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

TL;DR

ROBO is a novel method for efficiently estimating the Pareto Front in bi-objective optimization, guaranteeing approximation accuracy within user-defined tolerances through theoretical bounds and practical demonstrations.

Contribution

The paper introduces ROBBO, a new sampling-based approach that guarantees Pareto Front approximation accuracy with finite samples and provides theoretical bounds on sample size.

Findings

ROBO outperforms existing methods in accuracy and efficiency.

Theoretical bounds on sample size ensure desired approximation quality.

Successful application to engineering problems demonstrates practical utility.

Abstract

A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite, pre-computed 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, for each of the two objective functions. Theoretical results are derived, about the worst-case number of PF samples required to guarantee the wanted 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. An open demo implementation of ROBBO is made available online.