A Time-Dependent TSP Formulation for the Design of an Active Debris Removal Mission using Simulated Annealing

This paper proposes a formulation of the Active Debris Removal (ADR) Mission Design problem as a modified Time-Dependent Traveling Salesman Problem (TDTSP). The TDTSP is a well-known combinatorial optimization problem, whose solution is the cheapest mono-cyclic tour connecting a number of non-stationary cities in a map. The problem is tackled with an optimization procedure based on Simulated Annealing, that efficiently exploits a natural encoding and a careful choice of mutation operators. The developed algorithm is used to simultaneously optimize the targets sequence and the rendezvous epochs of an impulsive ADR mission. Numerical results are presented for sets comprising up to 20 targets.

[1]  Lorenzo Casalino,et al.  Optimization of active debris removal missions with multiple targets , 2017 .

[2]  Janez Brest,et al.  Performance comparison of self-adaptive and adaptive differential evolution algorithms , 2007, Soft Comput..

[3]  Stephen C. Graves,et al.  An n-Constraint Formulation of the (Time-Dependent) Traveling Salesman Problem , 2016 .

[4]  G. Colasurdo,et al.  Indirect Optimization of Finite-Thrust Cooperative Rendezvous , 2015 .

[5]  Guido Colasurdo,et al.  Integrated Optimization of Ascent Trajectory and SRM Design of Multistage Launch Vehicles , 2019, ArXiv.

[6]  Ping Lu,et al.  Coast Arcs in Optimal Multiburn Orbital Transfers , 2012 .

[7]  Max Cerf.  Multiple Space Debris Collecting Mission: Optimal Mission Planning , 2015, J. Optim. Theory Appl..

[8]  Guido Colasurdo,et al.  GTOC8: Results and Methods of Team 22 , 2016 .

[9]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[10]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[11]  John E. Prussing,et al.  Optimal multiple-impulse time-fixed rendezvous between circular orbits , 1984 .

[12]  Dario Izzo,et al.  Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO , 2017, EvoCOP.

[13]  J. K. Lenstra,et al.  Complexity of vehicle routing and scheduling problems , 1981, Networks.

[14]  C. McDiarmid.  SIMULATED ANNEALING AND BOLTZMANN MACHINES A Stochastic Approach to Combinatorial Optimization and Neural Computing , 1991 .

[15]  N. Johnson,et al.  Instability of the Present LEO Satellite Populations , 2008 .

[16]  Dario Izzo,et al.  Parallel global optimisation meta-heuristics using an asynchronous island-model , 2009, 2009 IEEE Congress on Evolutionary Computation.

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  Chiara Toglia,et al.  Optimization of orbital trajectories using genetic algorithms , 2008 .

[19]  Max Cerf,et al.  Multiple Space Debris Collecting Mission—Debris Selection and Trajectory Optimization , 2011, J. Optim. Theory Appl..

[20]  D. Izzo.  Revisiting Lambert’s problem , 2014, 1403.2705.

[21]  J Bentner,et al.  Optimization of the time-dependent traveling salesman problem with Monte Carlo methods. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  John E. Prussing,et al.  Optimal multiple-impulse orbital rendezvous , 1967 .

[23]  Guido Colasurdo,et al.  Preliminary Capture Trajectory Design for Europa Tomography Probe , 2018, International Journal of Aerospace Engineering.

[24]  Dario Izzo,et al.  Evolving Solutions to TSP Variants for Active Space Debris Removal , 2015, GECCO.

[25]  O. Weck,et al.  Large Satellite Constellation Orbital Debris Impacts: Case Studies of OneWeb and SpaceX Proposals , 2017 .

[26]  S. Flegel,et al.  Active debris removal of multiple priority targets , 2013 .

[27]  Maurice Queyranne,et al.  The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling , 1978, Oper. Res..

[28]  Lorenzo Casalino,et al.  Tour of Jupiter Galilean moons: Winning solution of GTOC6 , 2014 .

[29]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[30]  Ozgur Gurtuna,et al.  On-Orbit Satellite Servicing: A Space-Based Vehicle Routing Problem , 2003 .

[31]  Lorenzo Casalino,et al.  Optimal Cooperative Deployment of a Two-Satellite Formation into a Highly Elliptic Orbit , 2012 .