Surrogate Approximation on Bilevel Multi Follower Optimization Problems

Bilevel programming means studying decentralized non-cooperative and cooperative decision systems which contains two levels known as upper (Leader) and lower (Follower) level problems. By nature these types of problems are computationally expensive and have nested characteristics. It is even more complex when multiple follower is involved at the lower level which requires Stackelberg Nash Equilibrium to be satisfied. As these type of problems are involved in the scenario of transportation, logistics and environmental science, it is highly demanding to make efficient algorithm which requires comparatively low cost. However, so far in our knowledge nobody has tried to solve multi follower bilevel problems by using surrogate approximation approach which uses less computational cost than the traditional meta heuristics algorithm. In this paper, we incorporate Design and Analysis of Computer Experiments (DACE) model for solving lower level problems which contributes to the reduction of the computational cost. Our analysis involved memetic bilevel approach with surrogate approximation at the lower level and upper level contains traditional differential evaluation strategy. Our proposed approach shows competitive result with low cost than the existing approaches.