Harnessing Symbolic Regression and Nonlinear Programming for Computationally Expensive Multi-Objective Optimization
TL;DR
A surrogate-assisted multi-objective optimization approach that leverages symbolic regression (SR) to construct interpretable analytical approximations of expensive black-box functions and uses iterative construction of surrogates and Tchebycheff scalarization along a set of parallel reference vectors to search for well-distributed solutions on the Pareto front.
Abstract
This work presents a surrogate-assisted multi-objective optimization approach that leverages symbolic regression (SR) to construct interpretable analytical approximations of expensive black-box functions. It uses iterative construction of surrogates (symbolic models) and Tchebycheff scalarization along a set of parallel reference vectors to search for well-distributed solutions on the Pareto front. Optimization of the symbolic models is performed using a nonlinear programming (NLP) solver in lieu of heuristic search. A distance-based subset selection strategy is used to select a candidate for true evaluation, ensuring efficient use of limited evaluation budget in a steady-state framework. The approach is compared against a Kriging-assisted NSGA-II, also implemented within a steady-state framework. Experiments are performed on six benchmark problems—covering both constrained and unconstrained cases, including a practical engineering benchmark of bracket design problem. The findings highlight the strengths and limitations of SR-based surrogates combined with NLP, and position them as a viable alternative to conventional surrogate-assisted evolutionary algorithms.