Space Missions Engineering Laboratory

• Astrodynamics
• Space Robotics
• On-Board Autonomy
• Optimization
  • Multiobjective Optimization
  • Multidisciplinary Optimization
  • Global Optimization
  • Local Optimization
  • Heuristic Methods
• Soft Computing
• Autonomous Navigation

Multiobjective Optimization

In the frame of design optimization, a given performance of a product is evaluated as a numerical value resulting from the application of an appropriate mathematical function, called the objective function. However, most real problems involve the achievement of several performances; then, the process of the product improvement can ask for the simultaneous optimization of several objective functions, leading to a so-called multiobjective optimization problem. However, the result of a multiobjective optimization problem is typically represented by a set of optimal solutions, rather than a single global optimum. Then, useful mathematical techniques for multiobjective optimization must be able to describe this set of solutions, usually called Pareto optimal solutions, identifying as much of them as possible. The previous considerations are immediately applicable to all the fields of engineering. The space mission design represents a relevant example: it aims at satisfying several requirements, concerning the mission objectives, the technological constraints, and the necessity of minimizing the mission cost. These requirements lead to the necessary definition of several evaluation criteria, corresponding to several objective functions.

The mathematical procedure that has best solved the problems involved in the multiobjective design optimization concerns with the application of the so-called Evolutionary Algorithms. The advantages of this procedure, due for example to the possibility of handling several solutions in each optimization process in order to identify more optimal solutions at the end of a simulation, led to the development of several multiobjective optimization tools in the past. However, new and more effective algorithms are required to improve the performances related to a complete identification of the Pareto optimal fronts and to the efficient management of multiobjective optimization problems involving more than two objective functions.

Our group is dedicating great effort to study and develop algorithms to efficiently solve multiobjective optimization problems typically characterizing space related applications. Results of classical methods have been improved through the extensive use of innovative heuristics during the optimization process and tools have been developed based on Fast Evolutionary Programming and Particle Swarm Optimization methods, which can efficiently describe the Pareto optimal front of problems characterized by a large number of objective functions.