Multi-Objective Optimization of Space Exploration Campaign Schedules with Stochastic Launch Delay

Complex, multimission space exploration campaigns are particularly vulnerable to payload development and launch delays due to program-level schedule constraints and interactions between the payloads. While deterministic space logistics problems seek strongly performing (e.g., minimized cost) solutions, stochastic models must balance performance with robustness. The introduction of stochastic delays to the otherwise deterministic problem produces large and computationally intractable optimization problems. This paper presents and compares two multi-objective (minimized cost vs robustness) formulations for the stochastic campaign scheduling problem. First, a multi-objective mixed-integer quadratically constrained program (MOMIQCP) formulation is presented. Secondly, due to the computational intractability of the MOMIQCP for large problems, a method for constructing restricted, deterministic scheduling subproblems is defined. These subproblems are input to a noisy multi-objective evolutionary algorithm (NMOEA), which is used for the purpose of stochastically applying delays to the deterministic subproblem and building approximations of the objectives of the stochastic problems. Both methods are demonstrated through case studies, and the results demonstrate that the NMOEA can successfully find strongly performing solutions to larger stochastic scheduling problems.