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 keeping 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 express that the set of rules is in a position to fixing real-world portfolio issues of facts from US inventory marketplace and randomly generated attempt issues of as much as one hundred twenty securities.

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1. Two examples of convex sets. F F Fig. 2. Two examples of non-convex sets. 10 1 Basic Concepts Pareto Terminology Having several objective functions, the notion of “optimum” changes, because in MOPs, the aim is to find good compromises (or “trade-offs”) rather than a single solution as in global optimization. The notion of “optimum” most commonly adopted is that originally proposed by Francis Ysidro Edgeworth [425] and later generalized by Vilfredo Pareto [1242]. Although some authors call this notion the Edgeworth-Pareto optimum (see for example [1517]), the most commonly accepted term is Pareto optimum.

In this method, the DM has to assign targets or goals that wishes to achieve for each objective. These values are incorporated into the problem as additional constraints. The objective function then tries to minimize the absolute deviations from the targets to the objectives. 29) i=1 where Ti denotes the target or goal set by the decision maker for the ith objective function fi (x), and Ω represents the feasible region. The criterion, then, is to minimize the sum of the absolute values of the differences between target values and actually achieved values.

13. 6 Origins of Multiobjective Optimization Multiobjective optimization theory is not as recent as we might think. In fact, some authors (see for example [1516]) indicate that multiobjective optimization is an inherent part of economic equilibrium and, in consequence, it can be traced back to 1776 in which Adam Smith’s treatise The Wealth of Nations was published. The general concept of economic equilibrium is often attributed to L´eon Walras. However, William Stanley Jevons, Carl Menger, Francis Ysidro Edgeworth and Vilfredo Pareto also did very important work in this regard in the period between 1874 and 1906.

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