This thesis is concerned with developing algorithms for solving exact optimal design and clustering problems in statistics. To alleviate the possibility of being trapped at a local optimum, which is frequently the case in the existing algorithms, we developed Tabu search(TS)-based algorithms for both single- and multi-objective problems.
We first developed TS-based algorithms for the exact optimal design and clustering problems with a single objective. We further developed TS-based direct algorithms(TSDA) which can handle multi-objective problems. TSDA is based on the difinition of Pareto-efficient solutions.
Computational experiments for single-objective problems indicate that for the exact optimal problems, TS-based algorithms perform better than simulated annealing(SA) and Fedorov algorithm(FEA) in terms of the number of successes per unit time which may be considered as a combining measure of solution quality and computational efforts required, although SA is better in terms of solution quality and FEA requires less computing than the others. For the clustering problem, SA generally performs better than TS and K-Means algorithm in terms of solution quality. The K-Means algorithm requires less computing time than the others. In terms of the number of successes per unit time for complex problems, TS performs better than the others.
The experimental results for multi-objective problems show that for the exact optimal design problem, TSDA is far superior to the existing algorithm. However, for the clustering problem, TSDA tends to require more computing time than the other algorithm as the number of criteria increases.
In summary, TS-based algorithm are believed to be useful alternatives to the existing algorithms for solving the exact optimal design and the clustering problems in statistics. It is recommended that future research be directed towards improving the present TSDA with respect to the required amount of computing time for the clustering problem with many criteria.
