Design of the GA

As the name suggests, GAs follow the principle of Darwinism to improve a 'population' of solutions. Although there are many operators on the solutions possible, the most basic ones are selection, mutation, and recombination by crossover.

In a first step the GA chooses a population by random. Note that this property to always work with several solutions at the same time makes it very easy to take advantage of parallel computing.

Afterwards, some individuals are chosen and mutated, that means a small number of information units are changed arbitrarily. Often the fittest individuals, that is, the solutions with highest values with respect to the objective function, are given a bigger chance to be improved by this local search operator. Some GAs are elite preserving, that is, copying an existing solution before mutation, then comparing this copy with the results of the mutation, preserving only the solution of both with the highest fitness value.

The mating operator is maybe the most important thing about GAs, because it does global search by recom-bining parts of the solutions, thus using symmetries in the search space, that otherwise are hard to make use of. Again there are many possible ways to actually melt information of two or even more solutions to build up new ones. Figure 1 shows a 1-point crossover, that splits two parent solutions at one position (n positions for ยป-point crossover), to create two child solutions by crosswise putting together the pieces. Of course, again it is possible to favor fitter solutions in the mating process and again elite preserving options might be implemented.

If the computing of the objective function is very time consuming, it is often possible to use at least parts of the calculations made for the parents to obtain the fitness for the children. In our example, there is the possibility to save the emission changes due to some measures' implementation degrees for different blocks of technologies while calculating the emission reduction of a solution and to use these figures when a whole block is kept unchanged by the mating operator. The same idea can of course also be used when calculating the emission changes of mutated solutions. However, because the computing of resulting concentration changes or even resulting savings in external costs is far more time-consuming, these options were not used in the MERLIN project.

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