Skip to main content
Log in

On using density maps for the calculation of ship routes

  • Original Paper
  • Published:
Evolving Systems Aims and scope Submit manuscript

Abstract

This paper presents a research on the calculation of short- to mid-range ship routes that are based on density maps derived by previous historical locations of liner or merchant ships. Two main approaches are presented. In the first one, the route finding problem is formulated as an evolutionary-optimization problem. In the second one, a modified A* algorithm is presented, which is able to handle density data and smoothing requirements. Both methods are able to calculate accurate and smooth ship routes that comply with exiting density data of common sea paths. A combination of both methods is also presented for deriving smooth ship routes that comply with density data without the need for post processing. Several examples are presented and discussed to illustrate the effectiveness and the performance of all proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Albiach J, Sanchis JM, Soler D (2008) An asymmetric TSP with time windows and with time-dependent travel times and costs: An exact solution through a graph transformation. Eur J Oper Res 189(3):789–802

    Article  MathSciNet  MATH  Google Scholar 

  • Ari I, Aksakalli V, Aydogdu V, Kumb S (2013) Optimal ship navigation with safety distance and realistic turn. Eur J Oper Res 229:707

    Article  Google Scholar 

  • Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, New York

    MATH  Google Scholar 

  • Bijlsma JS (2008) Minimal time route computation for ships with pre-specified voyage fuel consumption. J Navigat 61:723–733

    Article  Google Scholar 

  • Bijlsma JS (2010) Optimal ship routing with ocean current included. J Navigat 63:565–568

    Article  Google Scholar 

  • Chang CY et al (2013) Ship routing utilizing strong ocean currents. J Navigat 66:825–835

    Article  Google Scholar 

  • Chen C, Shigeaki S, Kenji S (2013) Numerical ship navigation based on weather and ocean simulation. Ocean Eng 69:44

    Article  Google Scholar 

  • Chinchuluun A, Pardalos PM (2007) A survey of recent developments in multiobjective. Ann Oper Res 154:29–50

    Article  MathSciNet  MATH  Google Scholar 

  • Chuang TN, Lin CT, Ku JY (2012) Planning the route of container ships: a fuzzy genetic approach. Expert Syst Appl 37:2948

    Article  Google Scholar 

  • Daniel K, Nash A, Koenig S, Felner A (2010) Theta*: any-angle path planning on grids. J Artif Intell Res 39:533–579

    MathSciNet  MATH  Google Scholar 

  • Ewing JA (1990) Wind wave and current data for the design of ships and offshore structures. Marine Structures 3:421

    Article  Google Scholar 

  • Fagerholt K, Heimdal SI, Loktu A (2000) Shortest path in the presence of obstacles: an application to ocean shipping. J Oper Res Soc 51(6):683–688

    Article  MATH  Google Scholar 

  • Gill PE, Walter M, Wright M (1981) Practical optimization. Academic Press, New York

    MATH  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison Wesley Publishing Company, Boston

    MATH  Google Scholar 

  • Google (2013) Google Maps JavaScript API v3. [Online]. Available at: https://developers.google.com/maps/documentation/javascript/maptypes

  • Gutierrez E, Medaglia AL (2008) Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks. Ann Oper Res 157(1):169–182

    Article  MathSciNet  MATH  Google Scholar 

  • Hagiwara H (1989) Weather routing of sail assisted motor vessels, Delft: Ph.D Thesis, Delft University

  • Haimes YY, Lasdon LS, Wismer DA (1971) On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans Syst Man Cyber 1:296–297

    MathSciNet  MATH  Google Scholar 

  • Harris CJ, Hong X, Wilson P (1999) An intelligent guidance and control system for ship obstacle avoidance. Proc IMechE Part I J Syst Cont Eng 213(14):311–320

    Article  Google Scholar 

  • Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci 4(2):100–107

    Article  Google Scholar 

  • Hvattum LM, Fagerholt K, Armentano VA (2009) Tank allocation problems in maritime bulk shipping. Comput Oper Res 36:3051

    Article  MATH  Google Scholar 

  • International Marine Organization, 2010. Reduction of GHG emissions from ships, s.l.: IMO-MEPC61/INF.22

  • Ito M, Zhang F, Yoshida N (1999) Collision avoidance control of ship with genetic algorithm. Kohala Coast, Hawaii, USA, Proceedings of the 1999 IEEE International Conference on Control Applications 2:1791–1796

