Showing papers on "Minimum weight published in 1996"
TL;DR: In this paper, the authors considered the problem of finding a tree of minimum weight spanning at least k nodes in an edge-weighted graph and showed that the problem is NP-hard even for points in the Euclidean plane.
Abstract: We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of treewidth-bounded graphs, which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane.
We also investigate the problem of finding short trees and, more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.
135 citations
TL;DR: In this work a population of binary strings or ‘chromosomes’ are used, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population.
Abstract: Genetic algorithms, a search technique which combines Darwinian ‘survival-of-the-fittest’ with randomized well structured information, is applied to the problems of real-world truss optimization. In this work a population of binary strings or ‘chromosomes’, which represent the coded truss design variables, a ‘fitness’ as a ranking measure of the adaptability to the environment, selection criteria and mechanical natural operators such as crossover and mutation are used to improve the population, so that over the generations the genetic algorithm gets better and better and at the end of the convergence, a ‘rebirth’ of the population is used to improve the usual process.
An overview of the genetic algorithm will be described, continuing the rebirth effect; then, the chromosome representation of trusses is exposed. Afterwards, the objective scalar function is defined taking into account that it seems reasonable in real world to optimize trusses in minimum weight trying, at the same time, to use the minimum number of cross-section types obtained from the market. It also seems reasonable to have the possibility to change the shape of the conceptual design, moving some joints. To simulate nearly real conditions, several load cases, constraints in the elastic joint displacements, ultimate tensile and elastic and plastic buckling in the bars have been taken into account. A hyperstatic 10 bars truss is subjected to a deep analysis in different situations in order to evaluate with other authors when possible as truss optimization with two criteria and buckling effect has not been found in specialized literature. A 160-bar transmission tower is also optimized.
123 citations
28 Jan 1996
TL;DR: The answer to the first question is that the known lower bound is tight, and the second question is answered in the affirmative by using a slight modification of anO(nlogn) algorithm for the greedy triangulation.
Abstract: This article settles the following two longstanding open problems:?What is the worst case approximation ratio between the greedy triangulation and the minimum weight triangulation??Is there a polynomial time algorithm that always produces a triangulation whose length is within a constant factor from the minimum?The answer to the first question is that the known lower bound is tight. The second question is answered in the affirmative by using a slight modification of anO(nlogn) algorithm for the greedy triangulation. We also derive some other interesting results. For example, we show that a constant-factor approximation of the minimum weight convex partition can be obtained within the same time bounds.
82 citations
TL;DR: In this paper, the authors evaluate two structural design methods for application in an aircraft synthesis code and quantifies the differences between these methods for joined wings in terms of weight, stress, direct operating cost, and computational time.
Abstract: The joined wing is an innovative aircraft configuration with a rear wing, or horizontal tail, that is attached near the top of the vertical tail and sweeps forward to join the trailing edge of the main wing. This study evaluates two structural design methods for application in an aircraft synthesis code and quantifies the differences between these methods for joined wings in terms of weight, stress, direct operating cost, and computational time. A minimum weight optimization method and a fully stressed design method are used to design joined-wing structures. Both methods determine the sizes of 204 structural members, satisfying 1020 stress constraints and five buckling constraints. Monotonic splines are shown to be a very effective way of linking spanwise distributions of material to a few design variables. Five beam buckling constraints for the horizontal tail are included in both design methods. Without this constraint on buckling, the fully stressed design is shown to be very similar to the minimum weight structure. Adding a beam buckling constraint for the horizontal tail increased the structural weight by 13% and produced a fully stressed design that is 0.9% heavier than the minimum weight structure. Using the minimum weight optimization method to design the structure and to save 0.9% in weight required 20 times the computational time. Furthermore, the minimum weight structure produced only a 0.02% savings in direct operating cost. This study suggests that a fully stressed design method based on nonlinear analysis is adequate for a joined-wing synthesis study. The same joined wing considered in this study was shown, in an earlier study, to be slightly more expensive to operate than a conventional configuration designed for the same medium range transport mission. Since the same fully stressed design method was used in this earlier study, this work supports the comparisons of joined-wing and conventional aircraft performance presented in the earlier study. Of course, a different set of mission specifications and design assumptions may produce joined wings that perform significantly better.
