A new epsilon-dominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems

This study focuses on the development of a next generation multiobjective evolutionary algorithm (MOEA) that can learn and exploit complex interdependencies and/or correlations between decision variables in monitoring design applications to provide more robust performance for large problems (defined in terms of both the number of objectives and decision variables). The proposed MOEA is termed the epsilon-dominance hierarchical Bayesian optimization algorithm (ε$\epsilon$-hBOA), which is representative of a new class of probabilistic model building evolutionary algorithms. The ε$\epsilon$-hBOA has been tested relative to a top-performing traditional MOEA, the epsilon-dominance nondominated sorted genetic algorithm II (ε$\epsilon$-NSGAII) for solving a four-objective LTM design problem. A comprehensive performance assessment of the ε$\epsilon$-NSGAII and various configurations of the ε$\epsilon$-hBOA have been performed for both a 25 well LTM design test case (representing a relatively small problem with over 33 million possible designs), and a 58 point LTM design test case (with over 2.88×10¹⁷$2.88\times {10}^{17}$ possible designs). The results from this comparison indicate that the model building capability of the ε$\epsilon$-hBOA greatly enhances its performance relative to the ε$\epsilon$-NSGAII, especially for large monitoring design problems. This work also indicates that decision variable interdependencies appear to have a significant impact on the overall mathematical difficulty of the monitoring network design problem.