ROBBO: An Efficient Method for Pareto Front Estimation With Guaranteed Accuracy

A new method to estimate the Pareto front (PF) in bi-objective optimization problems (BOPs) is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced BOP), needs to sample at most a finite, precomputed number of PF points. Upon termination, it guarantees that the worst case approximation error lies within a desired tolerance range, predefined by the decision maker (DM), for each of the two objective functions. Theoretical results are derived about the worst case number of PF samples required to guarantee the desired accuracy, both in general and for specific sampling methods from the literature. A comparative analysis, both theoretical and numerical, demonstrates the superiority of the proposed method with respect to popular ones. The approach is finally showcased in a constrained path-following problem for a 2-axis positioning system and in a steady-state optimization problem for a continuous-flow stirred tank reactor (CSTR). An open demo implementation of ROBBO is made available online.