What's the best pitch shifting algorithm in your opinion?

“Elastique” time stretch algorithm by zplane (0) seems to be a common choice by plug-in companies. Their C++ library is pretty straightforward to use, and most importantly it sounds good.

Generally speaking, phase vocoder (1) algorithms are what you’d want for developing your own pitch shifting algorithm.

[0]https://licensing.zplane.de/

[1]https://cmtext.indiana.edu/synthesis/chapter4_pv.php

Not sure of any of the theory behind it but Melodyne's is probably the best I've ever worked with.

Serato Pitch n Time is used on master mixes to correct wholesale tuning issues.

but really depends on what you're after (creative or precision)