Evolutionary algorithms (EAs) are a nature-inspired population based search method for solving difficult optimisation problems. They apply principles of natural evolution that allow populations of species to adapt to their environment, such as the genetic inheritance and the survival of the fittest. In general, the process of EAs is based on the concepts of exploration and exploitation of the search space through selection and reproduction (mutation and crossover) operators. The efficiency of an EA depends heavily on the selection of suitable values of these operators. One can set these parameter values in advance, before the optimisation (parameter tuning) or can change them during the run (parameter control), by getting some kind of feedback from the evolution process itself.
Bilevel problem is a class of problems, where one optimisation problem (upper level/ leader) has another optimisation problem (lower level/ follower) as a constraint, following a hierarchy of decisions. Applications of such problems can be found in a variety of domains such as transportation, economics, engineering, reliability based design optimisation and optimal control. The optimisation of a bilevel problem aims to achieve the optimum solution of the upper level, taking into consideration the optimal lower level values too. This procedure becomes rather challenging, as the landscape of the lower level is changing for each upper level candidate solution. Parameter control when using EAs to tackle with this problem, can be useful.
In our approach, we aim to investigate the effect of parameter control in a nested bilevel evolutionary algorithm. The evolutionary algorithm that is used in both levels is the Differential Evolution algorithm, a simple yet powerful EA for global optimisation. The parameters that we adapt are the mutation (F), the crossover probability (CR), and the selection ranking schema, while the performance of the algorithm is evaluated by solving test-problems taken from literature.