Minimum weight

Abstract: In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is asked for a minimum weight set of edges that separates each terminal from all the others. When the number $k$ of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. It is shown that the problem becomes NP-hard as soon as $k=3$, but can be solved in polynomial time for planar graphs for any fixed $k$. The planar problem is NP-hard, however, if $k$ is not fixed. A simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of $2-2/k$ of the optimal cut weight is also described.

Abstract: An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.

Abstract: Optimization of truss-structures for finding optimal cross-sectional size, topology, and configuration of 2-D and 3-D trusses to achieve minimum weight is carried out using real-coded genetic algorithms (GAs). All the above three optimization techniques have been made possible by using a novel representation scheme. Although the proposed GA uses a fixed-length vector of design variables representing member areas and change in nodal coordinates, a simple member exclusion principle is introduced to obtain differing topologies. Moreover, practical considerations, such as inclusion of important nodes in the optimized structure is taken care of by using a concept of basic and non-basic nodes. Stress, deflection, and kinematic stability considerations are also handled using constraints. In a number of 2-D and 3-D trusses, the proposed technique finds intuitively optimal or near-optimal trusses, which are also found to have smaller weight than those that are reported in the literature.

Abstract: Starting from the distance distribution of an unrestricted code and its Mac Williams transform, one defines four parameters that, in the linear case, reduce to the minimum weight and the number of distinct weights of the given code and of its dual. In the general case, one exhibits the combinatorial meaning of these parameters and, using them, one obtains various results on the distance properties of the code. In particular, a method is suggested to calculate the weight distributions of cosets of a code. A “dual concept” of that of perfect codes is also presented and examined in detail.

Abstract: A method for optimal design of structures is presented. It is based on an energy criteria and a search procedure for design of structures subjected to static loading. The method can handle very efficiently, (a) design for multiple loading conditions, (b) stress constraints, (c) constraints on displacements, (d) constraints on sizes of the elements. Examples of bar and beam structures are presented to illustrate the effectiveness of the method. Some of these examples are compared with the designs obtained by linear and nonlinear programming methods. The method is extremely efficient in obtaining minimum weight structures and in a small fraction of the computer time required by linear and nonlinear programming methods.