A hybrid intelligent method to dynamic real-time optimization

Wanlu Zhou; Huan Li; Jun Fu; Siheng Yao; Ying Jin; Wanlu Zhou; Huan Li; Jun Fu; Siheng Yao; Ying Jin

doi:10.3934/jimo.2026170

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 4926-4944. doi: 10.3934/jimo.2026170

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Research article

A hybrid intelligent method to dynamic real-time optimization

1.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110000, China
2.
School of Mathematics and Statistics, Liaoning University, Shenyang, Liaoning, 110036, China

Received: 25 June 2026 Revised: 21 August 2026 Accepted: 31 August 2026 Published: 11 September 2026
90C26, 90C39

A novel hybrid intelligent dynamic real-time optimization (DRTO) algorithm is proposed for dynamic optimization problems under time-varying disturbances. First, due to the existence of time-varying disturbances in dynamic systems, a shrinking-horizon optimization framework that is progressively shortened at a fixed sampling period is employed to suppress them. Second, at each prediction horizon, a particle swarm optimization (PSO) algorithm explores the entire search space to identify the region containing the global optimum. A sequential quadratic programming (SQP) algorithm is then applied within this detected area to obtain a global optimal prediction control sequence. Subsequently, the first control component of the control sequence is implemented to update the system state initial estimate based on the latest disturbance measurement for the next prediction horizon. While the horizon shrinks, the optimization process is repeated until a near-global optimal control sequence is generated. Finally, simulation results of the cart-spring-damper (CSD) system demonstrate the effectiveness of the proposed hybrid intelligent algorithm, whose optimization performance outperforms both a pure deterministic algorithm and existing intelligent algorithms.
- hybrid intelligent,
- dynamic real-time optimization,
- time-varying disturbances,
- shrinking-horizon optimization,
- improved particle swarm optimization
Citation: Wanlu Zhou, Huan Li, Jun Fu, Siheng Yao, Ying Jin. A hybrid intelligent method to dynamic real-time optimization[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 4926-4944. doi: 10.3934/jimo.2026170

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Abstract

A novel hybrid intelligent dynamic real-time optimization (DRTO) algorithm is proposed for dynamic optimization problems under time-varying disturbances. First, due to the existence of time-varying disturbances in dynamic systems, a shrinking-horizon optimization framework that is progressively shortened at a fixed sampling period is employed to suppress them. Second, at each prediction horizon, a particle swarm optimization (PSO) algorithm explores the entire search space to identify the region containing the global optimum. A sequential quadratic programming (SQP) algorithm is then applied within this detected area to obtain a global optimal prediction control sequence. Subsequently, the first control component of the control sequence is implemented to update the system state initial estimate based on the latest disturbance measurement for the next prediction horizon. While the horizon shrinks, the optimization process is repeated until a near-global optimal control sequence is generated. Finally, simulation results of the cart-spring-damper (CSD) system demonstrate the effectiveness of the proposed hybrid intelligent algorithm, whose optimization performance outperforms both a pure deterministic algorithm and existing intelligent algorithms.

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