79 citations
TL;DR: In this article, the problem of optimum truss topology design based on the ground structure approach is considered, and it is shown that any minimum weight truss design (computed subject to equilibrium of forces and stress constraints with the same yield stresses for tension and compression) is subject to static equilibrium and a weight constraint.
Abstract: The problem of optimum truss topology design based on the ground structure approach is considered. It is known that any minimum weight truss design (computed subject to equilibrium of forces and stress constraints with the same yield stresses for tension and compression) is—up to a scaling—the same as a minimum compliance truss design (subject to static equilibrium and a weight constraint). This relation is generalized to the case when different properties of the bars for tension and for compression additionally are taken into account. This situation particularly covers the case when a structure is optimized which consists of rigid (heavy) elements for bars under compression, and of (light) elements which are hardly/not able to carry compression (e.g. ropes). Analogously to the case when tension and compression is handled equally, an equivalence is established and proved which relates minimum weight trusses to minimum compliance structures. It is shown how properties different for tension and compression pop up in a modified global stiffness matrix now depending on tension and compression. A numerical example is included which shows optimal truss designs for different scenarios, and which proves (once more) the big influence of bar properties (different for tension and for compression) on the optimal design.
57 citations
TL;DR: In this paper, the authors extended the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates, where two kinds of constraint conditions are considered in the EA method.
Abstract: This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.
37 citations
03 Jun 1996
TL;DR: In this article, a non-crossing property of minimum 3-cuts was established and a performance bounding technique based on cut trees was proposed for graph partitioning problems in weighted, undirected graphs.
Abstract: This paper describes two results on graph partitioning. Our first result is a non-crossing property of minimum 3-cuts. This property generalizes the results by Gomory-Hu on min-cuts (2-cute) in graphs. We also give an algorithm for finding minimum 3-cuts in O(n3) Max-Flow computations. The second part of the paper describes a Performance Bounding technique based on Cut Trees for solving Partitioning Problems in weighted, undirected graphs. We show how to use this technique to derive approximation algorithms for two problems, the Minimum k-cut problem and the Multi-way cut problem.Our first illustration of the bounding technique is an algorithm for the Minimum k-cut which requires O(kn(m + n log n)) steps and gives an approximation of 2(1-1/k). We then generalise the Bounding Technique to achieve the approximation factor 2 — f(j, k) wheref(j, k) = j/k — (j — 2)/k2 + O(j/k3), j ≥ 3. The algorithm presented for the Minimum k-cut problem is polynomial in n and k for fixed j. We also give an approximation algorithm for the planar Multi-way Cut problem.
30 citations
DOI•
01 Jan 1996TL;DR: In this paper, an extended study of the combinatorial optimization technique known as simulated annealing (SA) applied to the minimum weight design of plane trusses subject to a multiple loading case is reported.
Abstract: In this paper an extended study of the combinatorial optimization technique known as simulated annealing (SA) applied to the minimum weight design of plane trusses subject to a multiple loading case is reported The main tool for this study was a modular program developed in C where the truss structure may be optimized over an N-dimensional space of continuous values for the member cross sectional areas or a discrete set of chosen values A new heuristic is introduced in the SA's generation mechanism to perform changes in the topology of the structure while the member cross-sectional areas are minimized, enabling the program to remove the redundant members, for generating reduced structures
30 citations
01 May 1996
25 citations
TL;DR: In this article, the shape optimization of a cracked shell under complex criteria is studied, where the shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turbo-haft.
