Ship voyage optimization for safe and energy-efficient navigation: A dynamic programming approach R. Zaccone a, * , E. Ottaviani b , M. Figari a , M. Altosole a a DITEN - Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture, Polytechnic School, University of Genoa, Genoa, Italy b OnAIR s.r.l., Genoa, Italy ARTICLE INFO Keywords: Ship voyage optimization Dynamic programming Weather routing Ship propulsion Ship motions ABSTRACT The paper presents a 3D dynamic programming based ship voyage optimization method, aiming to select the optimal path and speed profile for a ship voyage on the basis of weather forecast maps. The optimization is performed in accordance to a minimum fuel consumption strategy taking also into account ship motions and comfort. The optimization is carried out in a discretized space-time domain: the ship voyage is parametrized as a multi-stage decision process in order to formulate a dynamic programming optimization problem. Waves and wind conditions are estimated for each route segment by weather forecasting maps then seakeeping related in- dexes and fuel oil consumption are computed taking into account wave-induced ship motions and added resis- tance. The best routing solution is thus selected by a dynamic programming algorithm developed and implemented by the authors. Results and discussion of the proposed method are presented for a merchant ship application in a test case voyage through the Northern Atlantic Ocean and compared to the constant speed great circle solution. 1. Introduction In the recent years the continuously increasing availability of reliable weather forecast data has significantly improved the safety of the ship voyages, helping the operators to select proper routes to avoid rough weather and have an estimate of the time of arrival (ETA) and the voyage cost. Moreover, increased attention is put nowadays to seakeeping abil- ities of ships in order to improve passage safety even with rough sea. However, most of the time medium intensity weather conditions are encountered; these conditions do not affect ship safety but influence fuel consumption and comfort on board. In this framework optimization al- gorithms can provide a significant support to the decision making process in order to select the best choice in sight of one or more objectives. The selection of the optimal route combines a number of objective functions as well as various constraints. In principle a ship voyage is characterized by a starting point, an arrival point, a constrained arrival time window, eventually a number of fixed way points. Geographical (static) constraints need to be considered as well: for example, the shore line, traffic separation schemes, restricted areas, bathymetry. Realistic modeling of the ship behaviour in relation to weather conditions is crucial to correctly estimate and compare the ship performance in different conditions. Decision making needs to be based on ship response, rather than on external conditions (Chen, 2013), in order to better fit different ship types, shapes and dimensions: different ships have different responses in the same weather and speed conditions. Ship and human life safety, fuel consumption, energy efficiency, crew and passengers com- fort, voyage time management, control of delays are possible tasks which can be pursued by voyage optimization. Weather routing services and codes available on the market are usually not supported by public domain scientific papers due to confi- dentiality reasons. In author's knowledge very often they are based on the principle of ‘storm avoidance’. The typical approach is to implement a set of generic speed reduction curves in function of sea state parameters (for example the Beaufort Wind Force Scale) and a number of global ship parameters (for example, displacement and length). The fuel consump- tion is estimated on the basis of empirical relationships, while ship hull geometry, seakeeping abilities and propulsion system features are neglected. This approach can lead to unnecessary diversions to avoid rough weather, badly affecting the fuel consumption. The ship speed decrease in rough weather can occur as a consequence of two reasons: involuntary speed reduction due to the additional resistance induced by wind and waves, and/or voluntary speed reduction to avoid navigation hazards and excessive ship motions which would result in propeller racing, slamming or green water. Additional constraints related to safety * Corresponding author. E-mail address: raphael.zaccone@edu.unige.it (R. Zaccone). Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng https://doi.org/10.1016/j.oceaneng.2018.01.100 Received 16 March 2017; Received in revised form 19 October 2017; Accepted 25 January 2018 0029-8018/© 2018 Elsevier Ltd. All rights reserved. Ocean Engineering 153 (2018) 215–224