Comparative evaluation of some interactive reference point-based methods for multi-objective optimisation

Many real-world optimisation applications include several conflicting objectives of possibly nondifferentiable character. However, the lack of computationally efficient, interactive methods for nondifferentiable multi-objective optimisation problems is apparent. To satisfy this demand, a method called NIMBUS has been developed. Two versions of the basic method are presented and compared both theoretically and computationally. In order to give variety to the comparison, a related approach, called reference direction method, is included. Theoretically, the methods differ in handling the information requested from the user. Numerical experiments indicate differences in computational efficiency and controllability of the solution processes.