Heuristic and metaheuristic algorithms for the generation of optimal experimental designs

Date: 15 June 2015

Venue: University of Antwerp, Promotiezaal Grauwzusters - Lange SInt-Annastraat 7 - 2000 Antwerp

Time: 2:00 PM

PhD candidate: Daniel Palhazi Cuervo

Principal investigator: Prof Peter Goos

Co-principal investigator: Prof Kenneth Sörensen

Short description: PhD defence Daniel Palhazi Cuervo - Faculty of Applied Economics



Abstract

Experimentation is arguably one of the fundamental pillars that enables the creation of new knowledge. The appropriate execution and analysis of a carefully controlled experiment is the main (and perhaps the only) way to establish a cause-effect relationship. The purpose of an experiment is to identify the influence that a set of experimental variables has on the process under study. The design of an experiment mainly 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 have been proposed to achieve this goal. Although these designs have very good properties, they cannot always be applied to the complex experimental scenarios found in practice. A better strategy is to generate a custom design that is specifically 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 optimization algorithms to solve it.

The benefits of using algorithmic techniques for the optimal design of experiments have been extensively documented in the literature. This approach, however, has been criticized by important members of the statistical community and is not yet considered a routine practice. One of their main arguments is that the designs generated by algorithmic methods do not always match the quality of the standard experimental designs. Many statisticians are therefore reluctant to opt for this approach and remain faithful to standard designs.

This dissertation addresses such criticism levelled against this approach: it proposes new and more efficient algorithmic techniques for the generation of optimal experimental designs. These techniques are based on a family of optimization algorithms known as metaheuristics. 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.

This dissertation is divided into two parts. The first part focusses on the generation of optimal designs of industrial experiments. These experiments are widely used for quality control in the development and improvement of products and processes. The second part focuses on the generation of optimal designs of stated choice experiments. These experiments are widely used to study how people make choices and to identify the elements that drive people's preferences.