A fun anecdote from past experience while working in industry. In optimizing chemical reactions I have worked with chemists who insisted on randomly selecting their reaction parameters. Ten experiments were performed with a random set of lets say reaction temperature, stoichiometry and choice of base. The best performing reaction was then presented to management as the 'optimized reaction'. Why? For the chemist it conveniently lifted the burden of rationalizing the outcome of the reaction. Did management want more optimizations? Ten new random experiments were selected from the magicians hat.
Murray et al. are also industrial chemists but represent the other extreme of the quality scale. In the latest issue of OPRD they play an interesting numbers game (DOI). In a concept article the key question they pose: how do you optimise a chemical reaction knowing that even with a limited set of variables the number of unique reactions can easily run in the thousands. Case at hand: a typical Suzuki reaction has 7 continuous variables (stoichiometry for reactants, base, water, precatalyst loading, metal:ligand ratio, concentration and temperature ) resulting in 128 variable sets with just two levels. Adding 500 ligands, 2 Pd precursors, 4 bases and 100 solvents (all discrete variables and industrially relevant) increases the number to a staggering 51.2 million. As Murray points out, even on a 10 mg test scale 512 Kg of starting material would be required.
Solution: a combination of Design of Experiments and Principal Component Analysis. Testing a bunch of very similar ligands is nonsensical. What you would like to have is a set of ligands the occupy different spots in so-called ligand space defined by three axes of measurable chemical properties such as Hansen solubility parameter, boiling point or a bond length. With for example 9 representative ligands occupying the corners of a cube and one in the centre the best performing reaction will reveal where in ligand space the opportunities are. Through a method of iterations the reaction can then be further refined. Murray boasts that by using this method optimizing a Buchwald-Hartwig amination only required 35 reactions.