Gorithm was employed, but in the Stackelberg case, the authors define a leader and a follower for each experimental scheme. The experimental results reveal that the Stackelberg approach attains better results (although it is more computationally expensive). They conclude that Nash and Stackelberg get AZD-8835 frameworks are significantly different and the correct approach depends on the particular problem. Also, [42] adapted multi-objective optimization techniques to solve a particular class of bi-level programming problems; where the optimal bi-level solution is determined by the Pareto optimal points, corresponding to the non-dominated points that belong to the intersection of the two efficiency sets. However,PLOS ONE | DOI:10.1371/journal.pone.0128067 June 23,3 /GA for the BLANDPTable 1. Relevant previous work. Reference Mathieu et al. [29] Type A Description To the fpsyg.2014.00726 best of our knowledge this is the first application in the literature of genetic algorithms for solving bi-level programming problems. In this paper, the initial population of solutions was leader solutions and the follower responses were obtained by directly optimizing the linear lower level problem. For each leader’s solution the follower’s Cibinetide web problem is solved exactly. Propose a general scheme for a genetic algorithm capable of solving different applications of bi-level programming problems. It is assumed that the follower cooperates with the leader when the former obtains the lower level optimal response. The cooperation is made at the end of each iteration when a synchronization (interchange) between leader’s and follower’s populations is conducted in order to preserve the interactive nature of the problem. Several variations of genetic algorithms are proposed to solve a wide variety of location problems, including competitive location problems. In order to solve the lower level problem they designed a greedy heuristic, which was implemented every time a new leader’s solution was generated. Propose a hybrid algorithm that combines the Simplex method, genetic algorithms, stochastic and fuzzy simulations, to solve a bi-level location problem where the flow from the lower level to the upper level is stochastic. For each leader’s solution the lower level is solved exactly. Propose a memetic hybrid algorithm that combines the wcs.1183 principles of evolutionary algorithms with tabu search for a competitive p-Median problem. For each leader evaluation they solve the lower level problem through a commercial software. Design a hybrid algorithm that combines the simulated annealing method with the branch-and-cut method, in order to obtain upper bounds for the facility location problem with users’ preferences. During the simulated annealing method they solved the lower level problem for each leader’s solution. Propose a scatter search algorithm to solve urban transportation network design problem. The upper level can be seen as a model for solving the topological network design problem. The lower level model aims to solve the signal setting problem. In order to avoid the necessity of solving the lower level at each iteration they propose to solve the signal setting problem with a local approach. Accordingly, the signal setting problem was formulated as an asymmetric equilibrium assignment problem, where only the topological variables assume the role of decision variables, and both, the signal settings and the equilibrium traffic flows, are descriptive variables reducing the bi-level problem into a sin.Gorithm was employed, but in the Stackelberg case, the authors define a leader and a follower for each experimental scheme. The experimental results reveal that the Stackelberg approach attains better results (although it is more computationally expensive). They conclude that Nash and Stackelberg frameworks are significantly different and the correct approach depends on the particular problem. Also, [42] adapted multi-objective optimization techniques to solve a particular class of bi-level programming problems; where the optimal bi-level solution is determined by the Pareto optimal points, corresponding to the non-dominated points that belong to the intersection of the two efficiency sets. However,PLOS ONE | DOI:10.1371/journal.pone.0128067 June 23,3 /GA for the BLANDPTable 1. Relevant previous work. Reference Mathieu et al. [29] Type A Description To the fpsyg.2014.00726 best of our knowledge this is the first application in the literature of genetic algorithms for solving bi-level programming problems. In this paper, the initial population of solutions was leader solutions and the follower responses were obtained by directly optimizing the linear lower level problem. For each leader’s solution the follower’s problem is solved exactly. Propose a general scheme for a genetic algorithm capable of solving different applications of bi-level programming problems. It is assumed that the follower cooperates with the leader when the former obtains the lower level optimal response. The cooperation is made at the end of each iteration when a synchronization (interchange) between leader’s and follower’s populations is conducted in order to preserve the interactive nature of the problem. Several variations of genetic algorithms are proposed to solve a wide variety of location problems, including competitive location problems. In order to solve the lower level problem they designed a greedy heuristic, which was implemented every time a new leader’s solution was generated. Propose a hybrid algorithm that combines the Simplex method, genetic algorithms, stochastic and fuzzy simulations, to solve a bi-level location problem where the flow from the lower level to the upper level is stochastic. For each leader’s solution the lower level is solved exactly. Propose a memetic hybrid algorithm that combines the wcs.1183 principles of evolutionary algorithms with tabu search for a competitive p-Median problem. For each leader evaluation they solve the lower level problem through a commercial software. Design a hybrid algorithm that combines the simulated annealing method with the branch-and-cut method, in order to obtain upper bounds for the facility location problem with users’ preferences. During the simulated annealing method they solved the lower level problem for each leader’s solution. Propose a scatter search algorithm to solve urban transportation network design problem. The upper level can be seen as a model for solving the topological network design problem. The lower level model aims to solve the signal setting problem. In order to avoid the necessity of solving the lower level at each iteration they propose to solve the signal setting problem with a local approach. Accordingly, the signal setting problem was formulated as an asymmetric equilibrium assignment problem, where only the topological variables assume the role of decision variables, and both, the signal settings and the equilibrium traffic flows, are descriptive variables reducing the bi-level problem into a sin.