This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The second framework is probabilistic optimization, where the instance to optimize is not fully known at the time when a solution is to be proposed, but results from a determined Bernoulli process. Then, the goal is to compute a solution with optimal expected value.
Mots-clés : approximation, reoptimization, hereditary problem, complexity, graph, on-line algorithms, probabilistic optimization
@article{RO_2011__45_3_241_0,
author = {Boria, Nicolas and Paschos, Vangelis T.},
title = {A survey on combinatorial optimization in dynamic environments},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {241--294},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
doi = {10.1051/ro/2011114},
zbl = {1254.90186},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2011114/}
}
TY - JOUR AU - Boria, Nicolas AU - Paschos, Vangelis T. TI - A survey on combinatorial optimization in dynamic environments JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2011 SP - 241 EP - 294 VL - 45 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2011114/ DO - 10.1051/ro/2011114 LA - en ID - RO_2011__45_3_241_0 ER -
%0 Journal Article %A Boria, Nicolas %A Paschos, Vangelis T. %T A survey on combinatorial optimization in dynamic environments %J RAIRO - Operations Research - Recherche Opérationnelle %D 2011 %P 241-294 %V 45 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2011114/ %R 10.1051/ro/2011114 %G en %F RO_2011__45_3_241_0
Boria, Nicolas; Paschos, Vangelis T. A survey on combinatorial optimization in dynamic environments. RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 3, pp. 241-294. doi : 10.1051/ro/2011114. http://archive.numdam.org/articles/10.1051/ro/2011114/
[1] , On randomized online scheduling, in Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, ACM (2002) 134-143. | MR | Zbl
[2] , Online algorithms: a survey. Math. Program. 97 (2003) 3-26. | MR | Zbl
[3] , and , Reoptimizing the traveling salesman problem. Networks 42 (2003) 154-159. | MR | Zbl
[4] , and , Reoptimizing the 0-1 knapsack problem. Discrete Appl. Math. 158 (2010) 1879-1887. | MR | Zbl
[5] , , and , A theoretical framework of hybrid approaches to max sat, in ISAAC, Lecture Notes in Computer Science 1350, edited by H.W. Leong, H. Imai and S. Jain. Springer (1997) 153-162. | MR
[6] , , and , Incremental algorithms for minimal length paths. J. Algorithms 12 (1991) 615-638. | MR | Zbl
[7] , , , and , Algorithms for the on-line traveling salesman problem. Algorithmica 29 (2001) 560-581. | MR | Zbl
[8] , , and , Reoptimization of minimum and maximum traveling salesman's tours, in SWAT, Lecture Notes in Computer Science 4059, edited by L. Arge and R. Freivalds. Springer (2006) 196-207. | MR | Zbl
[9] , , and , Reoptimization of minimum and maximum traveling salesman's tours. J. Discrete Algorithms 7 (2009) 453-463. | MR | Zbl
[10] , and , Complexity and approximation in reoptimization. Cahier du LAMSADE 281. Université Paris-Dauphine (2008). | Zbl
[11] and , Probabilistic sales-delivery man and sales-delivery facility location problems on a tree. Transp. Sci. 29 (1995) 184. | Zbl
[12] , and , Probabilistic a priori routing-location problems. Nav. Res. Logist. 41 (1994) 973-989. | MR | Zbl
[13] and , A linear-time approximation algorithm for the weighted vertex cover problem. J. Algorithms 2 (1981) 198-203. | MR | Zbl
[14] , and , A conceptional outline of a DSS for scheduling problems in the building industry. Decis. Support Syst. 5 (1989) 321-344.
[15] , and , Design aspects of an advanced model-oriented DSS for scheduling problems in civil engineering. Decis. Support Syst. 5 (1989) 321-344.
[16] , and , The shortest path through many points, in Mathematical Proceedings of the Cambridge Philosophical Society 55. Cambridge Univ Press (1959) 299-327. | MR | Zbl
[17] , Problèmes d'optimisation combinatoires probabilistes. Ph.D. thesis, École Nationale des Ponts et Chaussées, Paris, France (1993).
