# Preference-Based Whale Optimization Algorithm for Multi-Objective Struc- tural Optimization Problems Using Reference Points

## Palavras-chave:

Multi-objective structural optimization problem, Whale optimization algorithm, Reference point## Resumo

Several structural optimization problems can be formulated as multi-objective optimization problems

(MOOPs) due to the existence of multiple conflicting objectives, which must be minimized simultaneously. Most

MOOP solvers find the Pareto front formed by the best trade-off solutions, and then the decision-maker (DM)

chooses the one that best meets his/her personal preferences. However, many Pareto front solutions have no

chance of being chosen once they are outside DM’s region of interest (ROI). On the other hand, some solvers use

information from the DM’s preferences and can focus only on DM’s ROI rather than all Pareto front, consequently

obtaining better solutions from the DM’s perspective. This work proposes an algorithm named R-WOA to solve

the multi-objective structural optimization problems (MOSOPs) using the Whale Optimization Algorithm (WOA)

guided by reference points formed by DM’s desired values for the objective functions. MOSOPs having 10-,

25-, 60-, 72-, and 942-bar trusses are carried out to test the R-WOA’s performance. The numerical experiments

compare the R-WOA with algorithms R-NSGA-II, R-GDE3, and R-GDE3+APM regarding Hypervolume and

IGD+ performance measures. Using a non-parametric statistical test and the Performance Profile, the R-WOA

proves to be competitive in most of test scenarios.