The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output. 相似文献
We prove the following theorem. Let m and n be any positive integers with mn, and let
be a subset of the n-dimensional Euclidean space n. For each i=1, . . . , m, there is a class
of subsets Mij
of Tn. Assume that
for each i=1, . . . , m, that M
ij
is nonempty and closed for all i, j, and that there exists a real number B(i, j) such that
and its jth component xjB(i, j) imply
. Then, there exists a partition
of {1, . . . , n} such that
for all i and
We prove this theorem based upon a generalization of a well-known theorem of Birkhoff and von Neumann. Moreover, we apply this theorem to the fair allocation problem of indivisible objects with money and obtain an existence theorem. 相似文献
Ring structures in telecommunications are taking on increasing importance because of their self-healing properties. We consider a ring design problem in which several stacked self-healing rings (SHRs) follow the same route, and, thus, pass through the same set of nodes. Traffic can be exchanged among these stacked rings at a designated hub node. Each non-hub node may be connected to multiple rings. It is necessary to determine to which rings each node should be connected, and how traffic should be routed on the rings. The objective is to optimize the tradeoff between the costs for connecting nodes to rings and the costs for routing demand on multiple rings. We describe a genetic algorithm that finds heuristic solutions for this problem. The initial generation of solutions includes randomly-generated solutions, complemented by seed solutions obtained by applying a greedy randomized adaptive search procedure (GRASP) to two related problems. Subsequent generations are created by recombining pairs of parent solutions. Computational experiments compare the genetic algorithm with a commercial integer programming package. 相似文献
A new type of biosensor has been developed based on detection of nanosized superparamagnetic particles that serve as labels in bioreactions. The method is based on non-linear magnetic material detection by a magnetic field having components at two frequencies f1 and f2. The response is measured at the combinatorial frequencies fi=mf1+nf2, where m and n are integers, e.g., fi=f1±2f2. Several highly sensitive readers of superparamagnetic particles have been designed and used for development of various formats of immunoassays, including those compatible with immunoconcentration and magnetic enrichment of antigens. 相似文献
An experimental investigation with 5 kW CW CO2 laser system was carried out to study the effects of different laser and process parameters on the microstructure and hardness of carbon steel specimen with varying carbon percentage. The laser beam is allowed to scan on the surface of the work piece varying the power (1.1–2.5 kW) and traverse speed (6–15 mm/s) at two different spot sizes using TEM01* mode laser beam. The most hardenable microstructure achieved in case of three grades of carbon steel and the most influencing parameter on the value of hardness are reported. Besides the above study, some multipass operations are also carried out to recommend an appropriate gap between consecutive passes. 相似文献
The role of optimization is central to economic analysis, particularly in its “neoclassical” phase, since about 1870, and is therefore highly compatible with the impulse behind linear programming (LP), as developed by Dantzig. LP’s stress on alternative activities fits very well with modern economic analysis. The concept of economic equilibrium, properly understood, required the central notion of complementary slackness. so central in LP.
LP was seen as a tool for actual implementation of neoclassical principles precisely at a time when the market was under attack from several directions. The economists Koopmans and Hurwicz played an important role both in stimulating the crucial development of the simplex method and in relating LP to the world of economics.
LP became widely used in national economic planning, particularly for developing countries, and for the study of individual industries, especially the energy sector. The works of Chenery and of Manne are central in these fields.
As respect for the usefulness of the market increased, the emphasis on national planning diminished and was replaced by an emphasis on equilibrium analysis, in which LP still plays a large part in the study of individual sectors, particularly energy. 相似文献
A library of resorcylic acid lactones (RAL) containing a cis‐enone moiety targeting kinases bearing a cysteine residue within the ATP‐binding pocket was prepared using a fluorous‐mixture synthesis and evaluated against a panel of 19 kinases thus providing important structure–activity trends. Two new analogues were then profiled for their selectivity against a panel of 402 kinases providing the broadest evaluation of this pharmacophores’ selectivity. 相似文献