This paper develops and compares four distinct constraint-aware and adaptive matheuristic approaches based on tabu search, simulated annealing, bacterial foraging optimisation and multi-ant colony optimisation. By integrating metaheuristic search with a mixed-integer linear programming (MILP) model, a hybrid framework is designed to optimise aircraft departure sequencing with rigorous precision. The core novelty lies in how this integration reconciles the exactness of mathematical programming with the interpretability of metaheuristics. Standard MILP models offer precise solutions but function as opaque ‘black boxes’, while standard metaheuristics operate via understandable moves but often rely on simplified feasibility checks. The proposed solution merges these strengths, employing adaptive metaheuristics to generate candidate sequences using interpretable moves while a restricted MILP acts as a high-fidelity evaluator. Fixing the sequence enables the MILP to focus solely on optimising continuous timings and holds. This ensures that every candidate step is strictly feasible and optimally timed, turning the solution process into a sequence of human-readable queue adjustments backed by the numerical precision of an exact solver. In a calibrated Antalya Airport case study with 40 aircraft, all algorithms attain the MILP optimum or remain within 1% of it, achieving a 29% reduction in hold fuel compared to first-come-first-served (FCFS). In denser 50-aircraft scenarios, the approach maintains high solution quality within feasible time limits, proving that explainability does not require sacrificing computational efficiency.
