Optimal exact experimental designs with correlated errors through a simulated annealing algorithm

Abstract

Simulated annealing (SA) is a stochastic optimization method with principles taken from the physical process called “annealing” which aims to bring a solid to its ground state or a state of minimum energy. SA is known as a simple heuristic tool suitable for providing direct or approximate solutions to a wide variety of combinatorial problems. This paper is concerned with the problem of determining optimal exact experimental designs with n observations and k two-level factors assuming the existence of correlated errors with a known correlation structure. A simulated annealing algorithm has been developed and applied for the search of D- and A-optimal designs. An extensive discussion regarding the right choices of the initial parameters is presented and a method of self-improvement of the algorithm is suggested via a series of repeated executions. Finally, a version of the SA algorithm is used to find optimal exact designs in the case of continuous observations with known covariance function.