An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

This paper proposes the use of the flexible tolerance method (FTM) modified with adaptive Nelder-Mead parameters and barrier to solve constrained optimization problems. The problems used to analyze the performance of the methods were taken from G-Suite functions, and the methods with the best performance were applied in mass integration problems. Four methods were proposed: (1) flexible tolerance method (FTM) using adaptive parameters (FTMA), (2) flexible tolerance method with scaling (FTMS) and with adaptive parameters (FTMAS), (3) FTMS including the barrier modification (MFTMS) and (4) MFTMS hybridized with PSO (MFTMS-PSO). The success rates of these methods were 100% (MFTMS), 85% (MFTMS-PSO), 40% (FTMAS) and 30% (FTMA). Numerical experiments indicated that the MFTMS could efficiently and reliably improve the accuracy of global optima. In mass integration, the method was able, from current process situation, to reach the optimum process configuration that includes integration issues, which was not possible using FTM in its standard formulation. The hybridization of FTMS with PSO (without barrier), FTMS-PSO, was also able to solve mass integration problems efficiently.