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In this paper, a new hybrid algorithm, based on multi-objective genetic programming and bond graphs in combination with Monte Carlo simulation, is proposed for Pareto optimal robust design of dynamical systems. For this purpose, first, an embryo model is considered for a dynamical system. Then, genetic programming is used to help this embryo model evolve through generations and achieve an optimum model. It is clear that without considering the uncertain parameters of the designing system, unwanted behaviors could occur. To overcome this, Monte Carlo simulation has been used to minimize the variations of objective functions by generating some samples around the nominal values of the uncertain parameters. In other words, the mean and variance of the objective function are minimized simultaneously through sampling, generated by Monte Carlo simulation, to reach a robust behavior. The proposed algorithm has been employed for robust design of two case studies, namely a closed-loop typewriter drive system and an optimum controller for quarter-car suspension system. A comparison between the results obtained using the proposed algorithm and those obtained through other approaches in the literature shows that more robust behavior in the presence of uncertainties can be observed in the proposed method.

Multi-objective robust design approach usage in integration of bond graph and genetic programming