As multiple approach technologies are combined, managing parallel-runway operations becomes increasingly complex and traditional sequencing methods no longer suffice. To optimize runway resource utilization and enhance operational efficiency, an arrival sequencing optimization model was formulated for mixed-approach operations that jointly accounts for heterogeneity in aircraft capabilities, feasible flight paths, available runways, and operating modes. A speed-based elastic relaxation strategy was introduced for conflict detection and resolution. The model was solved using a multi-waypoint rolling horizon control-elitist genetic algorithm (MWRHC-EGA). Using Kunming Airport as a case study, the proposed method was validated. Across traffic densities, the algorithm converges rapidly within a limited number of generations. Compared with first-come-first-served (FCFS), under typical traffic (40 arrivals) with required navigation performance authorization required (RNP AR) shares of 20%, 40%, and 60%, the landing time of the last aircraft is advanced by 505, 562, and 748 s, respectively. Under peak traffic (72 arrivals), the advances are 1 257, 1 375, and 1 532 s, respectively. Relative to Gurobi, the optimality gap remains within 1% while computation time is substantially reduced. Against benchmark genetic algorithm (GA) and particle swarm optimization (PSO) solvers, MWRHC-EGA achieves superior solution quality and efficiency. The approach improves runway utilization and overall operational efficiency across scenarios. Monte Carlo simulations with randomized arrival delays indicate robustness. Finally, comparison with total airspace and airport modeller (TAAM) simulations yields an R² of 0.842 8, demonstrating strong applicability to real-world arrival sequencing under mixed-approach conditions.