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 line with the Lagrangian twin leisure and non-stop rest is proposed for discrete multi-factor portfolio choice version with roundlot restrict 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 info from US inventory marketplace and randomly generated try issues of as much as a hundred and twenty securities.

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3 Simple Binary Search for Real Valued Encodings A similar search can be done using real valued representation that also cuts the search space in half after 2 evaluations. We again assume a 1-D bijective function. Evaluate points at 0, N/4, N/2, 3N/4, N-1 (rounding if necessary). Note this explicitly divides the space into 4 regions. After the minimum is identified, an optimum must lie in one of two quadrants. For example, let F be the evaluation function. If F (0) > F (N/4) < F (N/2) < F (3N/4) < F (N − 1) then the optimum must be between F (0) and F (N/2).

Genetic Quad Search. In GECCO 2003, pages 1469–1480. Springer, 2003. [Whi99] D. Whitley. A Free Lunch Proof for Gray versus Binary Encodings. In GECCO-99, pages 726–733. Morgan Kaufmann, 1999. [WM95] David H. Wolpert and William G. Macready. No free lunch theorems for search. Technical Report SFI-TR-95-02-010, Santa Fe Institute, July 1995. [WRB04] D. Whitley, J. Rowe, and K. Bush. Subthreshold Seeking Behavior and Robust Local Search. In GECCO 2004, pages v2:282–293. Springer, 2004. edu Abstract.

The following is an example of M4 . -> 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 3 3 3 3 2 2 3 3 3 3 1 3 3 3 3 3 3 1 3 2 2 3 2 2 1 Gray, Binary and Real Valued Encodings: Quad Search and Locality Proofs 31 The arrow points to row 2x−1 + 2x−2 − 1 which has a special importance. The first 2x−2 elements have value x − 1, and the remaining elements are identical to the last row of matrix Mx−1 .

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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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