I think it will not work, by construction: the bilevel problem (regardless of whether the lower-level is linear or not) is inherently a problem over one objective. I have seen an approach to the bilevel problem where the lower-level problem is transformed through the use of a "gap function", in which case the gap function in this case will have an ever increasing "penalty" parameter in front of it in the objective function. But that does not make it a biobjective problem.

In a bi-level mathematical program one is concerned with two optimization problems where the feasible region of the first problem, called the upper-level (or leader) problem, is determined by the knowledge of the other optimization problem, called the lower-level (or follower) problem. Problems that naturally can be modelled by means of bi-level programming are those for which variables of the first problem are constrained to be the optimal solution of the lower-level problem. In this sense These problems can not be transformed to multi-objective problems.

NO. BLP and MOLP problems are defined in two distinct situations, where BLP solution is an optimum of it (it is better than all feasible solutions) but MOLP has an efficient set of nondominated solutions (there is not any feasible solutions better than them).

However, in optimistic linear BLP, we can show that feasible solutions of it is equal to the efficient set of an MOLP.

See "Fulop J. On the equivalence between a linear bilevel programming problem and linear optimization over the efficient set. Technical Report WP93-1, Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences (1993)"

In this way, linear BLP can transform to the problem of optimization of leader objective function on efficient set of an MOLP. Note that solving this problem is not easy due to nonconvexity of the solution space.

Thank you for your answers. So, it is not possible to search a Pareto front for BLP. Doesn't it?

Only MOLP problems have Pareto frontier (set of efficient solutions) and BLP problems have optimal solution.

But feasible solution set of linear BLP is equal to the Pareto frontier of a special MOLP problem. There are search algorithms (based on 1. enumeration of Efficient Basic Feasible Solutions of MOLP, 2. cutting plane method) for optimization of leader objective function on feasible solution of BLP problem (or equivalently on Pareto frontier of MOLP problem). But due to nonconvexity of the search area, finding the global optimum is time consuming and we usually have to accept a local optimum produced by the algorithm.

Yes, you can! I am aware of 2 types of connections between bilevel optimization and multiobjective optimization: (1) You can write a bilevel optimization as a minimization over the efficient set of a certain multiobjective optimization problem; see Fulop (1993)--linear case & Eichfelder (2010)--nonlinear case. (2) You can write write a bilevel optimization as a multiobjective optimization problem; see Fliege and Vicente (2006) and Ruuska, Miettinen and Wiecek (2012). An overview of this topic and details of the references above can be found in the latter reference: Ruuska, S., Miettinen, K., Wiecek, M.M.: Connections between single-level and bilevel multiobjective optimization. J. Optim. Theory Appl. 153(1), 6074 (2012). However, I have to emphasize that the corresponding multiobjective optimization problems are not easy to solve as they are based on complicated order relations constructed from the bilevel optimization problem.

A feasible solution of a bilevel program has to be an optimal one for the lower-level model, be it linear or non-linear. In a broader look, a bilevel model essentially has a single objective, which corresponds to that of the upper level. Hence, it is not conceptually correct to think of the two objectives of the bilevel model - corresponding to the upper and lower problems - as equivalent to the objectives in a multiobjective optimization case.

That being said, I would be interested to have a look at the above references mentioning modelling connections between the two paradigms. Nevertheless, I would expect highly complicated multiobjective problems.

After reading the answers, I have a small follow up question that one of you might be able to enlighten me with.

As I understood (and please feel free to correct me), the optimal solution to a BLP will always be a solution in the pareto set of the corresponding MOLP. Am I right, or is it possible that the BLP might choose an optimal solution that is not in the pareto set of the corresponding MOLP?

See the following publications:

Fülöp, J.: On the equivalence between a linear bilevel programming problem and linear optimization over the efficient set. Working Paper 93-1, Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, February 1993, 6 p. http://www.oplab.sztaki.hu/WP_1993_1_Fulop.pdf

Konno, H., Thach, P.T. and Tuy, H.: Optimization on Low Rank Nonconvex Structures, Kluwer, Dordrecht, 1997.

Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic Pubishers, Dordrecht, 2002.

For the relations between solutions of a (linear) bilevel optimization problem and the Pareto frontier of the problem where the objective functions of both the leader and the follower are considered at the same time you can have look into my article below. There you can find an example where the optimal solution of the bilevel problem is not in the Pareto frontier and the only point in the Pareto frontier which is feasible for the bilevel problem has the worst objective function value there.

@article{dempe2011comment, title={Comment to “interactive fuzzy goal programming approach for bilevel programming problem” by SR Arora and R. Gupta}, author={Dempe, Stephan}, journal={European journal of operational research}, volume={212}, number={2}, pages={429--431}, year={2011}, publisher={Elsevier} }

Thank you very much. Your information is valuable!