What is really important about genetic algorithms? Genetic algorithms can be adapted in order to solve directly multi- objective programming optimisation problems. We can implement a parallel search of many Pareto-optimal solutions within the design variables domain.
The fitness function has to be modified. Fitness can be selected according to the non-dominated (Pareto-optimality) property. If we find a non-dominated solution, we set a very high fitness value, according to the formula. If the solution is dominated, the fitness value is lower.
The population is divided into two sub-population. The first one, denoted as rank 1, is constituted by the solutions that belong to the approximated Pareto-optimal set. The remaining solutions are sorted according to the definition, generating a second rank. And so on for all the elements inside the population. This implementation is generally more efficient than using non-linear programming techniques after a scalarisation.