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Showing papers on "Minimum weight published in 2008"


Journal ArticleDOI
TL;DR: It is NP-hard to approximate the Steiner tree problem within a factor 96/95, and explicit hardness factors would be improved automatically by providing gadgets and/or expanders with better parameters.

142 citations


Journal ArticleDOI
TL;DR: In this article, the optimum design of geometrically nonlinear steel space frames using tabu search and genetic algorithm was presented. But the results showed that the former algorithm resulted in lighter structures.

60 citations


Journal ArticleDOI
TL;DR: In this paper, an ant algorithm consisting of the Ant System and API (after “apicalis” in Pachycondylaapsicalis) was proposed to find optimal truss structures to achieve minimum weight objective under stress, deflection, and kinematic stability constraints.
Abstract: An ant algorithm, consisting of the Ant System and API (after “apicalis” in Pachycondylaapicalis) 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.

60 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the general problem of finding the minimum weight b-matching on arbitrary graphs and prove that, whenever the linear programing relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution for synchronous and asynchronous updating.
Abstract: We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programing relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating.

58 citations


Journal ArticleDOI
TL;DR: In this paper, a harmony search algorithm is presented for optimum design of steel frame structures, which is based on the analogy between the performance process of natural music and searching for solutions of optimization problems, and the results of the algorithm were compared to those of other optimization algorithms such as genetic algorithm, optimality criterion and simulated annealing for two planar and two space frame structures taken from the literature.
Abstract: In this article, a harmony search algorithm is presented for optimum design of steel frame structures. Harmony search is a meta-heuristic search method which has been developed recently. It is based on the analogy between the performance process of natural music and searching for solutions of optimization problems. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress Design (ASD) specifications, maximum (lateral displacement) and interstorey drift constraints, and also size constraint for columns were imposed on frames. The results of harmony search algorithm were compared to those of the other optimization algorithms such as genetic algorithm, optimality criterion and simulated annealing for two planar and two space frame structures taken from the literature. The comparisons showed that the harmony search algorithm yielded lighter designs for the design examples presented.

55 citations


Journal ArticleDOI
TL;DR: The results show that if the weight measure on the error vectors is the Hamming weight, the capability of a linear code is fully characterised by a single minimum distance, while for a nonlinear code, two different minimum distances are needed for characterising the capabilities of the code for error correction and for errordetection.
Abstract: In this paper, we first study the error correction and detection capability of codesfor a general transmission system inspired by network error correction. For a given weight measure on the error vectors, we define a corresponding minimum weight decoder. Then we obtain a complete characterisation of the capability of a code for (1) error correction; (2) error detection and (3) joint error correctionand detection. Our results show that if the weight measure on the error vectors is the Hamming weight, the capability of a linear code is fully characterised by a single minimum distance. By contrast, for a nonlinear code, two different minimum distances are needed for characterising the capabilities of the code for error correction and for errordetection. This leads to the surprising discovery that for a nonlinear code, the numberof correctable errors can bemore than half of the number of detectable errors. We also present a framework that captures joint error correction and detection. We further define equivalence classes of weight measures with respect to a channel. Specifically, for any given code, the minimum weight decoders for two different weight measures are equivalent if the two weight measures belong to the same equivalence class. In the special case of linear network coding, we study three weight measures, and show that they are inthe same equivalence class of the Hamming weight and induce the same minimum distance as the Hamming weight. Copyright © 2008 John Wiley & Sons, Ltd.

