Enhanced differential evolution using local Lipschitz underestimate strategy for computationally expensive optimization problems

Graphical abstractDisplay Omitted HighlightsThis study presents a DE with local Lipschitz underestimated strategy to reduce the number of function evaluations.Lipschitz supporting hyperplanes are constructed based on the evolutionary information to guide the DE process.The proposed local Lipschitz underestimate strategy is general and can be applied to other evolutionary algorithms. Differential evolution (DE) has been successfully applied in many scientific and engineering fields. However, one of the main problems in using DE is that the optimization process usually needs a large number of function evaluations to find an acceptable solution, which leads to an increase of computational time, particularly in the case of computationally expensive problems. The Lipschitz underestimate method (LUM), a deterministic global optimization technique, can be used to obtain the underestimate of the objective function by building a sequence of piecewise linear supporting hyperplanes. In this paper, an enhanced differential evolution using local Lipschitz underestimate strategy, called LLUDE, is proposed for computationally expensive optimization problems. LLUDE effectively combines the exploration of DE with the underestimation of LUM to obtain promising solutions with less function evaluations. To verify the performance of LLUDE, 18 well-known benchmark functions and one computationally expensive real-world application problem, namely, the protein structure prediction problem, are employed. Results obtained from these benchmark functions show that LLUDE is significantly better than or at least comparable to the state-of-the-art DE variants and non-DE algorithms. Furthermore, the results obtained from the protein structure prediction problem suggest that LLUDE is effective and efficient for computationally expensive problems.