Application to Multiobjective Bilevel Optimization

Despite multiobjective bilevel optimization has not yet received a broad attention in the literature, these problems are very interesting in the view of applications, see for instance [241]. For getting an idea of this we give an illustrative example. Let us consider a city bus transportation system financed by the public authorities. They have as targets the reduction of the money losses in this non-profitable business as well as the reduction of the number of cars on the streets. The public authorities can decide about the bus ticket price, but this influences the customers in their usage of the buses. The public has maybe several competing objectives, too, as to minimize their transportation time and costs. Hence the usage of the public transportation system can be modeled on the lower level with the bus ticket price as parameter. The solution of the lower level influences then the objective values of the public authorities on the upper level. Such a problem can thus be mapped by multiobjective bilevel optimization.

Multiobjective bilevel optimization problems are also closely related to equilibrium problems and the definition of non-dominated equilibrium solutions, see for instance [8, 30, 35, 171, 177, 205, 240].