Selecting Model Parameter Sets from a Trade-off Surface Generated from the Non-Dominated Sorting Genetic Algorithm-II

Abstract

There is increasing trend in the use of multi-objective genetic algorithms (GAs) to estimate parameter sets in the calibration of hydrological models. Multiobjective GAs facilitate the evaluation of several model evaluation objectives, and the examination of massive combinations of parameter sets. Typically, the outcome is a set of several equally-accurate parameter sets which make-up a trade-off surface between the objective functions, usually referred to as Pareto set. The Pareto set is a set of incomparable parameter sets as each solution has unique parameter values in parameter space with competing accuracy in the objective function space. As would be required for decision making purposes, a single parameter set is usually chosen to represent the model calibration procedure. An automated framework for choosing a single solution from such a trade-off surface has not been thoroughly investigated in the model calibration literature. As a result, this study has outlined an automated framework using the distribution of solutions in objective space and parameter space to select solutions with unique properties from an incomparable set of solutions. Our Pareto set was generated 4470 G. Dumedah et al.southern Ontario. Using cluster analysis to evaluate the distribution of solutions in both objective space and parameter space, we developed four auto-selection methods for choosing parameter sets from the trade-off surface to support decision making. Our method generates solutions with unique properties including a representative pathway in parameter space, a basin of attraction (or the center of mass) in objective space, a proximity to the origin in objective space, and a balanced compromise between objective space and parameter space (denoted BCOP). The BCOP method is appealing as it is an equally-weighted compromise for the distribution of solutions in objective space and parameter space. That is, the BCOP solution emphasizes stability in model parameter values and in objective function values-in a way that similarity in parameter space implies similarity in objective space.

Hydrological Impacts of Climate Change Simulated by HIMS Models in the Luanhe River Basin, North China

“…Traditional optimization methods to calibrate hydrological models include genetic algorithms (Dumedah et al 2010;Kaini et al 2012;Wang 1991Wang , 1997, shuffled complex evolution method (Chu et al 2010;Duan et al 1992Duan et al , 1994Guo et al 2013;Joseph and Guillaume 2013;Vrugt et al 2003a, b), and particle swarm optimization (PSO) (Gill et al 2006;Jiang et al 2010Jiang et al , 2013Shi et al 2013;. Recent research has shown that the PSO approach has many computational advantages over traditional evolutionary computing (Chau 2007).…”

Integration of evolutionary based assimilation into Kalman-type methods for streamflow simulations in ungauged watersheds

“…The multi-objective evolutionary method used is based on the Non-dominated Sorting Genetic Algorithm -II (NSGA-II) which has been developed by Deb et al (2002). The NSGA-II is an innovative stochastic search tool that is capable of finding diverse solutions to a problem, and has been applied in several hydrological studies (Dumedah et al, 2012a,;Dumedah et al, 2011;Dumedah et al, 2010;Wohling et al, 2008;Bekele and Nicklow, 2007;Confesor and Whittaker, 2007;Tang et al, 2006). A flowchart outlining computational procedure of the ParetoParticleEnKF method is shown in Fig.…”

An Integrated Framework for a Joint Assimilation of Brightness Temperature and Soil Moisture Using the Nondominated Sorting Genetic Algorithm II

“…One such tool is the NSGA-II. NSGA-II was developed by Deb et al (2002) and is a widely applied algorithm (Dumedah et al 2010;Wö hling et al 2008;Confesor and Whittaker 2007;Tang et al 2006;Khu and Madsen 2005;Madsen 2003) with advanced and standard concepts capable of providing diverse solutions to a problem. Typically, the outcome to multiobjective problems is a set of solution(s) usually referred to as Pareto set (or Pareto frontier), which forms a trade-off between objective functions under evaluation (Deb et al 2002;Deb and Goel 2001;Deb et al 2000).…”