How do you choose the best optimization method for a complex spaceflight trajectory problem?

2 Derivative-free methods

Derivative-free methods do not require the information of the derivatives of the objective function and the constraints, and can handle problems that are noisy, discontinuous, or black-box. They are usually more robust and flexible, but they may be slower, less accurate, and more computationally expensive than gradient-based methods. They also may have difficulty handling many constraints or objectives. Some examples of derivative-free methods are direct search methods (DSM), evolutionary algorithms (EA), and swarm intelligence methods (SI).

3 Multi-objective methods

Multi-objective methods aim to find a set of solutions that trade off different conflicting objectives, such as minimizing fuel consumption and maximizing payload mass. They usually combine a single-objective optimization method with a technique to generate, select, and evaluate a diverse and representative set of solutions, called the Pareto front. They can provide valuable insights into the problem and the design space, but they may be computationally intensive and require a suitable way to rank and compare the solutions. Some examples of multi-objective methods are weighted sum methods (WSM), goal programming methods (GPM), and non-dominated sorting genetic algorithm II (NSGA-II).

4 Uncertainty-based methods

Uncertainty-based methods aim to account for the effects of uncertainties in the problem parameters, such as the atmospheric conditions, the vehicle performance, or the mission requirements. They usually involve a probabilistic or stochastic formulation of the problem, and a technique to propagate, quantify, and optimize the uncertainties. They can improve the reliability and robustness of the solution, but they may be complex and challenging to implement and solve. Some examples of uncertainty-based methods are chance-constrained programming (CCP), robust optimization (RO), and stochastic programming (SP).

5 Hybrid methods

Hybrid methods combine two or more optimization methods to exploit their complementary advantages and overcome their limitations. They can be classified into sequential, parallel, or embedded hybrid methods, depending on how they coordinate and integrate the methods. They can offer improved performance and versatility, but they may also increase the complexity and difficulty of the problem and the algorithm. Some examples of hybrid methods are sequential quadratic programming with evolutionary algorithm (SQP-EA), multi-objective evolutionary algorithm with gradient-based local search (MOEA-LS), and direct collocation with adaptive mesh refinement (DC-AMR).

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?