Abstract: The authors study the shape optimization of a complex cracked shell under complex criteria. The shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turboshaft. The optimization criteria involved are of course the weight of the structure, but also the plastic instability and critical stress intensity factor. All computations have been made with the Ansys finite element program in which an optimization module exists.
24 citations
TL;DR: The main result is that, in a certain sense, thealgebraicsolutions of SC(w) are in one-to-one correspondence with all the codewords ofChaving weight lower thanw, in the particular case wherewis the minimum distance ofC, all minimum weightcodewords are described by SC (w).
Journal Article•
TL;DR: In this paper, a primal-dual algorithm was proposed to determine a minimum weight bibranching in a weighted digraph with running time O(n?(m+nlogn)), wherem=|A|,n=|V| andn?=min{|S|,|V\S|}.
Abstract: Given a directed graphD=(V,A) and a setS?V, a bibranching is a set of arcsB?Athat contains av?(V\S) path for everyv?Sand anS?vpath for everyv?V\S. In this paper, we describe a primal?dual algorithm that determines a minimum weight bibranching in a weighted digraph. It has running timeO(n?(m+nlogn)), wherem=|A|,n=|V| andn?=min{|S|,|V\S|}. Thus, our algorithm obtains the best known bounds for two important special cases of the problem: bipartite edge cover andr-branching.
TL;DR: This work provides a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties of their dual trees and exploits this characterization to devise a linear time algorithm that receives as input a maximal outerplanar graph G and produces as output a straight-line drawing of G that is a minimum weight Triangulation of the set of points representing the vertices of G.
Journal Article•
TL;DR: In this article, a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton is proposed, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al.
Abstract: We present improvements in finding the LMT-skeleton, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al, and Dickerson and Montague. Our improvements consist of: (1) A criteria is proposed to identify edges in all minimum weight triangulations, which is a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton; (2) A worst-case efficient algorithm is presented for performing one pass of Dickerson and Montague's method (with our new criteria); (3) Improvements in the implementation that may lead to substantial space reduction for uniformly distributed point sets.
TL;DR: In this article, the minimum weight design of laminated composite plates subject to strength and side constraints is studied via a constrained global optimization technique. And the effects of the failure criteria on the optimal design parameters are also investigated via the examples.
Abstract: The minimum weight design of laminated composite plates subject to strength and side constraints is studied via a constrained global optimization technique. The first-ply failure load that is treated as the strength of a laminated plate is determined by using a shear deformable finite element and one of the several commonly used phenomenological failure criteria. The optimal layer group parameters (fiber angles and thicknesses of layer groups) of the laminated composite plate are determined via the proposed constrained global optimization technique for attaining the global minimum weight of the plate and satisfying the imposed constraints. A number of examples of the minimum weight design of symmetrically laminated composite plates with various aspect ratios, different number of layer groups, and different boundary conditions are given to illustrate the applications of the present constrained global optimal design method. The effects of the failure criteria on the optimal design parameters are also investigated via the examples. Finally, experimental investigation of the capability of the present method in obtaining global optima is performed. Failure tests of a number of graphite/epoxy laminates designed by different methods are performed, and the superiority of the present method over the other methods is demonstrated via the test results.
TL;DR: The results, obtained using an IBM-compatible microcomputer, assert that the method leads to good results even when a very limited number of modes is used in calculating the sensitivities of the frequency response function.
16 Dec 1996
TL;DR: Improvements in finding the LMT-skeleton, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al, and Dickerson and Montague are presented.
Abstract: We present improvements in finding the LMT-skeleton, which is a subgraph of all minimum weight triangulations, independently proposed by Belleville et al, and Dickerson and Montague. Our improvements consist of: (1) A criteria is proposed to identify edges in all minimum weight triangulations, which is a relaxation of the definition of local minimality used in Dickerson and Montague's method to find the LMT-skeleton; (2) A worst-case efficient algorithm is presented for performing one pass of Dickerson and Montague's method (with our new criteria); (3) Improvements in the implementation that may lead to substantial space reduction for uniformly distributed point sets.
