Generating Mixed Multilevel Orthogonal Arrays By Simulated Annealing

We use the simulated annealing algorithm to construct mixed multilevel balanced orthogonal arrays. We demonstrate how this algorithm can be used to find the multilevel balanced experimental design matrix with the minimal number of runs. These orthogonal arrays are widely used in the quality improvement projects. By formulating the problem as an optimization problem, we show that simulated annealing can find the global optimum, while avoiding being trapped in local extrema. An important application of our results is in experimental designs where variables are discrete in nature. A well balanced design not only saves experimental cost but also arrives at conclusions robust to environmental changes.