Baier, C., Daum, M., Dubslaff, C., Klein, J., Klüppelholz, S.: Energy-utility quantiles. In: NASA Formal Methods, NFM. pp. 285–299 (2014). https://doi.org/10.1007/978-3-319-06200-6_24
Baier, C., Dubslaff, C., Klüppelholz, S.: Trade-off analysis meets probabilistic model checking. In: CSL-LICS. pp. 1:1–1:10. ACM (2014)
Google Scholar
Baier, C., Hermanns, H., Katoen, J.: The 10, 000 facets of MDP model checking. In: Computing and Software Science, LNCS, vol. 10000, pp. 420–451. Springer (2019)
Google Scholar
Baier, C., Katoen, J.P.: Principles of model checking. MIT Press (2008)
Google Scholar
Baier, C., Klein, J., Leuschner, L., Parker, D., Wunderlich, S.: Ensuring the reliability of your model checker: Interval iteration for Markov decision processes. In: CAV (1). LNCS, vol. 10426, pp. 160–180. Springer (2017)
Google Scholar
Barrett, L., Narayanan, S.: Learning all optimal policies with multiple criteria. In: (ICML). pp. 41–47 (2008)
Google Scholar
Benini, L., Bogliolo, A., Paleologo, G.A., De Micheli, G.: Policy optimization for dynamic power management. Trans. Comp.-Aided Des. Integ. Cir. Sys. 18(6), 813–833 (2006). https://doi.org/10.1109/43.766730
Berthon, R., Randour, M., Raskin, J.: Threshold constraints with guarantees for parity objectives in Markov decision processes. In: ICALP. LIPIcs, vol. 80, pp. 121:1–121:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)
Google Scholar
Bouyer, P., González, M., Markey, N., Randour, M.: Multi-weighted Markov decision processes with reachability objectives. In: GandALF. EPTCS, vol. 277, pp. 250–264 (2018)
Google Scholar
Bruno, J.L., Downey, P.J., Frederickson, G.N.: Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. ACM 28(1), 100–113 (1981). https://doi.org/10.1145/322234.322242
MathSciNet
CrossRef
MATH
Google Scholar
Bruyère, V., Filiot, E., Randour, M., Raskin, J.: Meet your expectations with guarantees: Beyond worst-case synthesis in quantitative games. Inf. Comput. 254, 259–295 (2017)
MathSciNet
CrossRef
Google Scholar
Chatterjee, K., de Alfaro, L., Henzinger, T.A.: Trading memory for randomness. In: QEST. pp. 206–217. IEEE Computer Society (2004)
Google Scholar
Chatterjee, K., Kretínská, Z., Kretínský, J.: Unifying two views on multiple mean-payoff objectives in markov decision processes. LMCS 13(2) (2017)
Google Scholar
Chatterjee, K., Majumdar, R., Henzinger, T.A.: Markov decision processes with multiple objectives. In: STACS. LNCS, vol. 3884, pp. 325–336. Springer (2006)
Google Scholar
Chen, T., Kwiatkowska, M.Z., Parker, D., Simaitis, A.: Verifying team formation protocols with probabilistic model checking. In: CLIMA. pp. 190–207 (2011)
Google Scholar
Dehnert, C., Junges, S., Katoen, J.P., Volk, M.: A Storm is coming: A modern probabilistic model checker. In: CAV. LNCS, vol. 10427. Springer (2017)
Google Scholar
Delgrange, F., Katoen, J.P., Quatmann, T., Randour, M.: Simple strategies in multi-objective MDPs (technical report). CoRR abs//1910.11024 (2019), http://arxiv.org/abs/1910.11024
Delgrange, F., Katoen, J.P., Quatmann, T., Randour, M.: Evaluated artifact for this paper. figshare (2020). https://doi.org/10.6084/m9.figshare.11569485
CrossRef
Google Scholar
von Essen, C., Giannakopoulou, D.: Probabilistic verification and synthesis of the next generation airborne collision avoidance system. STTT 18(2), 227–243 (2016)
Google Scholar
Etessami, K., Kwiatkowska, M.Z., Vardi, M.Y., Yannakakis, M.: Multi-objective model checking of Markov decision processes. Logical Methods in Computer Science 4(4) (2008). https://doi.org/10.2168/LMCS-4(4:8)2008
Feng, L., Wiltsche, C., Humphrey, L.R., Topcu, U.: Controller synthesis for autonomous systems interacting with human operators. In: ICCPS. pp. 70–79. ACM (2015)
Google Scholar
Forejt, V., Kwiatkowska, M.Z., Norman, G., Parker, D.: Automated verification techniques for probabilistic systems. In: SFM. LNCS, vol. 6659, pp.53–113. Springer (2011)
