Download e-book for iPad: A branch-and-bound algorithm for discrete multi-factor by Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling

By Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling

During this paper, a brand new branch-and-bound set of rules in response to the Lagrangian twin rest and non-stop rest is proposed for discrete multi-factor portfolio choice version with roundlot limit in monetary optimization. This discrete portfolio version is of integer quadratic programming difficulties. The separable constitution of the version is investigated by utilizing Lagrangian leisure and twin seek. Computational effects express that the set of rules is in a position to fixing real-world portfolio issues of information from US inventory marketplace and randomly generated try issues of as much as one hundred twenty securities.

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Even so, we have ignored occasional anomalous results which take much longer than usual. This means that the results are not completely representative of results that are regularly achieved in a real application. 1 the speed of the various parts of the sorting algorithm are shown for the 32-node AP1000 and CM5. In this example we are sorting 8 million 32-bit integers. For the communications operations both machines achieve very similar timing results. For each of the computationally intensive parts of the sorting algorithm, however, the CM5 achieves times which are between 60% and 70% of the times achieved on the AP1000.

The remainder of the difference is due to the fact that sorting a large number of elements is a very memory-intensive operation. A major bottleneck in the sorting procedure is the memory bandwidth of the nodes. When operating on blocks which are much larger than the cache size, this results in a high dependency on how often a cache line must be refilled from memory and how costly the operation is. Thus, the remainder of the difference between the two machines may be explained by the fact that cache lines on the CM5 consist of 32 bytes whereas they consist of 16 bytes on the AP1000.

This will mean that the initial column sort will not achieve anything. The worst case of log k + 1 passes can then be achieved. Additionally the data distribution required for the worst case of the internal sorting algorithm should be used. 6: Number of reads and writes per element for a range of k values A experiment with 10 million 64 bit elements and a k of 7 gave a slowdown for the worst case compared to random data of about a factor of 4. 3 First pass completion An important component of the algorithm is the fact that most slices are completed in the first pass, allowing the remaining passes to “clean up” the unfinished elements quickly.

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A branch-and-bound algorithm for discrete multi-factor portfolio optimization model by Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling

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