Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design

Abstract

This study compares the performances of four state-of-the-art evolutionary multi-objective optimization (EMO) algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGAII), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II ( ε-NSGAII), the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( εMOEA), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2), on a four-objective long-term groundwater monitoring (LTM) design test case. The LTM test case objectives include: (i) minimize sampling cost, (ii) minimize contaminant concentration estimation error, (iii) minimize contaminant concentration estimation uncertainty, and (iv) minimize contaminant mass estimation error. The 25-well LTM design problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the EMO algorithms. The performances of the four algorithms are assessed and compared using three runtime performance metrics (convergence, diversity, and ε-performance), two unary metrics (the hypervolume indicator and unary ε-indicator) and the first-order empirical attainment function. Results of the analyses indicate that the ε-NSGAII greatly exceeds the performance of the NSGAII and the εMOEA. The ε-NSGAII also achieves superior performance relative to the SPEA2 in terms of search effectiveness and efficiency. In addition, the ε-NSGAII’s simplified parameterization and its ability to adaptively size its population and automatically terminate results in an algorithm which is efficient, reliable, and easy-to-use for water resources applications.