Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs

Finding optimal designs for nonlinear models is complicated because the design criterion depends on the model parameters. If a plausible region for these parameters is available, a minimax optimal design may be used to remove this dependency by minimizing the maximum inefficiency that may arise due to misspecification in the parameters. Minimax optimal designs are often analytically intractable and are notoriously difficult to find, even numerically. A population-based evolutionary algorithm called imperialist competitive algorithm (ICA) is applied to find minimax or nearly minimax D-optimal designs for nonlinear models. The usefulness of the algorithm is also demonstrated by showing it can hybridize with a local search to find optimal designs under a more complicated criterion, such as standardized maximin optimality.