Affiliations: [a] Department of Genetics, Cell Biology, and Anatomy, University of Nebraska Medical Center, Omaha, NE, USA | [b] Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA
Correspondence:
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Correspondence to: Naomi Kochi, Department of Genetics, Cell Biology, and Anatomy, University of Nebraska Medical Center, Omaha, NE 68198, USA. Fax: +1 402 554 2975; E-mail: [email protected].
Abstract: Nonadditive set functions represent contribution rate of individual feature attributes and combinations of feature attributes toward the target. Their nonadditivity describes the interaction among contributions. The generalized weighted Choquet integral with respect to a nonadditive set function serves as an aggregation tool, which may be used in the nonlinear objective function of optimization problems, to project n-dimensional feature space onto a real axis with a corresponding projection value. In this paper, we propose a special genetic algorithm model to identify the values of feature attributes that maximize the value of the objective function involving a generalized weighted Choquet integral. Thus, we may find the values of the feature attributes giving the greatest contribution toward the target. This is a generalization of linear programming to nonlinear cases.
Keywords: Nonadditive set functions, the Choquet integral, genetic algorithms, linear and nonlinear programming
