Utilizing Innovization to Solve Large-Scale Multi-Objective Chesapeake Bay Watershed Problem

Innovization is a task for analyzing multiple Pareto-optimal solutions obtained by an evolutionary multi-objective optimization (EMO) algorithm to extract common features in the decision variables, leading to design rules or solution principles. The principles derived from innovized principles can provide valuable insights to the users about “how to create an optimal solution?”. Manual or automated machine learning-based innovization methods were proposed in the literature to extract innovized principles in a problem. Although different problems may demand different structures of the rules, the innovized rules can also be utilized to improve the performance of the subsequent iterations of the optimization algorithm or help in executing an efficient re-optimization of the same problem. In this paper, we consider a large-scale and multi-objective complex optimization task of minimizing cost and nitrogen loading in certain counties within the Chesapeake Bay Watershed (CBW) and find multiple trade-off solutions using the NSGA-III approach applied to the CBW's real evaluator tool (The Chesapeake Assessment Scenario Tool–CAST). 205 Best Management Practices (BMPs) are considered to be implemented at each land-river segment within a county, leading to as many as 65,260 variables for the resulting multi-objective optimization procedure. First, hundreds of trade-off solutions found by the CAST-NSGA-III procedure are analyzed manually to find the top-most BMPs used in them. After that, a re-optimization of CAST-NSGA-III is run with a few critical BMPs (resulting in a decrease of the variable to a range between 3% and 33%) found to commonly appear in the trade-off solution set of the previous runs. Interestingly, the resulting trade-off front with reduced BMPs is similar to the original run achieved with tens of thousands of variables. The findings are intriguing and demonstrate the efficacy of innovation in addressing intricate, real-world issues at a significant scale.