choose the options of tacking as soon as the yacht is headed (alternative A1). This is valid irrespectively of the factor combination considered (awaref and tws). Furthermore, alternative A3 turns out to be the ‘second- best’ choice for all factor combinations. This means that, within the four weather scenarios considered, alternative A1 is the choice yielding the highest expected utility and therefore represents the most advantageous strategic option when the evolution of the racing scenario is uncertain.
On the other hand, different results can be observed when deciding ‘under
risk’. As an example, let us
Figure.6 - scenario S2 : dashed line track corresponds to choice A1, solid line track to choice A2
Before commenting on the simulation results, let us focus our attention to the fact that, owing to the assumptions described
in Sect. 6.1, different scenarios involve
different number of tacks. As an example, let us consider scenario S2 (wind veering to East): if alternative A1 was selected (dashed line, Fig.6), the yacht would tack just once (onto starboard) since any subsequent windshift to the right would represent a lift for the starboard tacker, yielding
higher VMGs and DMGs. Conversely, if
alternative A2 was chosen (solid line, Fig.6), the yacht would still be sailing on port when hit by the subsequent 10° windshift: this would represent a further header for the port-tacker and the navigator would therefore call for a tack onto starboard. In conclusion, the lower payoff (C2,2 <C1,2) is due to a 120 seconds beat on the headed tack.
Now, let us focus on the simulation results of Tab.3. It can be seen that, when all weather scenarios are equally likely to occur, the most advantageous choice is A1: tacking as soon as the yacht is headed. Higher payoffs can indeed be obtained when selecting alternative A1, for any given outcome. Other alternatives (not
tacking or
delaying the tack) always yield lower payoffs; alternative A3 is the ‘second-best’ choice, despite the gap between C2,j and C3,j varies. When the judgement is made across outcomes instead than across alternatives, i.e. choosing an alternative first and then considering all possible outcomes, it can be observed that highest payoffs are always obtained under the outcome S2.
6.3 Two possible
DECISION MAKING STRATEGIES approaches
to decision making were
highlighted in Sect.4.4; their application to the present decision-making problem is investigated in the present Section. Let us consider the payoff matrices of Table.3 and Appendix A.
When hypothesizing a condition of ‘decision-making under ignorance’, it
can be shown that either an optimistic, a pessimistic and a neutral decider would
consider a possible high-dispersion probability distribution such as { P1 , P2 , P3 , P4 } = {0.05, 0.12, 0.15, 0.68}.
In this case, oscillating wind patterns
(outcomes S3 and S4) are more likely to occur than veering wind patterns (S1 and S2): it can be shown that delaying the decision can yield lower payoffs than deciding not to tack. When tws = 6m/s and awaref = 25°, if outcome S4 is considered, the yacht that delays the decision sails a 60s beat while headed and pays the price of two tacks (solid track, Fig.7). Conversely, the yacht that does not tack when hit by the first windshift (t1 =320s) sails a longer beat while headed, but will not tack afterwards (dashed track, Fig.7), since it experiences a constant lift after t2 =440s. Owing to the fact that higher payoffs are weighted by higher probabilities (P4 = 0.68), alternative A2 proves to be the ‘second-best’ choice after A1.
Figure.7 - scenario S4 : dashed line track corresponds to choice A2, solid line track to choice A3
7. CONCLUSIONS AND FUTURE WORK
A four-DOF dynamic VPP has been developed, making it possible to simulate a yacht racing solo on given racecourses and in predetermined wind patterns. The distinctive feature of the present VPP consists in built-in behavioural models, shaped as an ‘automatic crew’. The ‘crew’ is given tasks such as steering the yacht, trimming sails and making strategic decisions, with the purpose of sailing the course efficiently e.g. taking advantage of changes to the weather scenario.
©2008: Royal Institution of Naval Architects
B-17
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