[18] , and , Average-Case Analysis for the Probabilistic Bin Packing Problem, in Mathematics and Computer Science III: Algorithms, Trees, Combinatorics and Probabilities (2004) 149-159. | MR | Zbl
[19] and , The Steiner problem with edge lengths 1 and 2. Inf. Proc. Lett. 32 (1989) 171-176. | MR | Zbl
[20] , A characterization of linear admissible transformations for the m-travelling salesmen problem. Eur. J. Oper. Res. 3 (1979) 232-238. | MR | Zbl
[21] , Probabilistic combinatorial optimization problems. Ph.D. thesis, Massachusetts Institute of Technology (1988). | MR | Zbl
[22] , Traveling salesman facility location problems. Transp. Sci. 23 (1989) 184. | MR | Zbl
[23] , The probabilistic minimum spanning tree problem. Networks 20 (1990) 245-275. | MR | Zbl
[24] , A vehicle routing problem with stochastic demand. Oper. Res. 40 (1992) 574-585. | MR | Zbl
[25] and , A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper. Res. 44 (1996) 286-304. | Zbl
[26] , and , A priori optimization. Oper. Res. 38 (1990) 1019-1033. | MR | Zbl
[27] , and , A priori optimization. Oper. Res. 38 (1990) 1019-1033. | MR | Zbl
[28] , , , , , and . Reoptimization of steiner trees, in SWAT, Lecture Notes in Computer Science 5124, edited by J. Gudmundsson. Springer (2008) 258-269. | MR | Zbl
[29] , and , Reoptimization of weighted graph and covering problems, in WAOA, Lecture Notes in Computer Science 5426, edited by E. Bampis and M. Skutella. Springer (2008) 201-213. | MR | Zbl
[30] , , , , , and , Reoptimization of the shortest common superstring problem, in CPM, Lecture Notes Computer Science 5577, edited by G. Kucherov and E. Ukkonen. Springer (2009) 78-91. | Zbl
[31] , , and , The online-TSP against fair adversaries. Algorithms and Complexity (2000) 137-149. | MR | Zbl
[32] and , Reoptimization of the metric deadline TSP. J. Discrete Algorithms 8 (2010) 87-100. | MR | Zbl
[33] , , , , , and , Reusing optimal TSP solutions for locally modified input instances, in IFIP TCS IFIP 209, edited by G. Navarro, L.E. Bertossi and Y. Kohayakawa. Springer (2006) 251-270.
[34] , , , , , and , On the approximability of TSP on local modifications of optimally solved instances. Algorithmic Operations Research 2 (2007) 83-93. | MR | Zbl
[35] , , and , On the hardness of reoptimization, in SOFSEM, Lecture Notes in Computer Science 4910, edited by V. Geffert, J. Karhumäki, A. Bertoni, B. Preneel, P. Návrat and M. Bieliková. Springer (2008) 50-65. | Zbl
[36] , , , and , Reoptimization of steiner trees: Changing the terminal set. Theor. Comput. Sci. 410 (2009) 3428-3435. | MR | Zbl
[37] , , , , and , The steiner tree reoptimization problem with sharpened triangle inequality, in CIAC, Lecture Notes in Computer Science 6078, edited by T. Calamoneri and J. Díaz. Springer (2010) 180-191. | Zbl
[38] and , Fast reoptimization for the minimum spanning tree problem. J. Discrete Algorithms 8 (2010) 296-310. | MR | Zbl
[39] , and , On the probabilistic min spanning tree problem, in IMCSIT (2010) 893-900.
[40] , and , Reoptimization of maximum weight induced hereditary subgraph problems. Cahier du LAMSADE 311, LAMSADE, Université Paris-Dauphine (2011). | Zbl
[41] , and , Reoptimization of the maximum weight Pk-free subgraph under vertex insertion, in Proc. Workshop on Algorithms and Computation, WALCOM'12, Lect. Notes Comput. Sci. Springer-Verlag (2011), to appear. | MR
[42] , and , On the probabilistic min spanning tree problem. J. Mathematical Modelling and Algorithms. To appear.
