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This paper proposes a novel scheme of nonuniform discretizetion-based control vector parameterization (ndCVP, for short) for dynamic optimization problems (DOPs) of industrial processes. In our ndCVP scheme, the time span is partitioned into a multitude of uneven intervals, and incremental time parameters are encoded, along with the control parameters, into the individual to be optimized. Our coding method can avoid handling complex ordinal constraints. It is proved that ndCVP is a natural generalization of uniform discretization-based control vector parameterization (udCVP). By integrating ndCVP into hybrid gradient particle swarm optimization (HGPSO), a new optimization method, named ndCVP-HGPSO for short, is formed. By application in four classic DOPs, simulation results show that ndCVP-HGPSO is able to achieve similar or even better performances with a small number of control intervals; while the computational overheads are acceptable. Furthermore, ndCVP and udCVP are compared in terms of two situations: given the same number of control intervals and given the same number of optimization variables. The results show that ndCVP can achieve better performance in most cases.Note to Practitioners-This paper was motivated by the problems of operational optimization in industrial processes. Most problems in industrial processes are dynamic optimization problems, and the aim is to optimize control variables like feeding rates, heating/cooling for reaction over a time span. Most of existing optimization methods use uniform discretization-based control vector parameterization (udCVP for short), in which the time span for optimization is partitioned into a multitude of even intervals and thus merely the control parameters need to be optimized. In this paper, we propose a novel scheme of nonuniform-based discretization control vector parameterization (ndCVP), in which the time span is unevenly partitioned, and the incremental time parameters are encoded into the individual to be optimized as well. It is proved that ndCVP is a natural generalization of udCVP. Moreover, by integrating ndCVP into hybrid gradient particle swarm optimization (HGPSO), a new Manuscript optimization method, named ndCVP-HGPSO for short, is formed for DOPs. Numeric simulations show that ndCVP-HGPSO is a highly competitive method for DOPs, because ndCVP can adjust the time intervals to generate high precision results in compliance with the shape of control trajectories.Index Terms-Dynamic optimization, hybrid gradient particle swarm optimization, nonuniform discretizetion-based control vector parameterization.

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