Simulated Annealing for Optimal Ship Routing

arXiv:0811.2162v2 [physics.comp-ph] 4 May 2009 Simulated Annealing for Optimal Ship Routing O. T. Kosmasa, D. S. Vlachosa aLaboratory of Computer Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese GR-22 100 Tripolis, Terma Karaiskaki, GREECE Abstract A simulated annealing based algorithm is presented for the determination of optimal ship routes through the minimization of a cost function. This cost function is a weighted sum of the time of voyage and the voyage comfort (safety is taken into account too). The latter is dependent on both the wind speed and direction and the wave height and direction. The algorithm first discretizes an initial route and optimizes it by considering small deviations which are accepted by utilizing the simulated annealing technique. Using cal- culus of variations we prove a key theorem which dramatically accelerates the convergence of the algorithm. Finally both simulated and real experiments are presented. Key words: optimal ship routing,simulated annealing PACS: 89.40.Cc, 92.10.Hm, 02.60.Jh 1. Introduction Optimization of ship routing is closely related to both ship characteristics and environmental factors. Ship and cargo characteristics have a significant influence on the application of ship routing. Ship size, speed capability and type of cargo are important considerations in the route selection process prior to sailing and the surveillance procedure while underway. A ship’s characteristics identify its vulnerability to adverse conditions and its ability to avoid them [2]. Email addresses: odykosm@uop.gr (O. T. Kosmas), dvlachos@uop.gr (D. S. Vlachos) Preprint submitted to Elsevier May 28, 2018 On the other hand, environmental factors of importance to ship routing are those elements of the atmosphere and ocean that may produce a change in the status of a ship transit. In ship routing consideration is given to wind, waves, fog and ocean currents. While all of the environmental fac- tors are important for route selection and surveillance, optimum routing is normally considered attained if the effects of wind and waves can be opti- mized. The effect of wind speed on ship performance is difficult to determine. In light winds (less than 20 knots) ships lose speed in headwinds and gain speed slightly in following winds. For higher speeds, ship speed is reduced in both head and following winds. Wave height is the major factor affecting ship performance. Wave action is responsible for ship motions, which reduce propeller thrust and cause increased drag from steering corrections. The re- lationship of ship speed to wave direction and height is similar to that of wind. Head seas reduce ship speed, while following seas increase ship speed slightly to a certain point, beyond which they retard it. In heavy seas, the exact performance may be difficult to predict because of the adjustments of the course and speed for ship handling and comfort. Although the effect of sea and swell is much greater than wind, it is difficult to separate the two in ship routing. Fog, while not directly affecting ship performance, should be avoided as much as feasible, in order to maintain normal speed in safe conditions. Although the route may be longer by avoiding fog, transit time may be less due to not having to reduce speed in reduced visibility. In addi- tion, crew fatigue due to increased watch keeping vigilance can be reduced. Ocean currents do not present a significant routing problem, but they can be a determining factor in route selection and diversion. The important consid- eration to be evaluated are the difference in distance between a great circle route and a route selected for optimum current, with the expected increase of speed of advance from the following current. More details about the effect of environmental factors can be found in [1]. The role of routing is to allocate the available resources to best fulfill cer- tain requirements. In this paper we are interested in the problem of optimal ship routing taking into account only the wave height and direction by using the simulated annealing algorithm [5, 6]. The simulated annealing method is an extension of a Monte Carlo method developed by Metropolis et al [7], to determine the equilibrium states of a collection of atoms at any given temperature T. Since the method was first proposed in [5, 6], much research has been conducted on its use and properties [8, 9, 10, 11, 12, 13, 14, 15]. The method itself is a technique which has attracted significant attention as 2 suitable for optimization problems of large scale. It can give solution when a desired global extremum is hidden among many, poorer, local extrema. Even though other practical methods have also been found, surprisingly, the implementation of the algorithm is relatively simpler. At the heart of the method is an analogy with thermodynamics, specifically with the way liquids freeze and crystallize, or metals cool and anneal, when they ar

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