A Hyper-Heuristic of Scalarizing Functions

Scalarizing functions have been successfully used by Multi-Objective Evolutionary Algorithms (MOEAs) for the fitness assignment process. Their popularity has to do with their low computational cost, their capability to generate (weakly) Pareto optimal solutions, and their effectiveness in solving many-objective optimization problems. Nevertheless, recent studies indicate that the search behavior of MOEAs strongly depends on the choice of the scalarizing function. Besides, this specification varies according to the Pareto-front geometry of the problem at hand. In this work, we present a novel hyper-heuristic for continuous search spaces, which combines the strengths and compensates for the weaknesses of different scalarizing functions. These heuristics have been proposed within the evolutionary multi-objective optimization and mathematical programming communities. Furthermore, the selection of heuristics is conducted through the s-energy, which measures the even distribution of a set of points in k-dimensional manifolds. Experimental results indicate that our proposed approach outperforms the use of a single heuristic as well as other state-of-the-art algorithms in the majority of the ZDT, DTLZ and WFG test problems.