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Novel Hybrid Approaches For Real Coded Genetic Algorithm to Compute the Optimal Control of a Single Stage Hybrid Manufacturing Systems

Authors: M. Senthil Arumugam, M.V.C. Rao


This paper presents a novel two-phase hybrid optimization algorithm with hybrid genetic operators to solve the optimal control problem of a single stage hybrid manufacturing system. The proposed hybrid real coded genetic algorithm (HRCGA) is developed in such a way that a simple real coded GA acts as a base level search, which makes a quick decision to direct the search towards the optimal region, and a local search method is next employed to do fine tuning. The hybrid genetic operators involved in the proposed algorithm improve both the quality of the solution and convergence speed. The phase–1 uses conventional real coded genetic algorithm (RCGA), while optimisation by direct search and systematic reduction of the size of search region is employed in the phase – 2. A typical numerical example of an optimal control problem with the number of jobs varying from 10 to 50 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the validity of the proposed algorithm with the conventional RCGA and PSO techniques. Hypothesis t – test and analysis of variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm. The results clearly demonstrate that the proposed algorithm not only improves the quality but also is more efficient in converging to the optimal value faster. They can outperform the conventional real coded GA (RCGA) and the efficient particle swarm optimisation (PSO) algorithm in quality of the optimal solution and also in terms of convergence to the actual optimum value.

Keywords: Hybrid systems, Optimal Control, Particle Swarm Optimization (PSO), real coded genetic algorithm (RCGA), Hybrid real coded GA (HRCGA), and Hybrid genetic operators

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