Analysis of Two Algorithms for Multi-objective Min-max Optimization

This paper presents two memetic algorithms to solve multi-objective min-max problems, such as the ones that arise in evidence-based robust optimization. Indeed, 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. A number of problems, composed of functions whose uncertain space is modelled by means of evidence theory, and presenting multiple local maxima as well as concave, convex, and disconnected fronts, are used to test the performance of the proposed algorithms.