Computational Scaling Analysis of Multiobjective Evolutionary Algorithms in Long-Term Groundwater Monitoring Applications

This study contributes a detailed assessment of how increased problem sizes impact the computational complexity of using multiple objective evolutionary algorithms (MOEAs) for long-term groundwater monitoring (LTM) applications. Problem size in this study is measured in terms of the number of design decision variables being considered. Computational complexity (or scaling) can be defined as a measure of how increased problem sizes impact the growth rate of the average number of design evaluations required by an MOEA to successfully solve an application. Building on a recent comparative analyses of MOEA effectiveness, this study characterizes the computational complexities of the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (ϵ-NSGAII) developed by the authors. This algorithm has proved to be more efficient and reliable relative to other state-of-the-art MOEAs. This study's computational scaling analysis is based on a suite of long-term groundwater monitoring (LTM) test cases formulated to test a range of problem sizes. The purpose of this study is to provide guidance on the current computational complexity of MOEAs to clarify future research paths that will allow them to solve larger water resources applications efficiently and reliably.