A computational scaling analysis of multiobjective evolutionary algorithms in long-term groundwater monitoring applications

This study contributes a detailed assessment of how increasing problem sizes (measured in terms of the number of decision variables being considered) impacts the computational complexity of using multiple objective evolutionary algorithms (MOEAs) to solve long-term groundwater monitoring (LTM) applications. The epsilon-dominance non-dominated sorted genetic algorithm II (ε-NSGAII), which has been shown to be an efficient and reliable MOEA, was chosen for the computational scaling study. Four design objectives were chosen for the analysis: (i) sampling cost, (ii) contaminant concentration estimation error, (iii) local uncertainty, and (iv) contaminant mass estimation error. The true Pareto-optimal solution set was generated for 18-25 well LTM test cases in order to provide for rigorous algorithm performance assessment for problems of increasing size. Results of the study indicate that the ε-NSGAII exhibits quadratic computational scaling with increasing LTM problem size. However, if the user is willing to accept an approximation to the Pareto-optimal solution set, ε-dominance can be used to reduce the computational scaling of MOEAs to be linear with increasing problem sizes. This study provides a basis for advancing the size and scope of water resources problems that can be effectively solved using MOEAs.