### Multi-Criteria Decision Making: some notes

I’m attending in Paris the IEEE Symposium Series on Computational Intelligence 2011, and the program is full of interesting talks. Piero Bonissone, from the GE Global Research, gave a two hours tutorial on Multi-Criteria Decision Making (MCDM), explaining the main theories and presenting three real-world cases.

The main problem for MCDM is the necessity of cope with more criteria when ordering and classifying. One possibility is to use all the Pareto theory and apply some algorithms, like Evolutionary Algorithms: niching ones (NPGA, NSGA) or elitist micro-GA and PAES. However, you can try to aggregate the criteria with a linear combination or with a $\epsilon-$constraint approach: only one objective is optimized and the other ones are used as constraints, as:

$\mathrm{min} f_i(x), \quad f_j(x) \le \epsilon_j$