51 citations


Journal ArticleDOI
TL;DR: In this paper, failure maps are presented for a number of candidate high-temperature metallic alloys and ceramic composites, allowing direct comparison of their thermostructural performance.
Abstract: This article provides a materials selection methodology applicable to lightweight actively cooled panels, particularly suitable for the most demanding aerospace applications. The key ingredient is the development of a code that can be used to establish the capabilities and deficiencies of existing panel designs and direct the development of advanced materials. The code is illustrated for a fuel-cooled combustor liner of a hypersonic vehicle, optimized for minimum weight subject to four primary design constraints (on stress, temperatures, and pressure drop). Failure maps are presented for a number of candidate high-temperature metallic alloys and ceramic composites, allowing direct comparison of their thermostructural performance. Results for a Mach 7 vehicle under steady-state flight conditions and stoichiometric fuel combustion reveal that, while C-SiC satisfies the design requirements at minimum weight, the Nb alloy Cb752 and the Ni alloy Inconel X-750 are also viable candidates, albeit at about twice the weight. Under the most severe heat loads (arising from heat spikes in the combustor), only Cb752 remains viable. This result, combined with robustness benefits and fabrication facility, emphasizes the potential of this alloy for scramjets.

43 citations


Journal ArticleDOI
TL;DR: An exact and a heuristic algorithm is presented, based on new theoretical results for quadratic and convex optimization problems, that are able to solve StQP problems of at least one order of magnitude larger than those reported in the literature.

38 citations


Book ChapterDOI
14 May 2008
TL;DR: A faster exact exponential time algorithm for the edge dominating set problem and gives faster exact algorithms for: minimum weightedge dominating set, minimum (weight) maximal matching, matrix domination and the parametrised version of minimum weight maximal matching.
Abstract: In this paper we present a faster exact exponential timealgorithm for the edge dominating set problem. Our algorithm usesO(1.3226n) time and polynomial space. The algorithm combines an enumerationapproach based on enumerating minimal vertex covers withthe branch and reduce paradigm. Its time bound is obtained using themeasure and conquer technique. The algorithm is obtained by startingwith a slower algorithm which is refined stepwise. In this way a series ofalgorithms appears, each one slightly faster than the previous, resultingin the O(1.3226n) time algorithm. The techniques also gives faster exact algorithms for: minimum weightedge dominating set, minimum (weight) maximal matching, matrix dominationand the parametrised version of minimum weight maximal matching.

28 citations


Journal ArticleDOI
TL;DR: In this paper, a new general representation for the minimum weight Steiner tree problem was proposed that translates the topological connectivity constraint into a set of local conditions, which can be analyzed by the so-called cavity equation techniques.
Abstract: We analyze a new general representation for the minimum weight Steiner tree problem that translates the topological connectivity constraint into a set of local conditions, which can be analyzed by the so-called cavity equation techniques. For the limit case of the spanning tree, we prove that the fixed point of the algorithm arising from the cavity equations leads to the global optimum.

28 citations


Posted Content
TL;DR: In this article, an idea of the cutting plane method is employed to improve the fractional distance of a given binary parity check matrix, which is the minimum weight (with respect to l 1-distance) of vertices of the fundamental polytope.
Abstract: In this paper, an idea of the cutting plane method is employed to improve the fractional distance of a given binary parity check matrix. The fractional distance is the minimum weight (with respect to l1-distance) of vertices of the fundamental polytope. The cutting polytope is defined based on redundant rows of the parity check matrix and it plays a key role to eliminate unnecessary fractional vertices in the fundamental polytope. We propose a greedy algorithm and its efficient implementation for improving the fractional distance based on the cutting plane method.

Journal ArticleDOI
TL;DR: It is obtained that for someLDPC codes, there are no other minimum pseudocodewords except the real multiples of minimum weight codewords, which means that the LP decoding for these LDPC codes is asymptotically optimal in the sense that the ratio of the probabilities of decoding errors of LP decoding and maximum-likelihood decoding approaches as the signal-to-noise ratio (SNR) tends to infinity.
Abstract: In this correspondence, we study the minimum pseudoweight and minimum pseudocodewords of low-density parity-check (LDPC) codes under linear programming (LP) decoding. First, we show that the lower bound of Kelley, Sridhara, Xu, and Rosenthal on the pseudoweight of a nonzero pseudocodeword of an LDPC code whose Tanner graph has girth greater than is tight if and only if this pseudocodeword is a real multiple of a codeword. Then, the lower bound of Kashyap and Vardy on the stopping distance of an LDPC code is proved to be also a lower bound on the pseudoweight of a nonzero pseudocodeword of an LDPC code whose Tanner graph has girth , and this lower bound is tight if and only if this pseudocodeword is a real multiple of a codeword. Using these results we further obtain that for some LDPC codes, there are no other minimum pseudocodewords except the real multiples of minimum weight codewords. This means that the LP decoding for these LDPC codes is asymptotically optimal in the sense that the ratio of the probabilities of decoding errors of LP decoding and maximum-likelihood decoding approaches as the signal-to-noise ratio (SNR) tends to infinity. Finally, some LDPC codes are listed to illustrate these results.

