Comparative Analysis of Multiobjective Evolutionary Algorithms for Quantifying Agronomic and Water Quality Tradeoffs of Fertilizer Management Practices

Abstract:

Multiobjective evolutionary algorithms (MOEAs) are promising tools for fertilizer management decision support in Midwestern corn-soybean production systems. Our recent work demonstrates that an MOEA coupled with the Root Zone Water Quality Model (RZWQM2) can identify nondominated fertilizer rate decisions and generate well-defined Pareto fronts elucidating tradeoffs between profit, corn yield, and tile drainage nitrate-N yield for two field sites in east-central Illinois. Because true Pareto fronts are unknown, an ensemble of MOEAs must be statistically compared to ensure that the best-known Pareto front approximation represents true objective tradeoffs and determine which algorithm has the highest likelihood of generating an accurate approximation. The algorithms we chose to compare are Borg, ԑ-MOEA, ԑ-NSGAII, OMOPSO, and GDE3 because they cover the spectrum of algorithm classes and are consistently among the top performing algorithms for generic test suites and water resources applications. Building on Hadka and Reed (2011) and Reed et al. (2013), we will implement a computational experiment that quantifies algorithm effectiveness and efficiency for approximating Pareto optimal fertilizer rate, timing, and method decisions. Each algorithm will be run with random parameter samples to generate empirical probability distributions and attainment functions for three quality indicators: the hypervolume ratio, additive epsilon, and R3 utility indicator. In addition to visually comparing algorithm indicators, we will formally compare them with a Kruskal-Wallis test on hypervolume distributions followed by Dunn’s post hoc tests to determine if any algorithm stochastically dominates the rest. With the results from the top performing algorithm, we will apply a series of nonparametric tests designed for multiple comparisons to detect significant differences in optimal profit outcomes between study sites and identify management decisions with the greatest influence on system outcomes. This analysis will not only aid in prioritizing fertilizer management practices for waterway nutrient loss reductions but also will serve as a first step towards applying the latest, highly efficient MOEAs for optimal best management practice design, selection, and placement.