, Volume 46, Issue 11, pp 1918-1931

Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier

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Abstract

New hybrid methods for approximating the Pareto frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto frontiers are considered. Since the approximation of the Pareto frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.

Original Russian Text © V.E. Berezkin, G.K. Kamenev, A.V. Lotov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 11, pp. 2009–2023.