Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods

This paper proposes the use of the flexible tolerance method (FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems. The benchmark problems used to analyze the performance of the methods were taken from G-Suite functions. The original method (FTM) and other four proposed methods: (i) FTM with scaling of variables (FTMS), (ii) FTMS hybridized with BFGS (FTMS-BFGS), (iii) FTMS hybridized with modified Powell's method (FTMS-Powell) and (iv) FTMS hybridized with PSO (FTMS-PSO), were implemented. The success rates of the methods were 80%, 100%, 75%, 95% and 85%, for FTM, FTMS, FTMS-BFGS, FTMS-Powell and FTMS-PSO, respectively. Numerical experiments including real constrained problems indicated that FTMS gave the best performance, followed by FTMS-Powell and FTMS-PSO. Despite the inferior performance compared to FTMS and FTMS-Powell, the FTMS-PSO method presented some advantages since good different initial points could be obtained, which allow exploring different routes through the solution space and to escape from local optima. The proposed methods proved to be an effective way of improving the performance of the original FTM.