Graph colouring approaches for a satellite range scheduling problem
 Nicolas Zufferey,
 Patrick Amstutz,
 Philippe Giaccari
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A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NPhard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be scheduled on several resources, while respecting time and capacity constraints. In the permutation solution space, which is widely used by other researchers, a solution is represented by a permutation of the jobs, and a schedule builder is needed to generate and evaluate a feasible schedule from the permutation. On the contrary, our heuristics are based on the solution space which contains all the feasible schedules. Based on the similarities between the graph colouring problem and the MuRRSP, we show that the latter solution space has significant advantages. A tabu search and an adaptive memory algorithms are designed to tackle the MuRRSP. These heuristics are derived from efficient graph colouring methods. Numerical experiments, performed on large, realistic, and challenging instances, showed that our heuristics are very competitive, robust, and outperform algorithms based on the permutation solution space.
 BarNoy, A., Guha, S., Naor, J. S., Schieber, B. (2002) Approximating the throughput of multiple machines in realtime scheduling. SIAM Journal on Computing 31: pp. 331352 CrossRef
 Barbulescu, L., Watson, J.P., Whitley, L. D., Howe, A. E. (2004) Scheduling spaceground communications for the air force satellite control network. Journal of Scheduling 7: pp. 734 CrossRef
 Barbulescu, L., Howe, A. E., Whitley, L. D., & Roberts, M. (2004b). Trading places: how to schedule more in a multiresource oversubscribed scheduling problem. In International conference on automated planning and scheduling.
 Barbulescu, L., Howe, A. E., Whitley, L. D. (2006) AFSCN scheduling: how the problem and solution have evolved. Mathematical and Computer Modelling 43: pp. 10231037 CrossRef
 Bensana, E., Lemaitre, M., Verfaillie, G. (1999) Earth observation satellite management. Constraints 4: pp. 293299 CrossRef
 Bianchessi, N., Cordeau, J.F., Desrosiers, J., Laporte, G., Raymond, V. (2007) A heuristic for the multisatellite, multiorbit and multiuser management of earth observation satellites. European Journal of Operational Research 177: pp. 750762 CrossRef
 Bloechliger, I. (2005). Suboptimal colorings and solution of large chromatic scheduling problems. PhD thesis, École Polytechnique Fédérale de Lausanne, Switzerland.
 Bloechliger, I., Zufferey, N. (2008) A graph coloring heuristic using partial solutions and a reactive tabu scheme. Computers & Operations Research 35: pp. 960975 CrossRef
 Brélaz, D. (1979) New methods to color vertices of a graph. Communications of the Association for Computing Machinery 22: pp. 251256
 Cordeau, J.F., Laporte, G. (2005) Maximizing the value of an earth observation satellite orbit. Journal of the Operational Research Society 56: pp. 962968 CrossRef
 Culberson, J. (1992). Iterated greedy graph coloring and the difficulty landscape (Tech. rept. TR 9207). Department of Computer Science, University of Alberta, Edmonton.
 Culberson, J. C., & Luo, F. (1995). Exploring the kcolorable landscape with iterated greedy. DIMACS Series in Discrete Mathematics and Theoretical Computer Science.
 DauzèrePérès, S. (1995) Minimizing late jobs in the general one machine scheduling problem. European Journal of Operational Research 81: pp. 131142
 Davis, L. (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, New York
 Frank, J., Jonsson, A., Morris, R., & Smith, D. (2001). Planning and scheduling for fleets of earth observing satellites. In Proceedings of the sixth international symposium on artificial intelligence, robotics, automation and space.
 Gabrel, V., Murat, C. (2003) Operations research in space and air. Mathematical programming for Earth observation satellite mission planning. Kluwer Academic, Boston
 Galinier, P., Hao, J. K. (1999) Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization 3: pp. 379397 CrossRef
 Galinier, P., Hertz, A. (2006) A survey of local search methods for graph coloring. Computers & Operations Research 33: pp. 25472562 CrossRef
 Galinier, P., Hertz, A., Zufferey, N. (2008) An adaptive memory algorithm for the graph coloring problem. Discrete Applied Mathematics 156: pp. 267279 CrossRef
 Garey, M., Johnson, D. S. (1979) Computer and intractability: a guide to the theory of npcompleteness. Freeman, San Francisco
 Globus, A., Crawford, J., Lohn, J., & Pryor, A. (2003). Scheduling earth observing satellites with evolutionary algorithms. In International conference on space mission challenges for information technology, Pasadena, CA.
 Globus, A., Crawford, J., Lohn, J., & Pryor, A. (2004). A comparison of techniques for scheduling earth observing satellites. In Proceedings of the sixteenth innovative applications of artificial intelligence conference (IAAI04).
