Network design problem with congestion effects: A case of bilevel programming
Mathematical Programming: Series A and B
Artificial Intelligence: A Guide to Intelligent Systems
Artificial Intelligence: A Guide to Intelligent Systems
Parametric global optimisation for bilevel programming
Journal of Global Optimization
Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Application of particle swarm optimization algorithm for solving bi-level linear programming problem
Computers & Mathematics with Applications
Bilevel multi-objective optimization problem solving using progressively interactive EMO
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Particle swarm optimization for bi-level pricing problems in supply chains
Journal of Global Optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Hi-index | 0.00 |
Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leader's level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular level's optimization problem is solved the solution will be adapted the level's variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.