Compromise utilitarian solutions in multi-criteria optimization problems as a guide for evolutionary algorithms

Multi-criteria optimization problems are considered where the decision maker is unable to determine the exact weights of importance of the criteria but can provide some imprecise information about these weights. Two solution concepts are studied in this framework: the optimistic min-max solution and the compromise utilitarian solution, both of which can be exactly computed for linear problems. For general problems, it is shown that these solutions can be approximated by means of a slight modification of the evolutionary algorithm NSGA-II.