Journal ArticleDOI
TL;DR: It is shown that one can drop the divisibility condition on the weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979), and an improved upper bound is presented on this minimum weight of C(PG(n,q).
Abstract: In this paper, we study the p-ary linear code C(PG(n,q)), q = p h , p prime, h ? 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the weight of the codewords in Sachar's lower bound (Geom Dedicata 8:407---415, 1979).

Journal ArticleDOI
Yaodong Ni1
TL;DR: This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edgecover model, α -minimum weight edge cover model, and the most minimum weight Edge cover model.

01 Jan 2008
TL;DR: In this paper, the optimum design problem of a grillage system is formulated implementing LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction) limitations and the solution of this discrete programming problem is determined by using the harmony search algorithm.
Abstract: The spacing between the longitudinal and transverse beams of a grillage system has an important effect in the minimum weight design of these systems. In this study this effect is investigated using an optimum design algorithm which is based on recently developed harmony search algorithm. The optimum design problem of a grillage system is formulated implementing LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction) limitations. It is decided that W-Sections are to be adopted for the longitudinal and transverse beams of the grillage system. 169 W-Sections given in LRFD code are collected in a pool and the optimum design algorithm is expected to select the appropriate sections from this pool so that the weight of the grillage is the minimum and the design limitations implemented from the design code are satisfied. The solution of this discrete programming problem is determined by using the harmony search algorithm. This algorithm simulates jazz improvisation into a numerical optimization technique. Design example is presented to demonstrate the effect of beam spacing in the optimum design of grillage systems.

Book ChapterDOI
27 Jun 2008
TL;DR: Improved results are given by giving a (6 + e)-approximation for the minimum weight dominatingset and a (10 + e-approximating for theminimumweight connected dominating set in unit disk graphs whereeis any small positive number.
Abstract: It was a long-standing open problem whether the minimum weightdominating set in unit disk graphs has a polynomial-timeconstant-approximation. In 2006, Ambuhl et alsolvedthis problem by presenting a 72-approximation for the minimumweight dominating set and also a 89-approximation for the minimumweight connected dominating set in unit disk graphs. In this paper,we improve their results by giving a (6 +e)-approximation for the minimum weight dominatingset and a (10 + e)-approximation for the minimumweight connected dominating set in unit disk graphs whereeis any small positive number.

Journal ArticleDOI
TL;DR: It is shown that the class of SFA-LDPC codes which are denoted by CA (p, 4) contains a codeword whose minimum weight is 10 or less, if p is a prime number greater than 7 and the Yang's lower bound on the minimum weight of CA ( p,4) is exactly 10.
Abstract: We investigate the minimum weights of simple full-length array LDPC codes (SFA-LDPC codes). The SFA-LDPC codes are a subclass of LDPC codes, and constructed algebraically according to two integer parameters p and j. Mittelholzer and Yang et al. have studied the minimum weights of SFA-LDPC codes, but the exact minimum weights of the codes are not known except for some small p and j. In this paper, we show that the minimum weights of the SFA-LDPC codes with j = 4 and j = 5 are upper-bounded by 10 and 12, respectively, independent from the prime number p. By combining the results with Yang's lower-bound limits, we can conclude that the minimum weights of the SFA-LDPC codes with j = 4 and p >7 are exactly 10 and those of the SFA-LDPC codes with j = 5 are 10 or 12.

