Μέθοδοι βελτιστοποίησης και εφαρμογές στην υγρή χρωματογραφία υψηλής πίεσης

Abstract

The present work is about the evaluation of popular methods of optimization, the development of new ones and their application in reversed phase high pressure liquid chromatography. Initially the most popular optimization methods were selected and classificated according to their main principals to the following categories: Α) Random search methods Β) Heuristic methods C) Mathematical methods D) Physical methods and E) Tabu search The initial algorithms were combined in different ways, and new algorithms were produced. The main aim of this work was the discovery of the most appropriate, for our experimental studies, optimization method. The initial optimization methods as well as their combinations were encoded in C++ programming language. Then they were tested for their efficiency with well known, from the literature, mathematical functions. The criteria for the efficiency of the methods were the frequency and speed of finding the solution. After the evaluation of the methods, we selected the ones which gave the best results, in order to use them in applications of high pressure liquid chromatography. The optimization methods in high pressure liquid chromatography are used for two main reasons. The first reason is the determination of the parameters which control the calculation of the retention time of a solute (fitting). The second reason is the determination of the best gradient profile which leads to the optimum separation of chromatographic peaks in a mixture. It was found that the first aim can be achieved easily, with the majority of the methods studied. On the contrary the optimization in high pressure liquid chromatography presents many difficulties. There are a large number of local minima, which make the determination of global minimum, quite difficult. Another difficulty is that the mathematical function which describes a chromatographic system is discontinuous so the mathematical methods can not be included in the appropriate for HPLC applications methods. For the evaluation of the algorithms in chromatographic data, a series of experiments were performed, aiming at the best separation of a mixture of 13 o-phthalaldehyde (OPA) derivatives of amino acids. The mobile phase was modified by one or two modifiers. The algorithms used for fitting were a combination of mathematical and physical methods. The information obtained is fed to the optimization algorithm that searches for the best gradient profile, meaning the concentration of the modifiers of the mobile phase vs time. The tactic used was the same for one and two modifiers as well. The methods which presented the best results were a repeated application of the Levenberg–Marquardt (LM) method for fitting (R LM), a random search method combined with Levenberg–Marquardt and two modified descent algorithm for optimisation (RND_ND_D and RND_ND_LM). With these algorithms we achieved almost 100% success in the finding of the solution.