Adaptive differential evolution approaches in real-time optimization of co-generation systems for enhanced energy minimization

• RTO optimizes boilers and turbines to cut energy costs under varying demands. • DE ensures a strong global search but converges slower than HDE and ADE. • HDE improves cost savings by enhancing convergence and solution accuracy. • ADE excels in turbine control, offering precise tracking and lower effort. • HDE is the best for cost reduction, while ADE suits complex system dynamics. This paper examines Real Time Optimization (RTO) for an industrial cogeneration plant featuring a tightly coupled multi boiler turbine network, in which fluctuating steam and power demands and fuel price volatility necessitate continual economic re optimization while preserving closed loop stability. Three evolutionary optimizers are Differential Evolution (DE), Hybrid Differential Evolution (HDE), and Adaptive Differential Evolution (ADE) deployed as the supervisory RTO layer above the regulatory controllers, with Model Predictive Control (MPC) regulating boiler pressure (Control Variable 1, CV1) and drum level CV2 and PI or PI loops regulating turbine power. A deterministic, repeatable stress test is introduced through sequential step changes in high pressure steam demand, medium pressure steam demand, power demand, and natural gas price, enabling systematic evaluation of transient adaptability and robustness. Over five boilers and the turbine network, multi run mean and deviation results show that ADE delivers the most consistent overall behavior, yielding smoother operating trajectories, improved tracking, and lower energy usage. Specifically, the total integrated energy consumption is approximately 895 MWh with ADE, compared to 926 MWh with DE and 1259 MWh with HDE, equivalent to reductions of about 3 percent versus DE and 29 percent versus HDE. Control performance improves in parallel the mean boiler pressure (Integral Square Error) ISE CV1 drops by roughly 68 percent relative to DE and 71 percent relative to HDE, while turbine regulation shows substantial enhancement with turbine ISE reduced by about 98 percent compared with DE. Overall, the results demonstrate that adaptive evolutionary optimization strengthens coordination between the RTO and control layers, providing a robust and energy efficient strategy for real time cogeneration operation under dynamic demand and price disturbances.