A New Scalarization Technique and New Algorithms to Generate Pareto Fronts
Regina Sandra Burachik, C. Yalçın Kaya, M. M. Rizvi · SIAM Journal on Optimization · 2017
We propose a new scalarization technique for nonconvex multiobjective optimization problems and establish its theoretical properties. By combining our new scalarization approach with existing grid generation techniques, we design new algorithms for constructing reliable approximations of the Pareto fronts of three- and four-objective optimization problems. Our algorithms can be extended for problems with more objective functions to minimize. Four three-objective algorithms are formed by pairing up the new scalarization technique and three existing scalarization techniques with a grid of weights generated over the convex hull of individual minima (the CHIM grid) due to Das and Dennis. Four more algorithms are obtained by using, instead of the CHIM grid, the grid in the successive boundary generation algorithm (the SBG grid) by Mueller-Gritschneder, Graeb, and Schlichtmann. The new algorithms seem to perform better than existing algorithms, in terms of computational time and accuracy in constructing the boundary and the interior of the Pareto front. The advantages are tested, in particular, through a problem whose Pareto front has a hole in it. A rocket injector design problem with four objective functions illustrates the effectiveness of our new approach further.