Interval multi-objective planning of integrated energy systems via constrained multi-objective chaotic evolution algorithm under multiple uncertainties

The integration of demand response (DR) and renewable energy generation (REG) introduces significant uncertainties that challenge the reliability of integrated energy system (IES) planning. This research proposes a comprehensive interval multi-objective optimization (IMOO) framework designed to simultaneously optimize operational economy, energy efficiency, and carbon emissions while ensuring robustness against multi-source uncertainties. Box uncertainty sets are employed to characterize DR and REG fluctuations, and the resulting uncertain model is transformed into a deterministic equivalent using reliability-based interval probability degrees and interval order relations. To solve the non-linear, high-dimensional planning problem, a novel constrained multi-objective chaotic evolution algorithm (CMOCEO) is developed, incorporating a shift-based penalty constraint-handling mechanism and a reference-point-based non-dominated sorting strategy. Simulation results on a typical IES case demonstrate that the proposed method effectively identifies the optimal equipment capacities. For the case study with uncertainty level 0.2 and objective preference coefficient 0.5, the obtained intervals are total cost [9259587, 10372911] yuan, energy efficiency [0.9281, 1.0281], and carbon emission [5958025, 7367503] kg; for the deterministic model, CMOCEO achieves a runtime of 43.4 s, which is comparable to NSGA-III and significantly faster than other recent algorithms, whose runtimes range from 154.2 s to 482.8 s. Furthermore, decision-makers can flexibly balance system performance and robustness by adjusting objective weights. This study provides a practical tool for the scientific planning of modern energy systems in the presence of volatile demand and intermittent supply.