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Surrogate Global Optimization for Computationally Expensive Objective Functions with Integer and Continuous Variables with Applications

This talk presents a framework for parallel surrogate-based constrained nonlinear optimization algorithms for computationally expensive objective functions with continuous and/or integer variables. The algorithms converge almost surely. The methods are efficient when the objective function or the constraints are computationally expensive. “Efficient” indicates an algorithm gets solutions with relatively few evaluations of the objective function, which is often a computationally intensive simulation model (e.g. minutes or hours per simulation). The framework is designed for problems with a possibly multi-modal objective function that is black-box so that derivatives and the number of local minima are not known. The algorithm results are numerically compared to other pure and mixed integer and continuous variable algorithms on test problems. Applications to a continuous variable groundwater transport problem and to an integer optimization problem arising in watershed phosphorous pollution management will be presented.

Bio: Shoemaker’s algorithms address local and global continuous and integer optimization, stochastic optimal control, and uncertainty quantification problems. In her recent research algorithm efficiency is improved with the use of surrogate response surfaces iteratively built during the research process and with intelligent algorithms that effectively utilize parallel and distributed computing. Her applications areas include physical and biological groundwater remediation, carbon sequestration, pesticide management, ecology, and calibration of climate and watershed models. Algorithms that are efficient because they require relatively few simulations are essential for doing calibration and uncertainty analysis on computationally expensive engineering simulation models. Professor Shoemaker is a member of the National Academy of Engineering and is a Fellow in AGU, SIAM, INFORMS and Distinguished Member of ASCE.