The linear Bilevel Programming Problem (BLP) is an instance of a linear hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. In this paper we propose to solve this NP-hard problem using an adaptive search method related to the Tabu Search metaheuristic. Numerical results on large scale linear BLPs are presented.

Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy preserving AI. Integrating bilevel mathematical programming within deep learning thus an essential objective the Machine Learning community. Previously proposed approaches only consider single-level programming. In this paper, we extend existing optimization...

The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, ...

ABSTRACT: Feasible solutions of Bilevel programming (BLP) problem have to satisfy the optimality conditions of a lower level optimization problem which is defined as part of its constraints. Multiobjective BLP (MOBLP) problems are the special case of BLP problems with multiple objectives at the upper level which require every feasible solution to satisfy the Pareto optimality conditions of a lo...

We present a branch-and-cut algorithm for solving discrete bilevel linear programs where the upper-level variables are binary and the lower-level variables are either pure integer or pure binary. This algorithm performs local search to find improved bilevelfeasible solutions. We strengthen the relaxed node subproblems in the branch-and-cut search tree by generating cuts to eliminate all of the ...

This study deals with the effects of a supply chain (SC) with single product, multiple retailers and a manufacturer, where the manufacturer(he) produces lotsize of the product that contains a random portion of imperfect quality item. The imperfect quality products are sold in a secondary shop. The new contribution of this paper is a new non-linear demand function. Demand of the end customers va...

Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems, etc. In the present paper the monotonic approa...