A Single-Objective Mixed-Integer Formulation for Cassini2 Space Mission Trajectory Optimization (Cassini2-MINLP)

This paper introduces a new single-objective formulation of the mixed-integer Cassini2 interplanetary trajectory problem (Cassini2-MINLP), extending the GTOPX benchmark library. The formulation introduces four additional decision variables that determine the sequence of intermediate planetary flybys, expanding the set of feasible trajectories and increasing the dimensionality, flexibility, and structural complexity of the trajectory design problem. The resulting search space is 26-dimensional, consisting of 22 continuous trajectory variables and four variables encoding the discrete flyby sequence. The mission scenario assumes a fixed departure from Earth and arrival at Saturn, while the intermediate flyby planets are selected from the set of major Solar System planets. The encounter sequence is modeled using discrete variables derived from a relaxed continuous encoding through rounding and bounding operations, resulting in a mixed-integer nonlinear programming (MINLP) problem. The objective is to minimize the total ΔV, representing propellant consumption and overall energetic efficiency. To evaluate algorithmic performance on this challenging benchmark, eight well-established and recent optimization algorithms from three methodological families (ACO, DE, and CMA-ES) are evaluated under a consistent experimental setup with fixed random seeds to ensure reproducibility. Statistical analyses based on the 30 independent runs using the Friedman test confirm highly significant differences among the algorithms, with the DISHr algorithm achieving the best average rank at value 1.567 and statistically outperforming several other competing methods according to the Nemenyi post-hoc test. The results demonstrate that the Cassini2-MINLP formulation provides a challenging and practically relevant benchmark for trajectory optimization and establishes a foundation for future research on multi-objective formulations and advanced optimization strategies for complex interplanetary missions.