[43] , , , and , Probabilistic graph-coloring in bipartite and split graphs. J. Combin. Optim. 17 (2009) 274-311. | MR | Zbl
[44] , , and , A priori parallel machines scheduling. Comput. Ind. Eng. 58 (2010) 488-500.
[45] , , and , Paths, trees, and minimum latency tours, in FOCS. IEEE Computer Society (2003) 36-45.
[46] , Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976).
[47] and , On-line vertex-covering. Theor. Comput. Sci. 332 (2005) 83-108. | MR | Zbl
[48] and , Online coloring of comparability graphs: some results. Report, Chair ROSE-2007-001, École Polytechnique Fédérale de Lausanne (2007).
[49] , and , On-line maximum-order induced hereditary subgraph problems, in SOFSEM 2000 - Theory and Practice of Informatics, Lecture Notes in Computer Science 1963, edited by V. Hlavcáˇ, K. G. Jeffery and J. Wiedermann. Springer-Verlag (2000) 326-334. | Zbl
[50] , and , On-line maximum-order induced hereditary subgraph problems. Int. Trans. Operat. Res. 12 (2005) 185-201. | MR | Zbl
[51] , and , On the online track assignment problem. Discrete Appl. Math. To appear. | MR | Zbl
[52] and , A new approach to dynamic all pairs shortest paths. J. ACM 51 (2004) 968-992. | MR | Zbl
[53] and , Multiprocessor online scheduling of hard-real-time tasks. IEEE Trans. Softw. Eng. 15 (2002) 1497-1506.
[54] , , and , Sparsification - a technique for speeding up dynamic graph algorithms. J. ACM 44 (1997) 669-696. | MR | Zbl
[55] , and , Simple and fast reoptimizations for the steiner tree problem. Algorithmic Operations Research 4 (2009) 86-94. | MR | Zbl
[56] and , Updating distances in dynamic graphs. Methods Oper. Res. 49 (1985) 371-387. | MR | Zbl
[57] and , Improved approximation ratios for traveling salesperson tours and paths in directed graphs, in APPROX-RANDOM, Lecture Notes in Computer Science 4627, edited by M. Charikar, K. Jansen, O. Reingold and J.D.P. Rolim. Springer (2007) 104-118. | Zbl
[58] , Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput. 14 (1985) 781-798. | MR | Zbl
[59] , Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. SIAM J. Comput. 26 (1997) 484-538. | MR | Zbl
[60] , On the value of a random minimum spanning tree problem. Discrete Appl. Math. 10 (1985) 47-56. | MR | Zbl
[61] , and , On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12 (1982) 23-39. | MR | Zbl
[62] , and , Fully dynamic algorithms for maintaining shortest paths trees. J. Algorithms 34 (2000) 251-281. | MR | Zbl
[63] , , and , A new single model and derived algorithms for the satellite shot planning problem using graph theory concepts. A. Oper. Res. 69 (1997) 115-134. | Zbl
[64] , and , On finding minimal length superstrings. J. Comput. Syst. Sci. 20 (1980) 50-58. | MR | Zbl
[65] and , Sensitivity analysis for scheduling problems. J. Scheduling 7 (2004) 49-83. | MR | Zbl
[66] , Online coloring known graphs, in Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics (1999) 918. | MR | Zbl
[67] and , Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica 18 (1997) 145-163. | MR | Zbl
[68] , , and , Online independent sets. Theor. Comput. Sci. 289 (2002) 953-962. | MR | Zbl
[69] and , A 7/8-approximation algorithm for metric Max TSP. Inf. Proc. Lett. 81 (2002) 247-251. | MR | Zbl
[70] , Improved data structures for fully dynamic biconnectivity. SIAM J. Comput. 29 (2000) 1761-1815. | MR | Zbl
[71] and , Fully dynamic biconnectivity and transitive closure, in FOCS. IEEE Computer Society (1995) 664-672. | Zbl
[72] and , Maintaining minimum spanning trees in dynamic graphs, in ICALP, Lecture Notes in Computer Science 1256, edited by P. Degano, R. Gorrieri and A. Marchetti-Spaccamela. Springer (1997) 594-604. | MR | Zbl
[73] and , Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J. ACM 46 (1999) 502-516. | MR | Zbl
[74] and , Certificates and fast algorithms for biconnectivity in fully-dynamic graphs, in ESA, Lecture Notes in Computer Science 979, edited by P.G. Spirakis. Springer (1995) 171-184. | MR
[75] , and , Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM 48 (2001) 723-760. | MR | Zbl
[76] and , The 2-dimensional probabilistic bin packing problem: an average case analysis of the FBS algorithm, in Proceedings of the American Conference on Applied Mathematics. World Scientific and Engineering Academy and Society (WSEAS) (2008) 449-453.
