Construction of exact D-optimal designs by tabu search

Tabu search (TS) has recently emerged as a promising heuristic method for solving complex combinatorial optimization problems. By guiding the search using the so-called tabu list and accepting disimproved solutions at some iterations, TS helps alleviate the risk of being trapped at a local optimum. In this article, we introduce the essential features of TS, apply TS to the problem of constructing an exact D-optimal design for a main-effect or a quadratic model with a finite design space, and compare performances of TS and the Fedorov exchange algorithm (FEA) as modified by Nguyen and Miller (1992). Computational results indicate that although TS requires more computing time per try than FEA, its overall performance is generally better except for the case of quadratic models with a small number of factors. For some test problems, TS also identifies designs with larger determinants than the corresponding designs obtained by FEA.