Sometimes the preferences of solutions to a certain problem are not known in detail. In these cases, it can be useful to search for a set of solutions, which are as good and as dissimilar as possible, and leave the final selection of a single solution to human intuition. Although especially GAs (see below) can be applied in this context, we stick to cases, where the different objectives can be merged to a single objective function f for example, using well-defined weights for the different targets. So the problem can be represented by:
Given a function f : V ! R, we seek an element vp V with f (v) > f (w) 8 wpV
To judge, which algorithm fits best to solve this problem, it is advisable to first look at its general properties, like linearity, differentiability, convexity, or certain patterns in the search space. To get a hint, which type of algorithm might fit well to a given problem, the properties should be checked in the order above to see whether algorithms described in the following sections might be best suited.
Although most discussions about optimization algorithms start at this point, if we talk about ecological modeling, there often are several ways to encode the so-called search space V, which dictates the properties of the objective function and thus might make the optimization much easier, if chosen well. Although it is very hard to give general rules, how to do this, the next section shall give an idea of what is important.
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