Interval Robust Multi-objective Algorithm

• Published in: Nonlinear analysis Vol. 71; no. 12; pp. e1818 - e1825
• Main Authors: Soares, G.L., Parreiras, R.O., Jaulin, L., Vasconcelos, J.A., Maia, C.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15-12-2009; Elsevier
• Subjects: Algorithms; Enclosure; Genetic algorithm; Interval Analysis; Intervals; Mathematical analysis; Mathematical models; Optimization; Pareto optimality; Robust Multi-objective optimization; Robust Pareto frontier; Uncertainty; Robust Multi-objective optimization; Robust Pareto frontier; Genetic algorithm; Interval Analysis; Interval Analysis Genetic algorithm
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2009.02.077

This 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.