Journal ArticleDOI
TL;DR: The polynomial solvability of the optimal recombination problems (ORPs) is shown, including those for the maximum weight set packing problem, the minimum weight set partition problem, and for linear Boolean programming problems with at most two variables per inequality, and some other problems.
Abstract: We consider the optimization problem of finding the best possible offspring as a result of a recombination operator in an evolutionary algorithm, given two parent solutions. The optimal recombination is studied in the case where a vector of binary variables is used as a solution encoding. By means of efficient reductions of the optimal recombination problems (ORPs) we show the polynomial solvability of the ORPs for the maximum weight set packing problem, the minimum weight set partition problem, and for linear Boolean programming problems with at most two variables per inequality, and some other problems. We also identify several NP-hard cases of optimal recombination: the Boolean linear programming problems with three variables per inequality, the knapsack, the set covering, the p-median, and some other problems.

Journal ArticleDOI
TL;DR: In this paper, a technique for the optimization of stability-constrained geometrically nonlinear shallow trusses with snap-through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite-element formulation.

Journal ArticleDOI
TL;DR: In this article, a distributed version of Fischer's sequential algorithm with time complexity O(n) was proposed, where n is the number of nodes in the network, where D is the maximum degree of an initial minimum weight spanning tree.

Journal ArticleDOI
TL;DR: In this paper, a very simple method for finding the minimum weight of a structure designed from a list of available parameters is presented, where the structure can be subjected to multiple loading conditions with constraints imposed on displacements, stresses and eigenfrequency.
Abstract: A very simple method for finding the minimum weight of a structure designed from a list of available parameters is presented. The structure can be subjected to multiple loading conditions with constraints imposed on displacements, stresses and eigenfrequency. The method consists of a recursive removal of redundant material, starting from the heaviest structure. The number of analyses required is a factor of 102 less than for most stochastic methods. The knowledge needed for application of the method is limited to the finite-element method.

Journal ArticleDOI
TL;DR: Enough conditions for t-properness and a list of codes known to be proper, many of which have been studied by these sufficient conditions, are presented and special attention is paid to error detecting codes of interest in modern communication.

Proceedings ArticleDOI
12 Jul 2008
TL;DR: This paper has successfully proposed the formulation of CM tracing user-defined paths based on the precision points by modifying the NSGA-II algorithm by incorporating a helper objective and a domain specific crossover which assist in generating a diverse set of non-dominated solutions.
Abstract: While designing the Compliant Mechanisms (CM), an equal attention is required on both the problem formulation and the optimization algorithm used. Authors of this paper have successfully proposed the formulation of CM tracing user-defined paths based on the precision points. In this paper, authors modify the NSGA-II algorithm by incorporating (i) a helper objective and (ii) a domain specific crossover which assist in generating a diverse set of non-dominated solutions. First, the single-objective optimization problem of minimizing the weight of structure is solved and named the topology as a reference design. Thereafter, a bi-objective optimization problem is dealt to evolve 'trade-off' solutions for a primary objective of minimizing the weight and a secondary objective of maximizing the diversity with respect to the reference design. Both the optimization problems are solved using a local search based NSGA-II procedure. This study has further compared its results with another GA implementation having a different crossover operator.

Journal ArticleDOI
TL;DR: In this article, an improved genetic algorithm (GA) is proposed to perform the optimal design of a pressure vessel which aims to attain the minimum weight under burst pressure constraint, and the actual burst pressure is calculated using the arc-length and restart analysis in finite element analysis (FEA).
Abstract: As the idea of simulated annealing (SA) is introduced into the fitness function, an improved genetic algorithm (GA) is proposed to perform the optimal design of a pressure vessel which aims to attain the minimum weight under burst pressure constraint. The actual burst pressure is calculated using the arc-length and restart analysis in finite element analysis (FEA). A penalty function in the fitness function is proposed to deal with the constrained problem. The effects of the population size and the number of generations in the GA on the weight and burst pressure of the vessel are explored. The optimization results using the proposed GA are also compared with those using the simple GA and the conventional Monte Carlo method.

