An efficient hybrid differential evolutionary algorithm for zbilevel optimisation problems

Abstract

Bilevel problems are widely used to describe the decision problems with hierarchical upper–lower-level structures in many economic fields. The bilevel optimisation problem (BLOP) is intrinsically NP-hard when its objectives and constraints are complex and the decision variables are large in scale at both levels. An efficient hybrid differential evolutionary algorithm for BLOP (HDEAB) is proposed where the optimal lower level value function mapping method, the differential evolutionary algorithm, k-nearest neighbours (KNN) and a nested local search are hybridised to improve the computational accuracy and efficiency. To show the performance of the HDEAB, numerical studies were conducted on SMD (Sinha, Maro and Deb) instances and an application example of optimising a venture capital staged-financing contract. The results demonstrate that the HDEAB outperforms the BLEAQ (bilevel evolutionary algorithm based on quadratic approximations) greatly in solving the BLOPs with different scales.