 Glover, F. (1986) Future paths for integer programming and linkage to artificial intelligence. Computers & Operations Research 13: pp. 533549 CrossRef
 Glover, F., Laguna, M. (1997) Tabu search. Kluwer Academic, Boston
 Gooley, T. D. (1993). Automating the satellite range scheduling process. M.Phil. thesis, Air Force Institute of Technology, USA.
 Habet, D., & Vasquez, M. (2004). Solving the selecting and scheduling satellite photographs problem with a consistent neighborhood heuristic. In Sixteenth IEEE international conference on tools with artificial intelligence.
 Hansen, P. (1986). The steepest ascent mildest descent heuristic for combinatorial programming. In Congress on numerical methods in combinatorial optimization, Capri, Italy.
 Harrison, S. A., Philpott, M. S., & Price, M. E. (1999). Task scheduling for satellite based imagery. In Proceedings of the 18th workshop of the UK planning and scheduling special interest group (pp. 64–78), University of Salfort, UK.
 Hertz, A., Costa, D. (1997) Ants can color graphs. The Journal of the Operational Research Society 48: pp. 295305
 Hertz, A., Werra, D. (1987) Using Tabu search techniques for graph coloring. Computing 39: pp. 345351 CrossRef
 Hertz, A., Plumettaz, M., & Zufferey, N. (2007, accepted). Variable space search for graph coloring. Discrete Applied Mathematics.
 Lemaitre, M., Verfaillie, G., Jouhaud, F., Lachiver, J.M., Bataille, N. (2002) Selecting and scheduling observations of agile satellites. Aerospace Science and Technology 6: pp. 367381 CrossRef
 Marinelli, F., Nocella, S., Rossi, F., & Smriglio, S. (2006). A Lagrangian heuristic for satellite range scheduling with resource constraints (Tech. rept. TRCS 004/2005). Dip. di Informatica, Università L’Aquila, Italy.
 Meuwly, F.X., Ries, B., & Zufferey, N. (2007). Heuristiques pour la coloration de graphes mixtes. Master thesis. Swiss Federal Institute of Technology, EPFL, Lausanne, Switzerland.
 Mladenović, N., Hansen, P. (1997) Variable neighborhood search. Computers & Operations Research 24: pp. 10971100 CrossRef
 Mladenović, N., Plastria, F., Urošević, D. (2005) Reformulation descent applied to circle packing problems. Computers & Operations Research 32: pp. 24192434 CrossRef
 Morgenstern, C. (1996) Distributed coloration neighborhood search. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 26: pp. 335357
 Parish, D. A. (1994). A genetic algorithm approach to automating satellite range scheduling. M.Phil. thesis, Air Force Institute of Technology, USA.
 Pemberton, J. C. (2000). Toward scheduling overconstrained remotesensing satellites. In Proceedings of the second NASA international workshop on planning and scheduling for space.
 Pinedo, M. (2002) Scheduling: theory, algorithms, and systems. Prentice Hall, New York
 Rochat, Y., Taillard, E. (1995) Probabilistic diversification and intensification in local search for vehicle routing. Journal of Heuristics 1: pp. 147167 CrossRef
 Schlack, S. M. (1993). Automating satellite range scheduling. M.Phil. thesis, Air Force Institute of Technology, USA.
 Syswerda, G., Palmucci, J. (1991) The application of genetic algorithms to resource scheduling. Proceedings of the 4th international conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp. 502508
 Vasquez, M., Hao, J.K. (2003) A “logicconstrained” knapsack formulation and a tabu algorithm for the daily photograph scheduling of an earth observation satellite. Computational Optimization and Applications 7: pp. 87103
 Verfaillie, G., & Lemaitre, M. (2001). Selecting and scheduling observations for agile satellites: some lessons from the contraint programming community point of view. In T. Walsh (Ed.), Principles and practice of constraint programming (pp. 670–684).
 Wolfe, W. J., Sorensen, S. E. (2000) Three scheduling algorithms applied to the earth observing systems domain. Management Science 46: pp. 148168 CrossRef
 Zufferey, N. (2002). Heuristiques pour les problèmes de la coloration des sommets d’un graphe et d’affectation de fréquences avec polarités. Ph.D. thesis, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland.
 Title
 Graph colouring approaches for a satellite range scheduling problem
 Journal

Journal of Scheduling
Volume 11, Issue 4 , pp 263277
 Cover Date
 20080801
 DOI
 10.1007/s1095100800668
 Print ISSN
 10946136
 Online ISSN
 10991425
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Oversubscribed satellite scheduling
 Graph colouring heuristics
 Industry Sectors
 Authors

 Nicolas Zufferey ^{(1)}
 Patrick Amstutz ^{(2)}
 Philippe Giaccari ^{(3)}
 Author Affiliations

 1. HEC, Faculté des Sciences Économiques et Sociales, University of Geneva, Boulevard du Pontd’Arve 40, 1211, Geneva 4, Switzerland
 2. Department of Communication and Computer Science, Swiss Federal Institute of Technology, Lausanne, Switzerland
 3. Centre d’Optique, Photonique et Laser, Université Laval, Québec, Canada