  • Kosmas OT, Vlachos DS (2012) Simulated annealing for optimal ship routing. Comput Oper Res 39:576

    Article  Google Scholar 

  • Latombe JC (1991) Robot motion planning. Kluwer Academic Publishers, Boston

    Book  MATH  Google Scholar 

  • Lee H et al (2002) Optimum ship routing and it’s implementation on the Web. Lect Notes Comput Sci 2402:125–136

    Article  MATH  Google Scholar 

  • Lee KY, Roh MI, Jeong HS (2005) An improved genetic algorithm for multi-floor facility layout problems having inner structure walls and passages. Comput Oper Res 32:879

    Article  MATH  Google Scholar 

  • Lekkas D, Vosinakis S, Alifieris C, Darzentas J (2008) MarineTraffic: designing a collaborative interactive vessel traffic information system. Amantea, Italy, The International Workshop on Harbour, Maritime & Multimodal Logistics Modelling and Simulation, HMS’08

  • Lin TR, Pan J, O’Shea PJ, Mechefske CK (2009) A study of vibration and vibration control of ship structures. Marine Structures 22:730

    Article  Google Scholar 

  • Liu Y, Shi C (2005) A fuzzy-neural inference network for ship collision avoidance. Guangzhou, China, Proceedings of the IEEE Third International Conference on Machine Learning and Cybernetics, pp 4754–4759

  • Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs, 3rd edn. Springer-Verlag, New York

    MATH  Google Scholar 

  • Nearchou AC (1998) Path planning of a mobile robot using genetic heuristics. Robotica 16:575–588

    Article  Google Scholar 

  • Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313

    Article  MathSciNet  MATH  Google Scholar 

  • Nilsson NJ (1980) Principles of artificial intelligence. Morgan Kaufmann, Palo Alto

    MATH  Google Scholar 

  • Olcer AI (2008) A hybrid approach for multi-objective combinatorial optimisation problems in ship design and shipping. Comput Oper Res 35:2760

    Article  MATH  Google Scholar 

  • Pareto V (1964) Cours d’Économie Politique. Droz, Geneva: s.n

  • Piegl L, Tiller W (1997) The NURBS book. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes. Cambridge University Press, New York

    MATH  Google Scholar 

  • Pruski A, Rohmer S (1997) Robust Path Planning for Non-Holonomic Robots. J Intell Rob Syst 18(4):329–350

    Article  Google Scholar 

  • Pugliese L, Guerriero F (2012) Shortest path problem with forbidden paths: the elementary version. Euro J Operat Res

  • Rabin S (2000) Game programming gems: A* aesthetic optimizations. In: s.l.: Charles River Media, pp 264–271

  • Song G, Amato NM (2001) Randomized motion planning for car-like robots with C-PRM. Maui, HI, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1:37–42

  • Tsou CM (2010) Integration of a geographic information system and evolutionary computation for automatic routing in coastal navigation. J Navigation 63:323–341

    Article  Google Scholar 

  • Vanhove S, Fack V (2012) Route planning with turn restrictions: a computational experiment. Operat Res Letters 40(5):342–348

    Article  MATH  Google Scholar 

  • Vougioukas SG (2005) Optimization of robots paths computed by randomized planners. Barcelona, Spain, IEEE International Conference on Robotics Automation, pp 2160–2165

  • Xidias E, Azariadis P (2011) Mission design for a group of autonomous guided vehicles. Robot Auton Syst 59:34–43

    Article  Google Scholar 

  • Xue Y, Clelland D, Lee BS, Han D (2011) Automatic simulation of ship navigation. Ocean Eng 38:2290

    Article  Google Scholar 

  • Yang S, Li L, Suo Y, Chen G (2007) Study on construction of simulation platform for vessel automatic anti-collision and its test method. Jinan, China, Proceedings of the IEEE International Conference on Automation and Logistics, pp 2414–2419

  • Zadeh L (1963) Optimality and non-scalar-valued performance criteria. IEEE Trans Autom Control 8:59–60

    Article  Google Scholar 

Download references

Acknowledgments

I’m grateful to Dr. Dimitris Lekkas founder of marinetraffic.com for his valuable contribution in this research and for providing the required historical ship data. I’d like to thank very much all anonymous reviewers for their invaluable comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philip Azariadis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Azariadis, P. On using density maps for the calculation of ship routes. Evolving Systems 8, 135–145 (2017). https://doi.org/10.1007/s12530-016-9155-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12530-016-9155-7

Keywords

Navigation