Abstract
Probability theory is the most common method to solve the orienteering problems in the state of indeterminacy. However, it will no longer be applicable without available samples. In this paper, we focus on uncertain orienteering problem containing uncertain vector in the objective function. First, we creatively model the uncertain orienteering problem based on uncertainty theory. Second, we establish the minimum-risk model using uncertain measure instead of the expected-value policy. Third, after introducing some assumptions to deal with the uncertain vector in the minimum-risk model, we get an orienteering problem with fractional objective. Since it is more complex than the original orienteering problem, we design an one-dimensional ratio search algorithm. Finally, we perform some numerical tests on the uncertain datasets and analyze the effectiveness of our theoretical results and algorithm.
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References
Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl 28(7):1591–1610. https://doi.org/10.1007/s00521-015-2110-x
Abu Arqub O, AL-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302. https://doi.org/10.1007/s00500-015-1707-4
Abu Arqub O, AL-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(7):7971. https://doi.org/10.1007/s00500-016-2262-3
Campbell AM, Gendreau M, Thomas BW (2011) The orienteering problem with stochastic travel and service times. Ann Oper Res 186(1):61–81. https://doi.org/10.1007/s10479-011-0895-2
Chao IM, Golden BL, Wasil EA (1996) A fast and effective heuristic for the orienteering problem. Eur J Oper Res 88(3):475–489. https://doi.org/10.1016/0377-2217(95)00035-6
Clarke G, Wright J (1964) Scheduling of vehicles from a depot to a number of delivery points. Oper Res 12(4):568–581. https://doi.org/10.1287/opre.12.4.568
Dolinskaya I, Shi Z, Smilowitz K (2018) Adaptive orienteering problem with stochastic travel times. Transp Res Part E 109(1):1–19. https://doi.org/10.1016/j.tre.2017.10.013
Eksioglu B, Vural AV, Reisman A (2009) The vehicle routing problem: a taxonomic review. Comput Ind Eng 57(4):1472–1483. https://doi.org/10.1016/j.cie.2009.05.009
Evers L, Glorie K, Suzanne VDS, Barros AI, Monsuur H (2014) A two-stage approach to the orienteering problem with stochastic weights. Comput Oper Res 43(4):248–260. https://doi.org/10.1016/j.cor.2013.09.011
Flood MM (1956) The traveling-salesman problem. Oper Res 4(1):61–75. https://doi.org/10.1287/opre.4.1.61
Gunawan A, Lau HC, Vansteenwegen P (2016) Orienteering problem: a survey of recent variants, solution approaches and applications. Eur J Oper Res 255(2):315–332. https://doi.org/10.1016/j.ejor.2016.04.059
Henig M (1990) Risk criteria in a stochastic knapsack problem. Oper Res 38(5):820–825. https://doi.org/10.1287/opre.38.5.820
Ilhan T, Iravani SMR, Daskin MS (2008) The orienteering problem with stochastic profits. IIE Trans 40(4):406–421. https://doi.org/10.1080/07408170701592481
Ke L, Zhai L, Li J, Chan FT (2016) Pareto mimic algorithm: an approach to the team orienteering problem. Omega 61:155–166. https://doi.org/10.1016/j.omega.2015.08.003
Kobeaga G, Merino M, Lozano JA (2018) An efficient evolutionary algorithm for the orienteering problem. Ann Oper Res 90:42–59. https://doi.org/10.1016/j.cor.2017.09.003
Lau HC, Yeoh W, Varakantham P, Nguyen DT, Chen H (2012) Dynamic stochastic orienteering problems for risk-aware applications. In: Proceedings of the 28th conference annual conference on uncertainty in artificial intelligence (UAI-12), Corvallis, pp 448–458
Little JD, Murty KG, Sweeney DW, Karel C (1963) An algorithm for the traveling salesman problem. Oper Res 11(6):972–989. https://doi.org/10.1287/opre.11.6.972
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009a) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2009b) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin
Liu B (2010) Uncertainty theory—a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2012) Why is there a need for uncertainty theory. J Uncertain Syst 6(1):3–10
Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1(1):1–15. https://doi.org/10.1186/2195-5468-1-1
Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin
Liu B (2016) Uncertainty theory, 5th edn. Uncertainty Theory Laboratory, Beijing. http://orsc.edu.cn/liu/ut.pdf
Liu B, Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. J Uncertain Anal Appl 3(1):1–8. https://doi.org/10.1186/s40467-015-0036-6
Muthuswamy S (2009) Discrete particle swarm optimization algorithms for orienteering and team orienteering problems. PhD thesis, State University of New York
Ni Y, Chen Y, Ke H, Dan AR (2018) Models and algorithm for the orienteering problem in a fuzzy environment. Int J Fuzzy Syst 20(3):1–16. https://doi.org/10.1007/s40815-017-0369-z
Ostrowski K, Karbowska-Chilinska J, Koszelew J, Zabielski P (2017) Evolution-inspired local improvement algorithm solving orienteering problem. Ann Oper Res 253(1):519–543. https://doi.org/10.1007/s10479-016-2278-1
Schilde M, Doerner KF, Hartl RF, Kiechle G (2009) Metaheuristics for the bi-objective orienteering problem. Swarm Intell 3(3):179–201. https://doi.org/10.1007/s11721-009-0029-5
Tang H, Miller-Hooks E (2005) Algorithms for a stochastic selective travelling salesperson problem. J Oper Res Soc 56(4):439–452. https://doi.org/10.1057/palgrave.jors.2601831
Tasgetiren F, Smith A (2002) A genetic algorithm for the orienteering problem. In: Proceedings of the congress on evolutionary computation (CEC’02), Hawaii
Vansteenwegen P, Souffriau W, Oudheusden DV (2011) The orienteering problem: a survey. Eur J Oper Res 209(1):1–10. https://doi.org/10.1016/j.ejor.2010.03.045
Verbeeck C, Sörensenb K, Aghezzafa EH, Vansteenwegen P (2014) A fast solution method for the time-dependent orienteering problem. Eur J Oper Res 236(2):419–432. https://doi.org/10.1016/j.ejor.2013.11.038
Verbeeck C, Vansteenwegen P, Aghezzafa EH (2016) Solving the stochastic time-dependent orienteering problem with time windows. Eur J Oper Res 255(3):699–718. https://doi.org/10.1016/j.ejor.2016.05.031
Wang Z, Guo J, Zheng M, Wang Y (2015) Uncertain multiobjective traveling salesman problem. Eur J Oper Res 241(2):478–489. https://doi.org/10.1016/j.ejor.2014.09.012
Wang Z, Zheng M, Guo J, Huang H (2017) Uncertain UAV ISR mission planning problem with multiple correlated objectives. J Intell Fuzzy Syst 32(1):321–335. https://doi.org/10.3233/JIFS-151781
Wang J, Guo J, Zheng M, Wang Z, Li Z (2018) Uncertain multiobjective orienteering problem and its application to uav reconnaissance mission planning. J Intell Fuzzy Syst 34(4):2287–2299. https://doi.org/10.3233/JIFS-171331
Zadeh L (1965) Fuzzy sets. Inf Control 8:338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zadeh L (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28. https://doi.org/10.1016/0165-0114(78)90029-5
Zheng M, Yuan Y, Wang X, Wang J, Mao S (2017a) The information value and the uncertainties in two-stage uncertain programming with recourse. Soft Comput 3–4:1–11. https://doi.org/10.1007/s00500-017-2662-z
Zheng M, Yuan Y, Wang Z, Liao T (2017b) Efficient solution concepts and their application in uncertain multiobjective programming. Appl Soft Comput 56:557–569. https://doi.org/10.1016/j.asoc.2016.07.021
Zheng M, Yuan Y, Wang Z, Liao T (2017c) Relations among efficient solutions in uncertain multiobjective programming. Fuzzy Optim Decis Mak 16(3):329–357. https://doi.org/10.1007/s10700-016-9252-x
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This study was funded by National Natural Science Foundation of China (Grant No. 61502521, 61502523).
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Wang, J., Guo, J., Zheng, M. et al. Research on a novel minimum-risk model for uncertain orienteering problem based on uncertainty theory. Soft Comput 23, 4573–4584 (2019). https://doi.org/10.1007/s00500-018-03699-1
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DOI: https://doi.org/10.1007/s00500-018-03699-1