This paper presents an evolutionary approach to solve the multi-objective min-max problem (MOMMP) that derives from the maximization of the Belief in robust design optimization. In evidence-based robust optimization, the solutions that minimize the design budgets are robust under epistemic uncertainty if they maximize the Belief in the realization of the value of the design budgets. Thus robust solutions are found by minimizing, with respect to the design variables, the global maximum with respect to the uncertain variables. This paper presents an algorithm to solve MOMMP, and a computational cost reduction technique based on Kriging metamodels. The results show that the algorithm is able to accurately approximate the Pareto front for a MOMMP at a fraction of the computational cost of an exact calculation.