Niu Shu-fen, Wang Guo-xin, Sun Xiao-ling's A branch-and-bound algorithm for discrete multi-factor PDF

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

During this paper, a brand new branch-and-bound set of rules in accordance with 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 through the use of Lagrangian leisure and twin seek. Computational effects exhibit 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 out issues of as much as one hundred twenty securities.

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In contrast, other schemes such as Gray coding reduce this problem. In Gray coding, the object is to create a code such that a single integer change only requires a 1-bit change in the binary genotype. This means that adjacent solutions in the (integer or real-valued) search space will be adjacent in the (binary) encoding space as well, requiring fewer mutations to discover. The Gray coding rule starts with a string of all zeros for the integer value zero, and to create each subsequent integer in sequence the rule successively flips the right-most bit that produces a new string.

027451. could be converted into a real value as follows: 0 + 255 Although the above decoding scheme for a binary string is quite simple, it can suffer from Hamming cliffs, in that sometimes a large change in the 44 3 Evolutionary Methodologies genotype is required to produce a small change in the resulting integer value. 5, it can be seen that the underlying genotype needs to change in all three bit positions. These Hamming cliffs can potentially create barriers that the GA could find difficulty in passing.

N , each of which encode a solution, is randomly initialised and evaluated using a fitness function f . During the search process, each individual (j) is iteratively refined. The modification process has three steps: i. Create a variant vector which encodes a solution, using randomly selected members of the population (mutation step). 50 3 Evolutionary Methodologies ii. Create a trial vector, by combining the variant vector with j (crossover step). iii. Perform a selection process to determine whether the newly-created trial vector replaces j in the population.

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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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