[77] and , Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22 (1975) 463-468. | MR | Zbl
[78] and , Fully dynamic maintenance of vertex cover, in Graph-Theoretic Concepts in Computer Science. Springer (1994) 99-111. | MR
[79] and , Fully dynamic algorithms for bin packing: Being (mostly) myopic helps. SIAM J. Comput. 28 (1998) 574-611. | MR | Zbl
[80] , Probabilistic traveling salesman problems. Ph.D. thesis, Massachusetts Institute of Technology (1985).
[81] , A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Oper. Res. 36 (1988) 929-936. | MR | Zbl
[82] , Shortest path problems with node failures. Networks 22 (1992) 589-605. | MR | Zbl
[83] , Analysis of probabilistic combinatorial optimization problems in Euclidean spaces. Math. Oper. Res. 18 (1993) 51-70. | MR | Zbl
[84] and , The probabilistic vehicle routing problem, in Vehicle routing: Methods and Studies, edited by B.L. Golden and A.A. Assad. North Holland, Amsterdam (1988) 293-318. | MR | Zbl
[85] and , Online routing problems: Value of advanced information as improved competitive ratios. Transp. Sci. 40 (2006) 200-210.
[86] , Near-optimal bin packing algorithms. Ph.D. thesis, Massachusetts Institute of Technology (1973). | MR
[87] , Fast algorithms for bin packing. J. Comput. Syst. Sci. 8 (1974) 272-314. | MR | Zbl
[88] and , A 71/60 theorem for bin packing. J. Complex. 1 (1985) 65-106. | MR | Zbl
[89] and , An efficient approximation scheme for the one-dimensional bin-packing problem, in FOCS, Chicago, IEEE Computer Society Illinois (1982) 312-320. | MR
[90] , Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane. Math. Oper. Res. 2 (1977) 209-224. | MR | Zbl
[91] , A patching algorithm for the nonsymmetric traveling-salesman problem. SIAM J. Comput. 8 (1979) 561. | MR | Zbl
[92] , Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs, in FOCS. IEEE Computer Society (1999) 81-91. | MR
[93] and , A fully dynamic approximation scheme for shortest paths in planar graphs. Algorithmica 22 (1998) 235-249. | MR | Zbl
[94] , and , Long tours and short superstrings (preliminary version), in FOCS. IEEE Computer Society (1994) 166-177.
[95] , On the shortest spanning subtree of a graph and the traveling salesman problem, in Proceedings of the American Mathematical Society 7 (1956). | MR | Zbl
[96] , A network evaluation procedure. Bay Area Transportation Study Commission (1967).
[97] and , The approximation of maximum subgraph problems, in Proc. ICALP'93, Lecture Notes in Computer Science 700. edited by A. Lingas, R.G. Karlsson and S. Carlsson. Springer-Verlag (1993) 40-51.
