Two-Phase Approach to Optimal Weather Routing Using Real-Time Adaptive A* Algorithm and Geometric Programming

실시간 적응 A* 알고리즘과 기하학 프로그래밍을 이용한 선박 최적항로의 2단계 생성기법 연구

  • Park, Jinmo (Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University) ;
  • Kim, Nakwan (Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University)
  • 박진모 (서울대학교 조선해양공학과, 해양시스템공학연구소) ;
  • 김낙완 (서울대학교 조선해양공학과, 해양시스템공학연구소)
  • Received : 2014.11.04
  • Accepted : 2015.06.22
  • Published : 2015.06.30


This paper proposes a new approach for solving the weather routing problem by dividing it into two phases with the goal of fuel saving. The problem is to decide two optimal variables: the heading angle and speed of the ship under several constraints. In the first phase, the optimal route is obtained using the Real-Time Adaptive A* algorithm with a fixed ship speed. In other words, only the heading angle is decided. The second phase is the speed scheduling phase. In this phase, the original problem, which is a nonlinear optimization problem, is converted into a geometric programming problem. By solving this geometric programming problem, which is a convex optimization problem, we can obtain an optimal speed scheduling solution very efficiently. A simple case of numerical simulation is conducted in order to validate the proposed method, and the results show that the proposed method can save fuel compared to a constant engine output voyage and constant speed voyage.



  1. Boyd, S., Kim, S.J., Vandenberghe, L., Hassibi, A., 2007. A tutorial on geometric programming. Optimization Engineering, 8(1):67–127.
  2. He-ping, H., 2007. The Development Trend of Green Ship Building Technology. Guangdong Shipbuilding, 3, 002.
  3. Hinnenthal, J., Clauss, G., 2010. Robust Pareto-optimum Routing of Ships utilising Deterministic and Ensemble Weather Forecasts. Ships and Offshore Structure, 5(2), 105–114.
  4. International Maritime Organization (IMO), 2007. Revised Guidance to the Master for Avoiding Dangerous Situations in Adverse Weather and Sea Conditions (MSC/Circ. 1228). International Maritime Organization, London.
  5. Koenig, S., Likhachev, M., 2006. Real-time Adaptive A*. Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, New York USA, 281-288.
  6. Roh, M.I., 2013. Determination of an Economical Shipping Route Considering the Effects of Sea State for Lower Fuel Consumption. International Journal of Naval Architecture and Ocean Engineering, 5(2), 246–262.
  7. Russell, S.J., Norvig, P., Canny, J.F., Malik, J.M., Edwards, D.D., 1995. Artificial Intelligence: a Modern Approach (Vol. 2). Prentice Hall, Englewood Cliffs.
  8. Shao, W., Zhou, P., Thong, S.K., 2012. Development of a Novel Forward Dynamic Programming Method for Weather Routing. Journal of Marine Science and Technology, 17(2), 239–251.
  9. Townsin, R.L., Kwon, Y.J., 1993. Estimating the Influence of Weather on Ship Performance. Royal Institute of Naval Architecture Trans 134(B), 191–210.