New hybrid genetic operators for real coded genetic algorithm to compute optimal control of a class of hybrid systems

This paper introduces new hybrid cross-over methods and new hybrid selection methods for real coded genetic algorithm (RCGA), to solve the optimal control problem of a class of hybrid system, which is motivated by the structure of manufacturing environments that integrate process and optimal control. In this framework, the discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics and a physical component whose evolution is described by continuous time-driven systems. The proposed RCGA with hybrid genetic operators can outperform the conventional RCGA and the existing Forward Algorithms for this class of systems. The hybrid genetic operators improve both the quality of the solution and the actual optimum value of the objective function. A typical numerical example of the optimal control problem with the number of jobs varying from 5 to 25 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the betterment of the proposed algorithm over the conventional RCGA and Forward Algorithm. Hypothesis t-test and Analysis of Variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm.