An Evolutionary Algorithm Driven by Correlation Coefficients to Solve Nonlinear Integer Bilevel Programming Problems

Abstract

Based on a simple branch-and-bound algorithm and correlation coefficients technique, this paper presents an evolutionary algorithm for solving nonlinear integer bilevel programming problem (NIBLPP). First, the upper-level decision variable values are selected as individuals in the population, and for each individual provided in the population, the branch-and-bound method is applied to obtain the optimal solutions to the lower-level problem. In order to make the offspring individuals in the population more diverse and uniformed. A crossover operator based on the sphere is designed which can produce more and better offspring individuals. In addition, the correlation coefficients technique is used to screen out potential better points among these offspring individuals, then the selected points will be further optimized to obtain an accurate solution to the lower-level problem. The simulation results show that the proposed evolutionary algorithm is effective for solving the NIBLPP problem.