A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints

A hybrid method called a flexible tolerance genetic algorithm (FTGA) is proposed in this paper to solve nonlinear, multimodal and multi-constraint optimization problems. This method provides a new hybrid strategy that organically merges a flexible tolerance method (FTM) into an adaptive genetic algorithm (AGA). AGA is to generate an initial population and locate the “best” individual. FTM, serving as one of the AGA operators, exploits the promising neighborhood individual by a search mechanism and minimizes a constraint violation of an objective function by a flexible tolerance criterion for near-feasible points. To evaluate the efficiency of the hybrid method, we apply FTGA to optimize four complex functions subject to nonlinear inequality and/or equality constraints, and compare these results with the results supplied by AGA. Numerical experiments indicate that FTGA can efficiently and reliably achieve more accurate global optima of complex, nonlinear, high-dimension and multimodal optimization problems subject to nonlinear constraints. Finally, FTGA is successfully implemented for the optimization design of a crank-toggle mechanism, which demonstrates that FTGA is applicable to solve real-world problems.