Multi-objective Trajectory Optimization Problem

In this chapter, the SMV trajectory optimization problem established in the previous chapter is reformulated and extended to a multi-objective continuous-time optimal control model. Because of the discontinuity or nonlinearity in the vehicle dynamics and mission objectives, it is challenging to generate a compromised trajectory that can satisfy constraints and optimize objectives. To effectively analyze the relationships between objectives and calculate the Pareto front, this chapter constructs a multi-objective optimal control solver based on the evolutionary multi-objective optimization. A dominance relationship criterion based on violation degree is also defined and used to select the new generation. Simulation results are provided to illustrate the effectiveness and feasibility of the proposed algorithm in dealing with the multi-objective SMV trajectory optimization problems. Furthermore, in order to take into account the preference requirements, different transformation techniques are also proposed and the original problem is then transcribed to a single-objective formulation. These techniques are discussed in detail in the following sections. Numerical simulations were carried out and the results indicate that the constructed strategies are effective and can provide compromised solutions for solving the multi-objective SMV trajectory design problem with the consideration of preference constraints.