A methodology for structural/control synthesis is presented in which the optimal location of active members is treated in terms of (0,1) variables. Structural member sizes, control gains, and (0,1) placement variables...
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A methodology for structural/control synthesis is presented in which the optimal location of active members is treated in terms of (0,1) variables. Structural member sizes, control gains, and (0,1) placement variables are treated simultaneously as design variables. Optimization is carried out by generating and solving a sequence of explicit approximate problems using a branch and bound strategy. Intermediate design variable and intermediate response quantity concepts are used to enhance the quality of the approximate design problems. Numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.
Let G(N;A) be a connected, undirected and weighted network with node set N and edge set A. Suppose that there is an available budget to spend on removing edges and there is a removal cost associated with each edge. Th...
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Let G(N;A) be a connected, undirected and weighted network with node set N and edge set A. Suppose that there is an available budget to spend on removing edges and there is a removal cost associated with each edge. The most vital edges problem is to find a set of edges such that the total removal cost is not greater than the available budget and whose removal from G(N;A) results in the greatest increase in the total weight of a minimum spanning tree. We show that this problem is NP-hard and propose a branch and bound algorithm to solve it.
We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems can be performed on...
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A controller design method is presented that gives the best linear-quadratic-Gaussian closed-loop performance over a set of worst plant parameter changes. The design algorithm combines a multiplant optimal design code...
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A controller design method is presented that gives the best linear-quadratic-Gaussian closed-loop performance over a set of worst plant parameter changes. The design algorithm combines a multiplant optimal design code, SANDY, with a new worst parameter algorithm that uses a quadratic norm on parameter changes. The minimax algorithm is unique in the way it weights worst plants to expand the stable region in the parameter space. The method is applied to a two-mass/spring American Control Conference "benchmark" problem. A minimax controller is first designed for the case where the spring constant alone is uncertain. Next, several minimax controllers, including a reduced-order design, are synthesized for the benchmark problem where both masses and the spring constant are uncertain. The results show that minimax control provides near-optimal nominal performance with significant robustness and parameter margin improvements.
Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization o...
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Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-boundalgorithm.
An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design...
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An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.
We present a branch and bound algorithm for the maximum clique problem in arbitrary graphs. The main part of the algorithm consists in the determination of upper bounds by graph colorings. Using a modification of a kn...
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The classical problem of finding a clique of largest cardinality in an arbitrary graph is NP-complete. For that reason earlier work diverges into two directions. The first concerns algorithms solving the problem for a...
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The classical problem of finding a clique of largest cardinality in an arbitrary graph is NP-complete. For that reason earlier work diverges into two directions. The first concerns algorithms solving the problem for arbitrary graphs in reasonable (but exponential) time, the other restricts to special classes of graphs where polynomial methods can be found. Here, the two directions are combined in a way. A branch and bound algorithm is developed treating the general case. Computational experiments on random graphs show that this algorithm compares favorable to the fastest known method. Furthermore, it consumes only polynomial time for quite a few graph classes. For some of them no polynomial solution method is given so far.
The paper presents a two step procedure for the selection of the most discriminative discrete as well as continuous features in the location model for mixed-variable discriminant analysis. The multivariate discriminat...
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The paper presents a two step procedure for the selection of the most discriminative discrete as well as continuous features in the location model for mixed-variable discriminant analysis. The multivariate discriminatory measure T2 is used as a criterion for subset choice. The first step consists in finding stepwisely the most discriminative discrete features. The second step enables one to select the subset of continuous variables for the previously chosen discrete feature set. The two steps may be reversed. When the number of discrete variables is already fixed the selection of continuous features is made efficiently by the branch and bound algorithm.
A min-max variant of the global criterion approach is proposed to obtain solutions to multiobjective optimum design problems involving a mix of continuous, discrete, and integer design variables. This modified global ...
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