In a recent blog contribution Fabien Le Floc’h  suggests to combine the adaptive successive over-relexation method  with an improved explicit approximate implied volatility formula  to calculate the initial guess. The implementation of both algorithms is straight forward.
A large set of OTM and ITM options together with different displacement factors has been identified to serve as a benchmark portfolio to compare the performance with the original QuantLib implementation. As can be seen in the diagram below the new method is – depending on the accuracy – two to three times faster than the current QuantLib implementation.
The implementation is available here, the diagram above is derived from the test case testImpliedVolAdaptiveSuccessiveOverRelaxation in the class BlackFormulaTest.
 Le Floc_h, F (2017) Implied Volatility from Black Scholes Price
 Li, M. (2008) An Adaptive Successive Over-relaxation Method for Computing the Black-Scholes Implied Volatility
 J. Gatheral, I. Matic, R. Radoicic, D. Stefanica (2017), Tighter Bounds for Implied Volatility