Gradient based methods for multi-objective optimization

摘要

Concurrent Gradients Analysis (CGA), and two multi-objective optimization methods based on CGA are provided: Concurrent Gradients Method (CGM), and Pareto Navigator Method (PNM). Dimensionally Independent Response Surface Method (DIRSM) for improving computational efficiency of optimization algorithms is also disclosed. CGM and PNM are based on CGA's ability to analyze gradients and determine the Area of Simultaneous Criteria Improvement (ASCI). CGM starts from a given initial point, and approaches the Pareto frontier sequentially stepping into the ASCI area until a Pareto optimal point is obtained. PNM starts from a Pareto-optimal point, and steps along the Pareto surface in the direction that allows improving a subset of objective functions with higher priority. DIRSM creates local approximations based on automatically recognizing the most significant design variables. DIRSM works for optimization tasks with virtually any (small or large) number of design variables, and requires just 2-3 model evaluations per Pareto optimal point for the CGM and PNM algorithms.