Solving nonlinear programming problems based on the Choquet integral by a genetic algorithm

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.