Applied Pareto multi-objective optimization by stochastic solvers

It is well known that many engineering design problems with different objectives, some of which can be opposed to one another, can be formulated as multi-objective functions and resolved with the construction of a Pareto front that helps to select the desired solution. Obtaining a correct Pareto front is not a trivial question, because it depends on the complexity of the objective functions to be optimized, the constraints to keep within and, in particular, the optimizer type selected to carry out the calculations. This paper presents new methods for Pareto front construction based on stochastic search algorithms (genetic algorithms, GAs and multi-objective genetic algorithms, MOGAs) that enable a very good determination of the Pareto front and fulfill some interesting specifications. The advantages of these applied methods will be proven by the optimization of well-known benchmarks for metallic supported I-beam and gearbox design.