TL;DR: The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values, however, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance.
Abstract: This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.
TL;DR: In this article, a method to design hull structures of surface effect ships with minimum weight is proposed, and computer programs following the method are also developed, and it can be shown that hull weight varies with the change of frame space and there exists optimum frame space.
28 Jan 1996
TL;DR: In this paper, a method for designing the hull of a TLP by a minimum criterion is presented, where the problem of finding the best size of a standard TLP hull with regards to its weight is carried out by adopting a simplified model, depending only on two design variables.
Abstract: This brief note deals with a method for designing the hull of a TLP by a minimum criterion. The very complicated problem of finding the best size of a standard TLP hull with regards to its weight is carried out by adopting a simplified model, depending only on two design variables, which is optimized under the same constraints considered for the effective structure. Subsequently, the dimensions of the hull are found imposing the constancy of the total buoyancy, and using again a minimum weight criterion. The results agree rather well with the cases known.
03 Jun 1996
TL;DR: This work presents a novel and effective approach through the application of interval arithmetic to the multilayer perceptron that allows one to compute strict bounds of the output error of the network and find robust solutions respect to weight inaccuracies.
Abstract: We address in this work the problem of weight inaccuracies in digital and analog feedforward networks. Both kind of implementations suffer from this problem due to physical limits of the particular technology. This work presents a novel and effective approach through the application of interval arithmetic to the multilayer perceptron. Results show that our method allows one to (1) compute strict bounds of the output error of the network, (2) find robust solutions respect to weight inaccuracies and (3) compute the minimum weight precision required to obtain the desired performance of the network.
TL;DR: A numerical model of the shape optimization of a rectangular machine foundation embedded in soil when subjected to external dynamic forces and moments is presented in this article, where a sequential programming method with move limits is used to obtain the minimum weight (mass) of the block.
Abstract: A numerical model of the shape optimization of a rectangular machine foundation embedded in soil when subjected to external dynamic forces and moments is presented. A sequential programming method with move limits is used to obtain the minimum weight (mass) of the block. Numerical examples are given to illustrate the application of the model which takes 3-D dynamic soil-foundation interaction into account.
TL;DR: In this paper, a new philosophy for optimisation of composite structures in relation to lightweight design is presented based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres.
Abstract: This work presents a new philosophy for optimisation of composite structures in relation to lightweight design. It is based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres. The fibres in the composite component micro structure are disposed orthogonally like the minimum weight Michell structures, with voids filled with resin. This is the same mechanical principle which governs the optimisation of natural composites such as bones, horn, trees etc. Based on this natural rule, a procedure to find the optimum topology for the design of optimum composite mechanical components has been developed. A CAD-CAE software system based on finite element analysis using ABAQUS produces interactively on a screen the structure of optimum topology where the optimum fibre arrangement will be made.
Proceedings Article•
03 Jul 1996
TL;DR: This work considers the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length, and finds an optimal partitioning in less than O(n4) time.
Abstract: We consider the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length. This problem is NP-hard for polygons with holes. Even for hole-free polygons no known algorithm can find an optimal partitioning in less than O(n4) time.
TL;DR: In this article, it was shown that the minimum-weight ideal problem for a signed poset can be reduced to a problem of finding a minimumweight (reduced) ideal of the associated ordinary poset and hence to a minimum cut problem.
