Three new algorithms for exact d-optimal design problems
Clark A. Mount‐Campbell, Baumin Lee · 1993
This paper presents an application of each of the Simulated Annealing, Tabu Search and Genetic Algorithm methods to solve the exact D-optimal design problems. This thesis is organized in three stand-alone working papers. Each paper describes the work on one of the algorithms, and is a separate chapter therein. In particular, chapter 2 is working paper 1: Experimental Evaluation of the Simulated Annealing Approach to Exact D-optimal Design Problems; chapter 3 is working paper 2: Application of Tabu Search to the Construction of Exact D-optimal Design Problems; and chapter 4 is working paper 3: Application of a Genetic Algorithm to the Construction of Exact D-optimal Design Problems. Performance of each algorithm is tested on a set of standard problems, as well as some large scale problems on the first-order and the second-order linear regression models. The results obtained from these three new algorithms are compared to those from other traditional heuristics, e.g., DETMAX, FDOP and modified DETMAX procedure. It is shown that under certain conditions the proposed Simulated Annealing and Tabu Search algorithms yield better quality (maximum determinant) solutions at comparable CPU times than all the other algorithms. In addition, the Simulated Annealing and Tabu Search algorithms are sensitive to a number of parameters respectively. Some of these effects are investigated and reported herein through the analysis of an experimental design. The Genetic Algorithm approach was unable to demonstrate a promising result for a set of first-order and second-order test cases under our limited computational experience.