Google Scholar
Forejt, V., Kwiatkowska, M.Z., Norman, G., Parker, D., Qu, H.: Quantitative multi-objective verification for probabilistic systems. In: TACAS. LNCS, vol. 6605, pp. 112–127. Springer (2011)
Google Scholar
Forejt, V., Kwiatkowska, M.Z., Parker, D.: Pareto curves for probabilistic model checking. In: ATVA. LNCS, vol. 7561, pp. 317–332. Springer (2012)
Google Scholar
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA (1979)
MATH
Google Scholar
Gleixner, A., Bastubbe, M., Eifler, L., Gally, T., Gamrath, G., Gottwald, R.L., Hendel, G., Hojny, C., Koch, T., Lübbecke, M.E., Maher, S.J., Miltenberger, M., Müller, B., Pfetsch, M.E., Puchert, C., Rehfeldt, D., Schlösser, F., Schubert, C., Serrano, F., Shinano, Y., Viernickel, J.M., Walter, M., Wegscheider, F., Witt, J.T., Witzig, J.: The SCIP Optimization Suite 6.0. Technical report, Optimization Online (July 2018), http://www.optimization-online.org/DB_HTML/2018/07/6692.html
Gurobi Optimization, L.: Gurobi optimizer reference manual (2019), http://www.gurobi.com
Hartmanns, A., Junges, S., Katoen, J., Quatmann, T.: Multi-cost bounded reachability in MDP. In: TACAS (2). LNCS, vol. 10806, pp. 320–339. Springer (2018)
Google Scholar
Junges, S., Jansen, N., Wimmer, R., Quatmann, T., Winterer, L., Katoen, J., Becker, B.: Finite-state controllers of POMDPs using parameter synthesis. In: UAI. pp. 519–529. AUAI Press (2018)
Google Scholar
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) Proc. 23rd International Conference on Computer Aided Verification (CAV’11). LNCS, vol. 6806, pp. 585–591. Springer (2011)
Google Scholar
Kwiatkowska, M.Z., Norman, G., Parker, D.: The PRISM benchmark suite. In: QEST. pp. 203–204 (2012). https://doi.org/10.1109/QEST.2012.14
Lacerda, B., Parker, D., Hawes, N.: Multi-objective policy generation for mobile robots under probabilistic time-bounded guarantees. In: ICAPS. pp. 504–512. AAAI Press (2017)
Google Scholar
Lizotte, D.J., Bowling, M., Murphy, S.A.: Linear fitted-Q iteration with multiple reward functions. J. Mach. Learn. Res. 13, 3253–3295 (2012)
MathSciNet
MATH
Google Scholar
Perny, P., Weng, P.: On finding compromise solutions in multiobjective Markov decision processes. In: ECAI. FAIA, vol. 215, pp. 969–970. IOS Press (2010)
Google Scholar
Pia, A.D., Dey, S.S., Molinaro, M.: Mixed-integer quadratic programming is in NP. Math. Program. 162(1-2), 225–240 (2017)
Google Scholar
Puterman, M.L.: Markov Decision Processes. John Wiley and Sons (1994)
Google Scholar
Qiu, Q., Wu, Q., Pedram, M.: Stochastic modeling of a power-managed system: Construction and optimization. In: ISLPED. pp. 194–199. ACM (1999)
Google Scholar
Quatmann, T., Junges, S., Katoen, J.: Markov automata with multiple objectives. In: CAV (1). LNCS, vol. 10426, pp. 140–159. Springer (2017)
Google Scholar
Randour, M., Raskin, J., Sankur, O.: Variations on the stochastic shortest path problem. In: VMCAI. Lecture Notes in Computer Science, vol. 8931, pp.1–18. Springer (2015)
Google Scholar
Randour, M., Raskin, J., Sankur, O.: Percentile queries in multi-dimensional Markov decision processes. FMSD 50(2-3), 207–248 (2017)
Google Scholar
Roijers, D.M., Vamplew, P., Whiteson, S., Dazeley, R.: A survey of multi-objective sequential decision-making. JAIR 48, 67–113 (2013)
MathSciNet
CrossRef
Google Scholar
Scheftelowitsch, D., Buchholz, P., Hashemi, V., Hermanns, H.: Multi-objective approaches to Markov decision processes with uncertain transition parameters. In: VALUETOOLS. pp. 44–51. ACM (2017)
Google Scholar
Srinivasan, M.: Nondeterministic polling systems. Management Science 37(6), 667–681 (1991). https://doi.org/10.1287/mnsc.37.6.667
CrossRef
MATH
Google Scholar
Wiering, M.A., de Jong, E.D.: Computing optimal stationary policies for multi-objective Markov decision processes. In: ADPRL. pp. 158–165 (2007). https://doi.org/10.1109/ADPRL.2007.368183