## Combination of Several Optimization Algorithms

It is recommendable to think about the advantages of the single algorithms to find the most suitable combination of them for a certain optimization problem. For example, in MERLIN we chose to first search with a kind ofsimulated annealing in the smaller subset of the pareto-optimal solutions, as described above. In a second phase, a GA was used to search in the complete set of all solutions. Finally, the pareto-optimal solution was entered into the population of the GA, because in some test runs, it became clear that an overhasty introduction of this solution results in premature convergence of the GA so that its power to search sensible solutions over a vast area of the search space is reduced.

Figure 2 shows a typical optimization run. Its target was to stay below some threshold for ozone (AOT6O < 2200 ppb.hyr-1 in every 50 km grid cell) so mainly NOx and NMVOC are to be reduced. AOT is the accumulated ozone over a threshold of xx parts per billion (ppb), and is calculated in hours times the exceedance of a certain

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Second parent strategy

Second child strategy

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Second parent strategy

Second child strategy

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Figure 1 The mating operator (1-point crossover).

Figure 2 Results from the application of a 3-phase optimization routine.

threshold, that is, Z ppb.h of AOT6O means, the threshold of 60 ppb has been exceeded by Xppb during Yh with Z = X ■ Y. There were two fitness functions used, one related to the ozone target, the other to the costs, and the solutions were ordered lexicographically, that is, one solution is better than the other if either it comes closer to the ozone target or else they both come equally close, but the first solution is less expensive.

The red curve shows the related costs per year for the best solution found so far. As we expect, the first phase of the algorithm is very fast in reaching a good solution but of course it is limited to the smaller search space. The GA needs more time per generation, because although the time to calculate the parametrization is saved, the GA does one mating (with two child solutions) and four mutations per generation, which means six calculations of ozone values for every grid cell. Its performance seems rather poor compared to the simpler algorithm on the smaller search space, but as soon as it is allowed to use the result of the first phase, it still improves the result by quite a bit.

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