Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints

A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate-based algorithms are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate-based algorithm that uses a linear combination of rectified linear units, defined in such a way that (local) optima satisfy the integer constraints. This method outperforms the state of the art on several synthetic benchmarks with up to 238 continuous and integer variables, and achieves competitive performance on two real-life benchmarks: XGBoost hyperparameter tuning and Electrostatic Precipitator optimisation.Comment: Ann Math Artif Intell (2020

Systematic methods for solvent design : towards better reactive processes

The focus of this thesis is the development of novel methodologies for systematic identification of optimal solvents for chemical reactions. Two aspects are considered: the integrated solvent and process design using a mixed solvent, and the design of an optimal solvent using ab initio methods that do not rely on experimental data. A methodology is developed for the integrated design of a CO2-expanded solvent in a reaction process. Posing as objective function the cost of the process, for a defined production rate, an optimisation problem is formulated, with decision variables that include the organic co-solvent, the composition and the mass of the mixed solvent. Emphasis is placed on the prediction of the reaction rate, for which the solvatochromic equation combined with a preferential solvation model are used, and on solid-vapour-liquid phase equilibrium, for which the group-contribution volume translated Peng-Robinson equation of state is used. The proposed methodology is applied to the Diels-Alder reaction of anthracene and 4-phenyl-1,2,4-triazoline-3,5-dione (PTAD), and three CO2-expanded solvents are considered (acetone, acetonitrile and methanol). Acetonitrile and acetone are found to offer good performance over a range of CO2 concentrations. The importance of taking into account multiple process performance indicators, when designing gas-expanded liquids, is highlighted. As a further step toward systematic solvent design approaches that are not limited by the availability of experimental data and consider a large number of candidate solvents, an ab initio methodology is developed for the design of optimal solvents for reactions. The developed method combines quantum mechanical calculations with a computer-aided molecular design formulation. In order to limit the number of QM calculations but also retain accuracy and ensure convergence, the Kriging approach is used. Kriging is a response surface approach, which has recently attracted a lot of attention because it is an exact extrapolator with a statistical interpretation which makes it stand out from other methods. The proposed approach is used successfully to identify promising solvents for the Menschutkin reaction of phenacyl bromide and pyridine and the Cope elimination of methylamine oxide. The use of Kriging as the surrogate model is found to lead to improved solvents when compared to the simpler solvatochromic equation used in previous work.Open Acces

On nonparametric maximum likelihood for a class of stochastic inverse problems

We establish the consistency of a nonparametric maximum likelihood estimator for a class of stochastic inverse problems. We proceed by embedding the framework into the general settings of early results of Pfanzagl related to mixtures