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Uncertainties are commonly present in optimization systems, and when they are considered in the design stage, the problem usually is called a robust optimization problem. Robust optimization problems can be treated as noisy optimization problems, as worst case minimization problems, or by considering the mean and standard deviation values of the objective and constraint functions. The worst case scenario is preferred when the effects of the uncertainties on the nominal solution are critical to the application under consideration. Based on this worst case scenario, we developed the [I]RMOEA (Interval Robust Multi-Objective Evolutionary Algorithm), a hybrid method that combines interval analysis techniques to deal with the uncertainties in a deterministic way and a multiobjective evolutionary algorithm. We introduce [I]RMOEA and illustrate it on three robust test functions based on the ZDT problems. The results show that [I]RMOEA is an adequate way of tackling robust optimization problems with evolutionary techniques taking advantage of the interval analysis framework.

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a b s t r a c tThis paper introduces a method for solving multi-objective optimization problems in uncertain environment. When the uncertainty factors of the optimization problem can be included into the mathematical model, through bounded intervals, [I]RMOA (Interval Robust Multi-objective Algorithm) can find an enclosure of the robust Pareto frontier. In this approach, the robust Pareto solutions are the ones that have the best performance when the worst case scenario, characterized by the uncertainty parameters, is considered.[I]RMOA has some positive aspects: it does not require the calculus of derivatives; it has only two input parameters; it is a reliable tool for solving different robust optimization problems, which can be nonlinear and discontinuous or have nonconvex Pareto frontier, for instance. The success of the method depends only on the quality of the objective inclusion functions and the precision parameters. Its disadvantage lies in the fact that it requires high computational effort, when high-dimensional problems are considered or when a very accurate enclosure is needed. Two analytical robust test functions are proposed to be treated by [I]RMOA and to validate the results provided by a stochastic multi-objective optimization method. The results are satisfactory.

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