Some properties of the bilevel programming problem
Journal of Optimization Theory and Applications
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Multiobjective bilevel optimization
Mathematical Programming: Series A and B
Bilevel model for production-distribution planning solved by using ant colony optimization
Computers and Operations Research
International Journal of Computer Mathematics
A fuzzy interactive method for a class of bilevel multiobjective programming problem
Expert Systems with Applications: An International Journal
Multiobjective programming using uniform design and genetic algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Evolutionary multi-objective optimization for mesh simplification of 3D open models
Integrated Computer-Aided Engineering
Hi-index | 0.00 |
Currently, the production-distribution planning problems are usually modeled as single-objective bilevel programming problems. However, many real world production-distribution planning problems involve several objectives simultaneously for decision makers at two different levels when the production and the distribution processes are considered. In this paper, a multiobjective bilevel production-distribution planning model with equilibrium between supply and demand is set up, in which the distribution company is the leader who controls the distributing process with the aims to minimize its overall cost, and the manufacturer is the follower who controls the production process with the aims to minimize its overall cost and storage cost. So in the proposed model, the leader has one objective and the follower has two objectives. To solve the model efficaciously, the lower level problem follower's problem is transformed into an equivalent single-objective programming problem by a weighted aggregation method. As a result, the multiobjective bilevel optimization problem is transformed into a single-objective bilevel optimization problem. To solve the transformed problem efficiently, a uniform design scheme is applied to generate some representative weight vectors and initial population. Thereafter, a uniform design based crossover and exponential mutation are designed, and a local search scheme is applied. Based on all these, a hybrid genetic algorithm is proposed. Finally, two real word problems are solved successfully by the proposed algorithm, and the effectiveness and efficiency of the proposed algorithm are also tested by other test problems.