Improved <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>x</mml:mi></mml:math>-space algorithm for min-max bilevel problems with an application to misinformation spread in social networks

In this work we propose an improvement of the $x$-space algorithm developed for solving a class min--max bilevel optimization problems (Tang Y., Richard J.P.P., Smith J.C. (2016), A algorithms mixed-integer optimization. Journal Global Optimization, 66(2), 225--262). setting, leader upper level problem aims at restricting follower's decisions by minimizing objective function, which follower intends to maximize in lower making still available her. The solves and bound consecutively until convergence, requires dualization approximation formulating problem. We first reformulate using properties optimal solution original formulation, makes step unnecessary. reformulation possible integration greedy covering heuristic into scheme, results considerable increase efficiency. new referred as improved is implemented applied recent that arises context reducing misinformation spread social networks. It also assessed on benchmark instances two other problems: zero-one knapsack with interdiction maximum clique interdiction. Numerical indicate performance superior algorithm, compares favorably linear programs.