Abstract
Trust region (TR) algorithms have been principally considered as a candid and constructive choice to address a vast majority of continuous nonlinear programming problems which frequently appear in the real-world applications. As known, in every iteration of a TR algorithm often a quadratic local estimation of the cost function should be approximately optimized within a region limited by the so-called TR radius, to obtain a trial step. Then, in order to measure the agreement between the cost function and its local estimation along the trial step, the TR ratio is devised. Recent studies have depicted efficiency of the TR algorithms which benefit from the nonmonotonicity aspects to determine the TR ratio. Nevertheless, the way of setting the TR ratio has been always considered as a matter of research. Here, as an effort to take advantage of the soft computing schemes in the classic algorithms, we plan to benefit from the fuzzy concepts to set the TR ratio. To this aim, we define a fuzzy number by several already proposed choices for the TR ratio. Then, we employ a defuzzification strategy to gain a scalar value for the TR ratio. Our computational experiments showed efficiency of such a hybrid algorithm.