In maritime navigation, one must consider ocean currents, areas with different wave heights and wind, which are constantly changing.
Recent events have highlighted the importance of selecting optimal maritime routes. The crisis in the Red Sea has forced many shipping companies to navigate around Africa instead of using the Suez Canal, raising questions about finding routes that consume less fuel or take less time. Meanwhile, the recent loss of containers full of plastic pellets from the freighter Toconao off the coast of Galicia, caused by a wave, has had a significant environmental impact. This leads to questions about designing safer routes to avoid such accidents. Mathematical optimization techniques can provide answers to these questions. These tools, initially explored by mathematicians such as Euler, Lagrange, and the Bernoulli brothers, allow for the theoretical description of the fastest, cheapest, or safest route from one point to another. The shortest distance is not always the best route. In maritime navigation, factors such as sea currents and wind conditions, which are constantly changing, must be taken into account. German mathematician Ernst Zermelo was the first to theoretically formulate and analyze this problem, finding the fastest trajectory between two fixed points for a vessel moving at a constant speed, taking into account variable wind or currents. For these models to be practically useful, reliable navigation condition predictions are necessary. Major American (NOAA) and European (Copernicus) prediction centers provide detailed 10-days forecast with a spatial resolution of less than 10 kilometers.
They use modern weather models, which have made remarkable progress in recent decades. The accuracy of a five-day forecast today is better than a one–day forecast in 1980. This is primarily due to a higher density of current atmospheric state observations. However, other mathematical disciplines, such as statistics, partial differential equations, numerical methods, and recently artificial intelligence, are also crucial. Detailed modeling of each specific vessel’s movement and fuel consumption per unit of time, based on navigation conditions, currents, wave height, angle of incidence, wind direction and intensity, etc., is possible using naval engineering and data science knowledge. With this information, mathematical optimization algorithms have been developed and are used today to find favorable maritime routes. Any prediction carries uncertainty, which must also be quantified and considered when optimizing navigation routes. Therefore, new dynamic and stochastic optimization algorithms must be developed to achieve robust results under any possible atmospheric evolution scenario. This is particularly important in a global warming scenario where the atmosphere is more unstable and extreme events are increasingly frequent. Recently, all these mathematical techniques have been integrated to optimize maritime routes in real time, based on weather and oceanographic predictions, with consumption models adapted to each vessel. This tool, intended to be a «Google Maps» of the ocean, is being developed by a multidisciplinary team, predominantly of Spanish researchers. It can save 5-10% of fuel on each trip, improve navigation safety by avoiding areas with adverse conditions, and reduce CO2 emissions. This is crucial as today, more than 80% of trade is transported by sea, which accounts for about 3% of global carbon dioxide emissions. Annual fuel expenditure amounts to 250 billion euros and represents more than 60% of the operating costs of maritime transport.
