Pareto simulated annealing for the design of experiments: illustrated by a gene expression study

Experimental design is concerned with the problem of allocating resources within an experiment to ensure that objectives of the experiment are achieved at the minimum cost. This paper focuses on the generation of optimal or near-optimal designs for large and complex experiments where it is infeasible to carry out an ex- haustive search of the design space. Optimal designs for gene expression studies, aimed at investigating the behaviour of genes, are considered, where the optimality criterion employed is Pareto optimality. We develop an adaptation of the metaheuris- tic method of Pareto simulated annealing to generate an approximation to the set of Pareto optimal designs for large and complex experiments. We develop algorithms that utilise response surface methodology to search systematically for the optimal values of parameters associated with Pareto simulated annealing and performance is evaluated using quality measures.