Multiobjective Optimization for Space Mission Design Problems

In a variety of applications in industry and finance the problem arises that several objective functions have to be optimized concurrently leading to a multiobjective optimization problem (MOP). For instance, in space mission design, which we address in this chapter, two typical important objectives are the time of flight (TOF) of the spacecraft to reach its destiny, and the cost of the mission (e.g., measured by the change in velocity v, which has a direct impact on the fuel consumption and hence also on the overall cost of the mission). As these objectives are typically contradicting—the ‘cheapest’ trajectory is certainly not the fastest one and vice versa—it comes as no surprise that the solution set, the so-called Pareto set, does not consist of one single solution (as for classical scalar optimization problems (SOPs)). Instead, it forms a (k − 1)-dimensional object where k is the number of objectives involved in the MOP. In this chapter, we introduce the concept of multiobjective optimization (MOO) and state some theoretical background. Further, we present the state-ofthe-art of both deterministic and stochastic search methods to compute a finite size representation of the Pareto set, respectively its image, the Pareto front. Furthermore, we discuss scenarios in which MOO has been considered for MOPs related to space mission design. The remainder of this chapter is organized as follows: In Sec. II, we give a brief introduction to MOO. In Sec. III, we state the most commonly used mathematical programming techniques for MOPs and in Sec. IV we give an overview of evolutionary MOO algorithms. In Sec. V, we briefly summarize some research works for which MOO techniques have been used to solve space mission design problems. Finally, in Sec. VI, we discuss potential future research trends in this field.