A new selection metric for multiobjective hydrologic model calibration

Abstract

A novel selection metric called Convex Hull Contribution (CHC) is introduced for solving multiobjective (MO) optimization problems with Pareto fronts that can be accurately approximated by a convex curve. The hydrologic model calibration literature shows that many biobjective calibration problems with a proper setup result in such Pareto fronts. The CHC selection approach identifies a subset of archived nondominated solutions whose map in the objective space forms convex approximation of the Pareto front. The optimization algorithm can sample solely from these solutions to more accurately approximate the convex shape of the Pareto front. It is empirically demonstrated that CHC improves the performance of Pareto Archived Dynamically Dimensioned Search (PA-DDS) when solving MO problems with convex Pareto fronts. This conclusion is based on the results of several benchmark mathematical problems and several hydrologic model calibration problems with two or three objective functions. The impact of CHC on PA-DDS performance is most evident when the computational budget is somewhat limited. It is also demonstrated that 1,000 solution evaluations (limited budget in this study) is sufficient for PA-DDS with CHC-based selection to achieve very high quality calibration results relative to the results achieved after 10,000 solution evaluations.

Multiobjective Automatic Parameter Calibration of a Hydrological Model

“…The Leaf River case study has been widely used for single and multiobjective hydrological model calibrations [8,9,12,27,53,69,70]. The two inputs are daily precipitation (mm/day) and potential evapotranspiration (mm/day; Figure 3).…”

“…Recently, calibration methodologies used specifically for pure multiobjective schemes have been introduced. Asadzadeh et al [27] proposed a selection measure known as convex hull control (CHC) for solving a multiobjective calibration problem with a known and approximated convex Pareto solution.…”

Watershed derived nutrients for Lake Ontario inflows: Model calibration considering typical land operations in Southern Ontario

“…The 3-objective hydrology calibration problem was solved by the multi-objective optimization (MO) algorithm called Pareto Archived Dynamically Dimensioned Search (PA-DDS) that was introduced for the first time by Asadzadeh and Tolson (2009). The efficiency of PA-DDS for solving MO calibration problems was recently enhanced by a selection metric called Convex Hull Contribution (CHC) in Asadzadeh et al (2014). PA-DDS with the CHC-based selection was used in this study to solve the three-objective calibration problem defined based on the hydrologic model behavior.…”

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

“…This helps to understand if near‐optimal values of the responses are possible, or if improvement of one response comes only at the cost of substantial compromise of the others. The HV considers both the proximity of the PF to the ideal result of simultaneously optimizing all the criteria, as well as the richness or cardinality of the front …”

“…The HV of the PF based on scaling the best possible value for a given response with a value of 1 and the least desirable value with 0 is referred to as the normalized HV, ie, NHV . This is similar to the scaling used with desirability functions .…”