Journal ArticleDOI
TL;DR: In this article, the authors presented an optimum design procedure of permanent magnet-type 60W transverse flux linear motor to reduce the weight of the machines with the constraints of thrust and detent forces using fractional factorial design and response surface methodology (RSM).
Abstract: This paper presents an optimum design procedure of permanent-magnet-type 60W transverse flux linear motor to reduce the weight of the machines with the constraints of thrust and detent forces using fractional factorial design and response surface methodology (RSM). RSM is well adapted to make the analytical model of minimum weight with constraints of thrust and detent forces, and it enables objective functions to be easily created, and a great deal of computation time can be saved. Therefore, the usefulness of this method is verified through the comparison of the performances of the optimal model and those of the initial model.

Journal ArticleDOI
TL;DR: An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods for minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses.
Abstract: An optimization procedure is presented for the minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses Both thickness and shape variables defining the natural line of the arch are considered The computer program which is developed in this study can be used to optimize thick, thin and variable thickness curved beams/arches An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods Several examples are presented to illustrate optimal arch structures with smooth shapes and thickness variations The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimization

Posted Content
TL;DR: This work considers the problem of rate and power allocation for a sensor network under the pairwise distributed source coding constraint and shows that the minimum sum rate assignment can be found by finding a minimum weight arborescence in an appropriately defined directed graph.
Abstract: We consider the problem of rate and power allocation for a sensor network under the pairwise distributed source coding constraint. For noiseless source-terminal channels, we show that the minimum sum rate assignment can be found by finding a minimum weight arborescence in an appropriately defined directed graph. For orthogonal noisy source-terminal channels, the minimum sum power allocation can be found by finding a minimum weight matching forest in a mixed graph. Numerical results are presented for both cases showing that our solutions always outperform previously proposed solutions. The gains are considerable when source correlations are high.

Book ChapterDOI
Ning Zhang1, Incheol Shin1, Bo Li1, Cem Boyaci1, Ravi Tiwari1, My T. Thai1 
26 Oct 2008
TL;DR: The paper is the first to study this problem, prove the hardness of this problem and propose an approximation framework, and presents a heuristic to approximate the solution with low time complexity.
Abstract: Our problem formulation is as follows. Given a weighted disk graph Gwhere the weight of edge represents the transmission energy consumption, we wish to determine a dominating tree Tof Gsuch that the total weight of edges in Tis minimized. To the best of our knowledge, this problem have not been addressed in the literature. Solving the dominating tree problem can yield a routing backbone for broadcast protocols since: (1) each node does not have to construct their own broadcast tree, (2) utilize the virtual backbone to reduce the message overhead, and (3) the weight of backbone is minimized. Our contributions to this problem is multi-fold: First, the paper is the first to study this problem, prove the hardness of this problem and propose an approximation framework. Second, we present a heuristic to approximate the solution with low time complexity. Third, a distributed algorithm is provided for practical implementation. Finally, we verify the effectiveness of our proposal through simulation.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the general problem of finding the minimum weight b-matching on arbitrary graphs and prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution for synchronous and asynchronous updating.
Abstract: We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating.

01 Jan 2008
TL;DR: Different alternatives to consider stress constraints and some important ideas about the numerical implementation of these algorithms are proposed.
Abstract: Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsoe and Kikuchi in 1988, most of the work has been dedicated to the so-called maximum stiffness (or minimum compliance) formulations. However, a growing effort is being invested since a few years in the possibility of stating and solving this kind of problems in terms of minimum weight with stress (and/or displacement) constraints formulations. These formulations give rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraints must be taken into account. In an attempt to reduce the computational requirements of these problems, in this paper, we propose different alternatives to consider stress constraints and some important ideas about the numerical implementation of these algorithms. Finally, we present some application examples.