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Robust Total Energy Optimization of Flexible Manufacturing Systems Based on Renyi Mean-Entropy Criterion

To deal with uncertainties in energy optimization of flexible manufacturing systems (FMSs), this paper presents a robust total energy optimization problem with productive and idle powers of resources being random variables (RVs). Using the weighted p-timed Petri net model of FMS, the robust energy-optimal schedule is determined by searching the robust shortest path of reachability graph based on Renyi mean-entropy criterion. The Renyi quadratic entropy is proposed as a robustness measure which does not depend on the Gaussianity of RVs and can be computed easily from samples. Next, Bellman's dynamic programming is applied to find the shortest path in Renyi mean-entropy criterion. The effectiveness of Renyi mean-entropy criterion is verified with mathematical rigour as well as extensive numerical results from simulations and an industrial stamping system, in terms of computational complexity and deviation from optimality.