Modelling the response of a fishing fleet to changing circumstances, using cautious non-linear optimization

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Abstract
Projecting the effects of changes in the availability of fish resources on the operations of a fishing fleet is a large and complicated allocation problem. We have found that linear programming is unsuitable for modelling such problems, because the solutions are inherently extreme, sparse, and ruthless, whereas the real fishing industry has substantial inertia. There are powerful socio-economic reasons why it cannot and should not depart too rapidly or radically from the status quo. We have developed the method of cautious non-linear optimization to handle the problem. This ascribes non-linear penalties to deviations from a reference solution, and any constraints which fail to be observed, and minimizes the resulting compound objective function using the conjugate gradient method. A fairly large problem (1500 variables) can be handled on a moderately sized computer. Excellent results have been obtained. The model is able to reproduce an actual situation when given the appropriate data, and can model changes which have happened during the past few years reasonably accurately. We believe that the uncertainties in the results are caused almost entirely by uncertainties in the assumptions and data used, and hardly at all by the modelling technique. A range of problems can be studied by varying the weights ascribed to the various terms of the objective function, and the results obtained seem to be meaningful even at a highly disaggregated level. We consider that the method is most powerful, and would be useful in many problems where a large and complex system with substantial inertia has to be modelled.

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