UNCONSTRAINED OPTIMIZATION USING INTERVAL ARITHMETIC AND INTERVAL ORDER RELATIONS

Unconstrained Optimization

This paper deals with discussion on the interval analysis, finite interval arithmetic, interval order relations and its application to find the global optimal solution of unconstrained optimization problems. The existing works on the interval order relations have been pointed out and the modified definitions have been presented. An interval technique is proposed to solve unconstrained unimodal/multimodal optimization problems with continuous variables. In this proposed method, the search region is divided into two equal sub-regions successively and in each sub-region, the lower and upper bounds of the objective function are computed with the help of interval arithmetic. Afterward, interval order relations are used to compare these two interval valued objectives and considering the sub-region containing the better objective value, the global optimal value or close to it of the objective function is obtained. As a final point, the proposed technique is applied to solve a number of test problems of global optimization with lower as well as higher dimensions available in the literature and is compared with the existing methods with respect to the number of function evaluations.

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