BMI optimization by using parallel UNDX real-coded genetic algorithm with Beowulf cluster

This paper deals with the global optimization algorithm of the Bilinear Matrix Inequalities (BMIs) based on the Unimodal Normal Distribution Crossover (UNDX) GA. First, analyzing the structure of the BMIs, the existence of the typical difficult structures is confirmed. Then, in order to improve the performance of algorithm, based on results of the problem structures analysis and consideration of BMIs characteristic properties, we proposed the algorithm using primary search direction with relaxed Linear Matrix Inequality (LMI) convex estimation. Moreover, in these algorithms, we propose two types of evaluation methods for GA individuals based on LMI calculation considering BMI characteristic properties more. In addition, in order to reduce computational time, we proposed parallelization of RCGA algorithm, Master-Worker paradigm with cluster computing technique.