Abstract
In this study, a mixed-integer programming formulation is developed for a team of homogeneous sensing agents under a bi-objective optimization framework to solve a discrete open-loop centralized multi-agent search and rescue path planning problem. The first objective represents the maximization of probability of target detection to ensure the success of mission planning and the second objective represents minimization of the cumulative path length of all the agents to ensure resource utilization and ensure adequate area coverage. A two-phase fuzzy programming technique is used to find the Pareto optimal solution. Numerical experiments are conducted with CPLEX to evaluate the effectiveness of the solution procedure with varying number of agents, and the impact of the size of a grid-based rectangular map with a sparsely distributed non-cooperative finite number of stationary targets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ali, S., Saha, S., Kaviraj, A.: Fermented mulberry leaf meal as fishmeal replacer in the formulation of feed for carp Labeo rohita and catfish Heteropneustes fossilis–optimization by mathematical programming. Trop. Anim. Health Produ. 52(2), 1–11 (2019)
Berger, J., Lo, N.: An innovative multi-agent search-and-rescue path planning approach. Comput. Oper. Res. 53, 24–31 (2015)
Berger, J., Lo, N., Barkaoui, M.: Static target search path planning optimization with heterogeneous agents. Ann. Oper. Res. 244(2), 295–312 (2016)
Chen, L., Peng, J., Zhang, B.: Uncertain goal programming models for bicriteria solid transportation problem. Appl. Soft Comput. 51, 49–59 (2017)
Chen, L.H., Chen, H.H.: A two-phase fuzzy approach for solving multi-level decision-making problems. Knowl.-Based Syst. 76, 189–199 (2015)
Chung, C.K., Chen, H.M., Chang, C.T., Huang, H.L.: On fuzzy multiple objective linear programming problems. Expert Syst. Appl. 114, 552–562 (2018)
Danancier, K., Ruvio, D., Sung, I., Nielsen, P.: Comparison of path planning algorithms for an unmanned aerial vehicle deployment under threats. IFAC-PapersOnLine 52(13), 1978–1983 (2019)
Eagle, J.N.: The optimal search for a moving target when the search path is constrained. Oper. Res. 32(5), 1107–1115 (1984)
Fajardo, D., Waller, S.T.: Dynamic Traveling Salesman Problem in stochastic-state network setting for search-and-rescue application. Transp. Res. Rec. 2283(1), 122–130 (2012)
Guu, S.M., Yu, J., Wu, Y.K.: A two-phase approach to finding a better managerial solution for systems with addition-min fuzzy relational inequalities. IEEE Trans. Fuzzy Syst. 26(4), 2251–2260 (2017)
Guua, S.M., Wu, Y.K.: Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets Syst. 107(2), 191–195 (1999)
Hollinger, G., Kehagias, A., Singh, S.: GSST: anytime guaranteed search. Auton. Robots 29(1), 99–118 (2010)
Janardhanan, M.N., Li, Z., Bocewicz, G., Banaszak, Z., Nielsen, P.: Metaheuristic algorithms for balancing robotic assembly lines with sequence-dependent robot setup times. Appl. Math. Model. 65, 256–270 (2019)
Lanillos, P., Yañez-Zuluaga, J., Ruz, J.J., Besada-Portas, E.: A Bayesian approach for constrained multi-agent minimum time search in uncertain dynamic domains. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, pp. 391–398, July 2013
Lee, E.S., Li, R.J.: Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets Syst. 53(3), 275–288 (1993)
Liang, T.F.: Fuzzy multi-objective project management decisions using two-phase fuzzy goal programming approach. Comput. Ind. Eng. 57(4), 1407–1416 (2009)
Liu, X., Gong, D.: A comparative study of A-star algorithms for search and rescue in perfect maze. In: 2011 International Conference on Electric Information and Control Engineering, pp. 24–27. IEEE, April 2011
