### A Multiobjective Global Optimization Algorithm with Application to the Calibration of Hydrologic Models

Abstract

This dissertation presents a new multiple objective optimization algorithm that is capable of solving for the entire Pareto set in one single optimization run.
The multi-objective complex evolution (MOCOM-UA) procedure is based on the following three concepts: (1) population, (2)rank-based selection, and (3) competitive evolution. In the MOCOM-UA algorithm, a population of candidate solutions is evolved in the feasible space to search for the Pareto set. Ranking of the population is accomplished through Pareto Ranking, where all points are successively placed on different Pareto fronts. Competitive evolution consists of selecting sub-sets of points (including all worst points in the population) based on their ranks and moving the worst points toward the Pareto set using the newly developed multiobjective simplex (MOSIM) procedure. Test analysis on the MOCOM-UA algorithm is accomplished on mathematical problems of increasing complexity and based on a bi-criterion measure of performance. The two performance criteria used are (1) efficiency, as measured by the ability of the algorithm to converge quickly and (2) effectiveness, as measured by the ability of the algorithm to locate the Pareto set. Comparison of the MOCOM-UA algorithm against three multiobjective genetic algorithms (MOGAs) favors the former. In a realistic application, the MOCOM-UA algorithm is used to calibrate the Soil Moisture Accounting model of the National Weather Service River Forecasting Systems (NWSRFS-SMA). Multi-objective calibration of this model is
accomplished using two bi-criterion objective functions, namely the Daily Root Mean Square-Heteroscedastic Maximum Likelihood Estimator (DRMS, HMLE) and rising limb-falling limb (RISE, FALL) objective functions. These two multiobjective calibrations provide some interesting insights into the influence of different objectives in the location of final parameter values as well as limitations in
the structure of the NWSRFS-SMA model.