Knowledge-Based Interval Modeling Method for Efficient Global Optimization

Abstract

Abstract A Knowledge-Based Interval Modeling (KBIM) Method is introduced for empirical search of the global optimum. The method takes advantage of the a priori knowledge of the system in terms of the linear/nonlinear, monotonic/nonmonotonic, sensitivity information between the objective function/constraints and the system variables and incorporates it in an interval model. This enables the KBIM Method to uniquely interleave model-building and model-refinement in the optimal search process, which makes it ideally suited to cases where exact input-output relationship is not defined. The efficiency of the KBIM Method is enhanced by an on-line learning scheme which improves the accuracy of the interval model after each search iteration by comparing the estimated range of its outputs with the actual outputs. The KBIM method has several advantages over conventional empirical search methods: (1) the interval model provides a generic form of representation for linear and nonlinear problems alike; therefore, there is no need for selecting the form of the empirical model through trial and error, (2) the use of a priori knowledge in modeling eliminates the need for initial trials to construct an empirical model, so from the beginning a plausible region can be identified within the input-space as the basis of search for the global optimum, (3) the use of intervals relaxes the need for precise information, so there is less demand for exploration within the input-space, and (4) the identification of a plausible region early on focuses the search within the plausible region, leading to a more complete model of this region by using the input/output data from the search for learning.