Using multivariate regression trees and multiobjective tradeoff sets to reveal fundamental insights about water resources systems

Abstract

This paper presents the use of Multivariate Regression Trees (MRTs) to analyze Multiobjective Evolutionary Algorithm (MOEA) tradeoff sets generated from a long-term water utility planning problem. MOEAs produce large sets of non-dominated solutions, where each solution represents an observation of how multiple predictor variables (decision levers) impact performance in multiple response variables (objectives). Because they explicitly accommodate multiple response variables, MRTs can preserve the relationships between objectives revealed through MOEA-assisted optimization. We generated MRTs for two tradeoff sets that resulted from optimizing the Eldorado Utility planning problem under two climate change scenarios. A single MRT helped identify the subset of core planning decisions that led to preferred performance and demonstrated how decision preferences impacted performance in different objectives. Comparing MRTs from two scenarios revealed decisions that performed well across scenarios. The systematic and repeatable MRT approach can help water managers understand large, high-dimensional tradeoff sets and prompt additional promising analyses.