Integrating interval method with a heuristic for solving nonlinear uncertain interval optimization problems

Abstract

In this work, we introduce a novel interval optimization technique to solve the nonlinear engineering uncertain constrained optimization problems with uncertainty in coefficients of objective function and constraints. We apply the arithmetic relation of interval numbers based on the midpoint and width of the interval to convert the uncertain objective function into two deterministic, objective functions. Unlike the traditional method, with time-consuming nested conditions involved for evaluating the possibility degree while handling the constraints. We introduce a new way for assessing the possibility degree, which is simple to compute and dependent on non-uniform distribution is proposed to deal with both inequality and equality constraints with the interval coefficients without much computational effort. To solve this unconstrained problem, we develop an optimization technique integrating the interval method with the artificial bee colony (ABC) algorithm. Finally, the benchmark problems are solved to test our proposed method's efficiency. With the linear combination of the objective function and penalty function method, an unconstrained single objective optimization problem having deterministic coefficients is formulated. To solve this unconstrained problem, we develop an optimization technique integrating the interval method with the ABC algorithm.