• Proposes a risk-adjustable chance-constrained goal programming (RACCGP) model that dynamically balances operational risk and cost for electricity-hydrogen integrated energy systems (EH-IES).
• Integrates chance-constrained programming with goal programming and employs an intelligent nonlinear solution method based on the state transition algorithm (STA) with an improved discretized step transformation for enhanced computational efficiency.
• Demonstrates that the proposed RACCGP model reduces operational costs while effectively controlling risk compared to traditional chance-constrained programming (CCP).
• Validates that the STA-based solution method outperforms average sample sampling in both computational efficiency and solution quality.