[98] , , and , Complexity models for incremental computation. Theor. Comput. Sci. 130 (1994) 203-236. | MR | Zbl
[99] and , The probabilistic longest path problem. Networks 33 (1999) 207-219. | MR | Zbl
[100] and , A priori optimization for the probabilistic maximum independent set problem. Theor. Comput. Sci. 270 (2002) 561-590. | MR | Zbl
[101] and , The probabilistic minimum vertex-covering problem. Int. Trans. Oper. Res. 9 (2002) 19-32. | MR | Zbl
[102] and , The probabilistic minimum coloring problem, in Graph-Theoretic Concepts in Computer Science, Springer (2003) 346-357. | MR | Zbl
[103] and , On the probabilistic minimum coloring and minimum k-coloring. Discrete Appl. Math. 154 (2006) 564-586. | MR | Zbl
[104] and , Probabilistic combinatorial optimization on graphs. Wiley Online Library (2006). | MR | Zbl
[105] , The effect of increasing or decreasing the length of a single arc on all shortest distances in a graph. London Businness School, Transport Network Theory Unit (1967).
[106] and , The traveling salesman problem with distances one and two. Math. Oper. Res. 18 (1993) 1-11. | MR | Zbl
[107] and , Non deterministic polynomial optimization problems and their approximations. Theor. Comput. Sci. 15 (1981) 251-277. | MR | Zbl
[108] , and , Online scheduling, in Handbook of Scheduling: Algorithms, Models, and Performance Analysis, edited by Joseph Y.-T. Leung, Chapter 15. CRC Press (2004) 15-1-15-41.
[109] , Improved bounds for harmonic-based bin-packing algorithms. Discrete Appl. Math. 3 (1991) 203-227. | MR | Zbl
[110] and , Graph minors. XX. Wagner's conjecture. J. Comb. Theory, Ser. B 92 (2004) 325-357. | MR | Zbl
[111] and , Improved steiner tree approximation in graphs, in SODA (2000) 770-779. | MR | Zbl
[112] , The parametric problem of shortest distances. USSR Comput. Math. Math. Phys. 8 (1968) 336-343. | MR | Zbl
[113] , A dynamization of the all pairs least cost path problem, in STACS, Lecture Notes in Computer Science 182, edited by K. Mehlhorn. Springer (1985) 279-286. | MR | Zbl
[114] and , P-complete approximation problems. J. ACM 23 (1976) 555-565. | MR | Zbl
[115] , Scheduling with forbidden sets. Discrete Appl. Math. 72 (1997) 155-166. | Zbl
[116] , Problèmes stochastiques de tournées de véhicules: un pas de plus vers le réalisme. Cahiers du Centre d'études de recherche opérationnelle 35 (1993) 187-226. | Zbl
[117] , On-line scheduling-a survey, in Online Algorithms: The State of the Art, edited by A. Fiat and G.J. Woeginger, Lect. Notes Comput. Sci. 1442. Springer (1998) 196-231. (1997). | MR | Zbl
[118] , The minimum latency problem is np-hard for weighted trees, in IPCO, Lecture Notes in Computer Science 2337, edited by W. Cook and A.S. Schulz. Springer (2002) 230-239. | MR | Zbl
[119] and , A data structure for dynamic trees. J. Comput. Syst. Sci. 26 (1983) 362-391. | MR | Zbl
[120] , Subadditive Euclidean functionals and nonlinear growth in geometric probability. Ann. Probab. 9 (1981) 365-376. | MR | Zbl
[121] , On Frieze's χ(3) limit for lengths of minimal spanning trees. Discrete Appl. Math. 18 (1987) 99-103. | MR | Zbl
[122] , A 2+1/2-approximation algorithm for shortest superstring. SIAM J. Comput. 29 (1999) 954-986. | MR | Zbl
[123] , An improved lower bound for on-line bin-packing algorithms. Inf. Proc. Lett. 43 (1992) 277-284. | MR | Zbl
[124] , Explicit inapproximability bounds for the shortest superstring problem, in MFCS, Lecture Notes in Computer Science 3618, edited by J. Jedrzejowicz and A. Szepietowski. Springer (2005) 793-800. | MR | Zbl
[125] , On finite affine line transitive planes. Math. Zeitschr. 87 (1965) 1-11. | MR | Zbl
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