The Soft Fixed Route Hybrid Electric Aircraft Charging Problem with Variable Speed

The shift toward sustainable aviation has accelerated research into hybrid electric aircraft, particularly in the context of regional air mobility. To support this transition, we introduce the Soft Fixed Route Hybrid Electric Aircraft Charging Problem with Variable Speed (S-FRHACP-VS), a novel optimization problem for managing hybrid electric aircraft operations that considers variable speed. The objective is to minimize total costs by determining charging strategies, refueling decisions, hybridization ratios, and speed decisions while adhering to a soft schedule. This paper introduces an iterative variable-based fixation heuristic, named Iterative Two-Stage Mixed-Integer Programming Heuristic (ITS-MIP-H), that alternatively optimizes speed and hybridization ratios while considering the soft schedule constraints, nonlinear charging, and nonlinear energy consumption functions. In addition, a metaheuristic genetic algorithm is proposed as an alternative optimization approach. Experiments on ten realistic flight instances demonstrate that optimizing speed leads to an average cost reduction of 7.64% compared to the best non-speed-optimized model, with reductions of up to 18.64% compared to an all-fuel-based heuristic. Although genetic algorithm provides a viable alternative that performs better than the best non-speed-optimized model, the proposed iterative variable-based fixation heuristic approach consistently outperforms the metaheuristic, achieving the best solutions within seconds. These results provide new insights into the integration of hybrid electric aircraft within transportation networks, contributing to advancements in aircraft routing optimization, energy-efficient operations, and sustainable aviation policy development.