Heuristic and metaheuristic algorithms for the generation of optimal experimental designs

Experimentation is arguably one of the fundamental pillars that enable the creation of new knowledge. The purpose of an experiment is to identify the influence that a set of experimental variables has on the process under study. By systematically manipulating the settings of these variables, it is possible to quantify how and to which extent they affect one or more response variables that measure the process' behaviour. The design of an experiment consists in determining the number of experimental runs, the settings of the experimental variables in each run, and the sequence in which the runs need to be executed. This should be done with the purpose of maximizing the amount of information produced by the experiment. Several standard experimental designs like full and fractional factorial designs, central composite design and Plackett-Burman designs, have been proposed to achieve this goal. Although these designs have very good properties, they cannot always be applied to the experimental scenarios found in practice. Traditionally, experimenters have tried to adapt the scenario in order to fit one of the standard designs available. Doing so requires a high level of expertise and usually leads to a simplification that might miss important features of the process under study. A better strategy is to generate a custom design that is tailored to the characteristics of the process. This approach is called optimal design of experiments and its goal is to find the best possible design that can be carried out for the experimental scenario at hand. To this end, this approach treats the generation of a design as an optimization problem and makes use of different algorithms to solve it. In this dissertation, we propose new and more efficient algorithmic techniques for the generation of optimal experimental designs. As shown by an extensive set of computational experiments, the proposed algorithms are able to generate designs with better quality and in shorter execution times than other algorithmic methods. Additionally, it is also shown how the flexibility of these algorithms can be leveraged in order to generate new,designs that, in many cases, have better properties than the standard designs