Some modeling problems have more than one objective. Occam's razor is one frequent source - model simplicity is desirable, and so is accuracy. Theoretically, an optimal tradeoff can be derived, but it is notoriously difficult to apply in practice, even for relatively simple models. Another common source, when ecological models are used to drive management decision models, lies in conflicting management objectives - for example, where two species may have conflicting management requirements, or where ecological objectives conflict with resource constraints or with alternative uses.
A pragmatic alternative uses multiobjective methods to generate a range of models with different tradeoffs allowing a modeler, or a manager, to choose the preferred model after seeing the results. Consider, for example, the topical issue of environmental river flows, where management policies must reconcile conflicting objectives between environmental and other uses. In a simple example, f might represent the predicted abundance of a threatened aquatic species, whereas f might represent the viability of a water-dependent industry. With single-objective methods, a tradeoff between the objectives would be chosen before the model was run, and a single policy alternative would be output, giving the best alternative for that particular tradeoff. Pareto methods aim to fi
find the Pareto front (solid line, Figure 4), the theoretical set of points having the property that it is not possible to improve one objective without worsening another. In practice, the aim is to find a widely distributed set of points, close to the actual Pareto front. For environmental flows, the manager would be presented with a range of alternative policies, each generating a combination of ecological and industry outcomes. The manager would be free to choose among these policies, secure in the knowledge that no other policy could generate better outcomes for both policy objectives.
Evolutionary multiobjective algorithms are often chosen for this task, for the same ease-of-use and robustness reasons as for single-objective problems. Unlike the single-objective case, for multiobjective problems, the computational cost of evolutionary algorithms is comparable to classical algorithms. Current widely used algorithms are reliable and effective with a small number of objectives (less than 5), but effectiveness diminishes rapidly with an increasing number of objectives.
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