On Testing Global Optimization Algorithms for Space Trajectory Design

Abstract

In this paper we discuss the procedures to test a global search algorithm applied to a space trajectory design problem. Then, we present some performance indexes that can be used to evaluate the effectiveness of global optimization algorithms. The performance indexes are then compared highlighting the actual significance of each one of them. A number of global optimization algorithms are tested on four typical space trajectory design problems. From the results of the proposed testing procedure we infer for each pair algorithm-problem the relation between the heuristics implemented in the solution algorithm and the main characteristics of the problem under investigation. From this analysis we derive a novel interpretation of some evolutionary heuristics, based on dynamical system theory and we significantly improve the performance of one of the tested algorithms.

A global optimization method for the design of space trajectories

“…As an example, in [27] an algorithm based on mixing Differential Evolution with a Basin Hopping scheme is proposed.…”

“…However, a recent study [27] reveals that a basic version of Monotonic Basin Hopping (MBH, see, e.g., [17,18]) is able to outperform some other algorithms, including DE, on some benchmark problems. This fact led us to propose a method based on the MBH approach.…”

“…Particularly relevant are recent studies carried on to compare the performance of different GO algorithms on different benchmark problems. The tested algorithms in these studies (see [5,13,14,20,[26][27][28]) include, besides GA and DE, also Particle Swarm Optimization, Adaptive Simulated Annealing, GLOBAL, COOP, Multilevel Coordinate Search, DIRECT. It is worth to note that, during last years, people at ESA ACT (Advanced Concept Team) carried on a considerable effort to make standard benchmark problems available to the optimization community,both in C/C++ language and in MATLAB (see http://www.esa.int/gsp/ACT/inf/op/globopt.htm).…”

A hybrid multiobjective optimization algorithm applied to space trajectory optimization

“…In order to avoid an excessive crowding of the solutions, two restart mechanisms are implemented to regenerate some parts of the population. The effectiveness of the use of local moves was recently demonstrated by Schütze et al [8], [9], while restart mechanisms have been successfully introduced in global single objective optimization of multi-gravity assist problems [10]. The algorithm proposed in this paper is based on the multiagent collaborative search approach proposed in [11], [12].…”

Automated Multigravity Assist Trajectory Planning with a Modified Ant Colony Algorithm

“…, [23][24][25] 100 runs give an error in the determination of the exact rate (admissibility or feasibility) of less than 6% with 92% confidence. This means that two results that differ by less than 12% cannot be said, with 100% confidence, to be different.…”