. A comparison with a flexural actuator made using a one-way shape memory alloy reveals the performance advantages of the electro-elastomer system. An assessment of the variation in minimum weight with nfilm has provided a basis for a future weight/cost trade-off analysis.

Structural Design Using Genetic Algorithm

Abstract: This paper describes the topology and the shape optimization scheme of continuum structures by using genetic algorithm (GA) and boundary element method (BEM). Structure profile is defined by the help of spline function surfaces. Then, the genetic algorithm is applied for determining the structure profile satisfying the design objectives and the constraint conditions. The present scheme is applied to minimum weight design of two-dimensional elastic problems in order to confirm the validity.

Domain Decomposition in Displacement Based Multi-Level Structural Optimization

Abstract: *† ‡ This paper presents the latest efforts to increase the capabilities of the Displacement based Multilevel Structural Optimization (DMSO) methodology and to improve the efficiency of DMSO in the treatment of large models. The DMSO approach optimizes structures for minimum weight by utilizing a single system level and multiple subsystems level optimizations. In the system level optimization, the load unbalance resulting from the use of approximate nodal displacements in the stiffness equations is minimized to ensure that the calculated loads match the actual applied loads. The system level optimization can be replaced with a system level FEM analysis to reduce execution time, but then the system level design can no longer be constrained. In the subsystems level optimizations, the weight of each element is minimized. Since the subsystems level optimizations are independent of each other, they can be performed in parallel. This has been done previously using the Message Passing Interface (MPI) on PCs, a network of SUN workstations, and on a Linux cluster. Now, the system level FE analysis and optimization are parallelized as well by using domain decomposition and a superelement formulation. Results are presented for a 30element truss, a 240-element truss, and a 2514-element truss for evaluation purposes. These demonstrate that runtime decreases due to the parallelization of the system level and/or the subsystems level.