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INTRODUCTION
Nowadays the most popular commercial approach to planning a ship voyage while taking weather conditions into account (known as "weather routing") is the one based on isochrones. The isochrone method was proposed by James (1957) for manual use and is based on geometrically determined and recursively defined time fronts, so called isochrones. The method allows single-objective optimisation only: time-optimal or fuel-optimal paths for the same voyage must be sought by different methods. Moreover, its support for optimisation constraints is limited - the isochrone method handles only static (time-independent) constraints such as land obstacles or other areas to be avoided. Despite these limitations the method became extremely popular as a simple, reliable and fast tool for finding usually a time-optimal route. In the late 1970s the first computer aided weather routing tools were developed based on the original isochrone method. Along with computer implementation some additional problems with isochrones arose, i.e. with so-called "isochrone loops". Numerous improvements to the method eliminating these problems have been proposed since the early 1980s by Spaans (1986), Hagiwara and Spaans (1987), Hagiwara (1989) and Wisniewski (1991) among others. Today, several commercial weather routing services utilise highly modified isochrone methods.
Apart from the isochrone method there are also some other approaches to this problem. Basic utilisation of dynamic programming for a grid of points has been proposed by de Wit (1990) and Motte and Calvert (1990). Moreover, a new European commercial weather routing service utilising a three-dimensional (3D) dynamic programming has been just announced in Chen (2013). As presented in Bijlsma (2008), solving a specified optimal control problem allows for finding a time-optimal path, particularly when voyage fuel consumption is restricted to a specific value. Another approach to weather routing assumes using the Dijkstra algorithm as presented in Mannarini et al. (2013).
All the abovementioned weather routing methods utilise single-objective optimisation, i.e. only one criterion (e.g. passage time) can be optimised by a single run of the method. A possibility to widen the optimisation towards a multi-objective approach, where more criteria can be taken into account simultaneously, came together with the introduction of evolutionary computation. However, some of the proposed approaches to multi-objective optimisation, though interesting, are largely simplified. In Wisniewski et al....