Interval-arithmetic-oriented interval computing technique for global optimization
Sanat Kumar Mahato, Asoke Kumar Bhunia · Applied Mathematics Research eXpress · 2006
Firstly, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented, and then pointing out the drawbacks of these definitions, a new approach is proposed in the context of decision maker's (optimistic and pessimistic) point of view. Secondly, an interval technique is proposed to solve unconstrained multimodal optimization problems with continuous variables. In this proposed method, the search region is divided into two equal subregions successively and in each subregion, the lower and upper bounds of the objective function are computed with the help of interval arithmetic. Then, by comparing these two interval objective values and considering the subregion containing the better objective value, the global optimal value of the objective function or close to it is obtained. Finally, the proposed method is applied to solve several number of test problems of global optimization with lower as well as higher dimension and is compared with the existing methods with respect to the number of function evaluations.