Scatter search with path relinking for linear bilevel problems

The literature includes very few instances of scatter search applications to bilevel optimization. These implementations have been proposed for problems in the field of logistics involving integer variables and are based on a structure where scatter search sets the values of the decisions at the upper level followed by the solution of the lower level problem. In this work, we develop a scatter search for solving linear bilevel problems. Our proposal employs a tailored path relinking procedure that generates solutions that are boundary feasible extreme points located in the trajectory between infeasible and feasible bilevel solutions. We perform scientific experimentation to determine the most effective configuration of our scatter search with path relinking. We also perform competitive experiments to determine where the proposed solution method stands when compared to the state of the art for tackling linear bilevel problems. • The first Scatter Search approach for solving Linear Bilevel Problems. • Only extreme point solutions of the constraint region are analyzed. • A novel path relinking procedure based on the properties of Linear Bilevel Problems. • The local search examines adjacent extreme points of the potential optimal solution. • The algorithm provides high-quality solutions in short computational times.