Lo, N., Berger, J., Noel, M.: Toward optimizing static target search path planning. In: 2012 IEEE Symposium on Computational Intelligence for Security and Defence Applications, pp. 1–7. IEEE, July 2012
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)
Moon, I., Jeong, Y.J., Saha, S.: Fuzzy bi-objective production-distribution planning problem under the carbon emission constraint. Sustainability 8(8), 798 (2016)
Nielsen, L.D., Sung, I., Nielsen, P.: Convex decomposition for a coverage path planning for autonomous vehicles: interior extension of edges. Sensors 19(19), 4165 (2019)
Park, Y., Nielsen, P., Moon, I.: Unmanned aerial vehicle set covering problem considering fixed-radius coverage constraint. Comput. Oper. Res. 119, 104936 (2020)
Perez-Carabaza, S., Besada-Portas, E., Lopez-Orozco, J.A., Jesus, M.: Ant colony optimization for multi-UAV minimum time search in uncertain domains. Appl. Soft Comput. 62, 789–806 (2018)
Pérez-Carabaza, S., Scherer, J., Rinner, B., López-Orozco, J.A., Besada-Portas, E.: UAV trajectory optimization for Minimum Time Search with communication constraints and collision avoidance. Eng. Appl. Artif. Intell. 85, 357–371 (2019)
Raap, M., Meyer-Nieberg, S., Pickl, S., Zsifkovits, M.: Aerial vehicle search-path optimization: a novel method for emergency operations. J. Optim. Theory Appl. 172(3), 965–983 (2017)
Sakawa, M., Yano, H., Nishizaki, I., Nishizaki, I.: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions. Springer, Cham (2013)
San Juan, V., Santos, M., Andújar, J.M.: Intelligent UAV map generation and discrete path planning for search and rescue operations. Complexity 6879419, 17 p. (2018)
Sanyal, S.N., Nielsen, I., Saha, S.: Multi-objective human resource allocation approach for sustainable traffic management. Int. J. Environ. Res. Public Health 17(7), 2470 (2020)
Sitek, P., Wikarek, P.: A hybrid method for modeling and solving constrained search problems. FedCSIS 2013, 385–392 (2013)
Sitek, P., Wikarek, J.: A multi-level approach to ubiquitous modeling and solving constraints in combinatorial optimization problems in production and distribution. Appl. Intell. 48(5), 1344–1367 (2018)
Sitek, P., Wikarek, J.: Capacitated Vehicle Routing Problem with Pick-up and Alternative Delivery (CVRPPAD) - model and implementation using hybrid approach. Ann. Oper. Res. 273(1–2), 257–277 (2019)
Stone, L.D.: Theory of Optimal Search. Elsevier (1976)
Thibbotuwawa, A., Nielsen, P., Zbigniew, B., Bocewicz, G.: Energy consumption in unmanned aerial vehicles: a review of energy consumption models and their relation to the UAV routing. Adv. Intell. Syst. Comput. 853, 173–184 (2019)
Thunberg, J., Ögren, P.: A mixed integer linear programming approach to pursuit evasion problems with optional connectivity constraints. Auton. Robots 31(4), 333 (2011)
Trummel, K.E., Weisinger, J.R.: The complexity of the optimal searcher path problem. Oper. Res. 34(2), 324–327 (1986)
Wu, Y.K., Liu, C.C., Lur, Y.Y.: Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals. Fuzzy Optim. Decis. Making 14(1), 43–55 (2015)
Xiong, C., Chen, D., Lu, D., Zeng, Z., Lian, L.: Path planning of multiple autonomous marine vehicles for adaptive sampling using Voronoi-based ant colony optimization. Robot. Auton. Syst. 115, 90–103 (2019)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Nielsen, I., Bocewicz, G., Saha, S. (2021). Multi-agent Path Planning Problem Under a Multi-objective Optimization Framework. In: Rodríguez González, S., et al. Distributed Computing and Artificial Intelligence, Special Sessions, 17th International Conference. DCAI 2020. Advances in Intelligent Systems and Computing, vol 1242. Springer, Cham. https://doi.org/10.1007/978-3-030-53829-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-53829-3_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-53828-6
Online ISBN: 978-3-030-53829-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)