A global optimization method for the design of space trajectories

The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization (GTOP database). We show that many trajectory optimization problems can be quite efficiently solved by means of relatively simple global optimization techniques relying on standard methods for local optimization. We show in this paper that our approach has been able to find trajectories which in many cases outperform those already known. We also conjecture that this problem displays a “funnel structure” similar, in some sense, to that of molecular optimization problems.

[1]  Fabio Schoen,et al.  Global Optimization of Morse Clusters by Potential Energy Transformations , 2004, INFORMS J. Comput..

[2]  Dario Izzo,et al.  1st ACT global trajectory optimisation competition: Problem description and summary of the results , 2007 .

[3]  Bernardetta Addis,et al.  Disk Packing in a Square: A New Global Optimization Approach , 2008, INFORMS J. Comput..

[4]  C. T. Kelley,et al.  Superlinear Convergence and Implicit Filtering , 1999, SIAM J. Optim..

[5]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[6]  Tamás Vinkó,et al.  Benchmarking different global optimisation techniques for preliminary space trajectory design , 2007 .

[7]  Dario Izzo ADVANCES IN GLOBAL OPTIMISATION FOR SPACE TRAJECTORY DESIGN , 2006 .

[8]  Hiroaki Kobayashi,et al.  International Symposium on Space Technology and Science , 2006 .

[9]  Slawomir J. Nasuto,et al.  Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories , 2007, J. Glob. Optim..

[10]  Pierre Hansen,et al.  Variable neighbourhood search: methods and applications , 2010, Ann. Oper. Res..

[11]  Massimiliano Vasile A global approach to optimal space trajectory design , 2003 .

[12]  Massimiliano Vasile,et al.  Design of Earth–Mars transfer trajectories using evolutionary-branching technique☆ , 2003 .

[13]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[14]  Robert H. Leary,et al.  Global Optimization on Funneling Landscapes , 2000, J. Glob. Optim..

[15]  Massimiliano Vasile,et al.  A hybrid multiagent approach for global trajectory optimization , 2009, J. Glob. Optim..

[16]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[17]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[18]  John Mark Bishop,et al.  Advanced global optimisation for mission analysis and design , 2004 .

[19]  Massimiliano Vasile,et al.  On testing global optimization algorithms for space trajectory design , 2008 .

[20]  Cass T. Miller,et al.  Solution of a Groundwater Control Problem with Implicit Filtering , 2002 .

[21]  Marco Locatelli,et al.  On the Multilevel Structure of Global Optimization Problems , 2005, Comput. Optim. Appl..

[22]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[23]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[24]  D. Mortari,et al.  On the n-Impulse Orbit Transfer using Genetic Algorithms , 2007 .

[25]  P. Cage,et al.  Interplanetary trajectory optimization using a genetic algorithm , 1994 .

[26]  David B. Spencer,et al.  Optimal Spacecraft Rendezvous Using Genetic Algorithms , 2002 .

[27]  C. T. Kelley,et al.  An Implicit Filtering Algorithm for Optimization of Functions with Many Local Minima , 1995, SIAM J. Optim..

[28]  G. Rauwolf,et al.  Near-optimal low-thrust orbit transfers generated by a genetic algorithm , 1996 .

[29]  Fabio Schoen,et al.  Local search based heuristics for global optimization: Atomic clusters and beyond , 2012, Eur. J. Oper. Res..