Multiobjective optimisation of fuzzy controllers using evolutionary algorithms

Evolutionary algorithms (EA) are a suitable technique for the optimisation of fuzzy controllers. A disadvantage is the very long time the optimisation mostly takes. This is even more important, if complex fuzzy controllers with several objectives are considered, because in this case the validation test for the assessment of the controllers becomes very costly. As an alternative, we propose to use several small, specific tests, which determine the performance of the controller in separate system conditions. As the fuzzy sets can be assigned to the different conditions, they can be optimised with respect to their specific test. The modified EA we use is able to melt together the different parts of the parameter string in a reasonable way, so that the complete fuzzy controller is optimised with regard to all the objectives. To achieve a simultaneous improvement of all objectives, we change the objective function after every generation using an adaptive weight factor. The method is illustrated by applying it to the extended control problem of the inverted pendulum with both the balancing of the pole and the positioning of the cart being considered