Abstract: The concept of signed poset has recently been introduced by V. Reiner as a generalization of that of ordinary poset (partially ordered set). We consider the problem of finding a minimum-weight ideal of a signed poset. We show a representation theorem that there exists a bijection between the set of all the ideals of a signed poset and the set of all the \"reduced ideals\" (defined here) of the associated ordinary poset, which was earlier proved by S. D. Fischer in his Ph.D. thesis. I t follows from this representation theorem that the minimum-weight ideal problem for a signed poset can be reduced to a problem of finding a minimum-weight (reduced) ideal of the associated ordinary poset and hence to a minimum-cut problem. We also consider the case when the weight of an ideal is defined in terms of two weight functions. The problem is also reduced to a minimum-cut problem by the same reduction technique as above. Furt,hermore, the relationship between the minimum-weight ideal problem and a certain bisubmodular function minimization problem is revealed.
03 Jul 1996
TL;DR: In this paper, the authors presented an O(n log n) algorithm for the minimum weight convex partition problem with the Delaunay triangulation, which was shown to be NP-hard.
Abstract: Minimizing the total length has been one of the main optimality criteria for triangulations and other kinds of partitions. Indeed, the minimum weight triangulation or MWT (i.e. a triangulation of minimum total edge length) has frequently been referred to as the "optimal triangulation". This triangulation has some good properties [1] and is e.g. useful in numerical approximation of bivariate data [23]. Its complexity is one of the most intriguing problems in computational geometry. No proof has yet been presented showing that it is NP-hard. On the other hand, no polynomial time heuristic for it was shown to guarantee even a constant approximation factor. However, very recently we proved that what we called the quasi-greedy triangulation has length within a constant factor from the minimum [13]. A standard implementation of that heuristic using known results would yield a quadratic time algorithm. In this paper, we improve on this by describing an O(n log n) algorithm for quasi-greedy triangulation. Moreover, if the Delaunay triangulation is given, our algorithm runs in linear time. The minimum weight convex partition (MWCP) problem has been shown to be NP-complete [7, 17]. By a MWCP we mean a set of non-crossing diagonals (i.e. without Steiner points) of minimum total length which includes the convex hull and partitions it into empty convex polygons. In [13] it was shown that, given the quasi-greedy triangulation, a convex partition of length within a constant factor from the MWCP can be computed in linear time. Thus from the results in this paper we also obtain a fast heuristic for approximating the MWCP. The quasi-greedy triangulation is very closely related to the greedy triangulation (both are defined in the next section). In fact, we will describe an algorithm that, given the Delannay triangulation, computes the greedy triangulation in linear time. This algorithm behaves in such a way that it is very easily adapted to yield an algorithm for the quasi-greedy triangulation. Consequently, we also present the first O(n log n) algorithm for greedy triangulation. (By using a substantially different approach, an attempt to develop an O(n log n) algorithm for greedy triangulation was done in [21]. Even if that approach could be corrected
Patent•
12 Jul 1996
TL;DR: In this article, the authors propose an approach to adjust the balance weight of a balance weight in accordance with the weight of the manually operated tool by providing an additional balance weight for adjusting the weight.
Abstract: PROBLEM TO BE SOLVED: To provide a structure capable of adjusting an entire weight so as to perform work without considering the weight of a manually operated tool by providing an additional balance weight for adjusting the weight of a balance weight in accordance with the weight of the manually operated tool. SOLUTION: In a manually operated tool balancer, a wire 2 is connected through pulleys 4a and 4 to the hook 1a of a manually operated tool 1 of a balance weight 5. A piston 7 in an oil pot 8 is fixed in the balance weight 5 by a connecting rod 6. The sum total of the weights of the balance weight 5, the connecting rod 6 and the piston 7 is a minimum weight and, as occasion demands, a balance weight 5a is added/removed from the minimum weight. Thus, a weight obtained by totaling the weights of the balance weight 5, the connecting rod 6, the piston 7 and the balance weight 5a is used while being set always equal to the weight of the manually operated tool 1 to be used.
03 Jul 1996
TL;DR: In this paper, the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length, is considered and shown to be NP-hard for polygons with holes.
Abstract: We consider the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length. This problem is NP-hard for polygons with holes. Even for hole-free polygons no known algorithm can find an optimal partitioning in less than O(n4) time.