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Multi-Gradient Analysis (MGA), and two multi-objective optimization methods based on MGA are presented: Multi-Gradient Explorer (MGE), and Multi Gradient Pathfinder (MGP) methods. Dynamically Dimensioned Response Surface Method (DDRSM) for dynamic reduction of task dimension and fast estimation of gradients is also disclosed.
MGE and MGP are based on the MGA’s ability to analyze gradients and determine the area of simultaneous improvement (ASI) for all objective functions. MGE starts from a
given initial point, and approaches Pareto frontier sequentially by stepping into the ASI area until a Pareto optimal point is obtained. MGP starts from a Pareto-optimal point, and steps along the Pareto surface in the direction that allows for improvement on a subset
of the objective functions with higher priority. DDRSM works for optimization tasks with virtually any number (up to thousands) of design variables, and requires just 5-7 model evaluations per Pareto optimal point for the MGE and MGP algorithms regardless of task
dimension. Both algorithms are designed to optimize computationally expensive models, and are able to optimize models with dozens, hundreds, and even thousands of design variables.