Multi-objective calibration by combination of stochastic and gradient-like parameter generation rules – the caRamel algorithm

Abstract. Environmental modelling is complex, and models often require the calibration of several parameters that are not able to be directly evaluated from a physical quantity or field measurement. Multi-objective calibration has many advantages such as adding constraints in a poorly constrained problem or finding a compromise between different objectives by defining a set of optimal parameters. The caRamel optimizer has been developed to meet the requirement for an automatic calibration procedure that delivers not just one but a family of parameter sets that are optimal with regard to a multi-objective target. The idea behind caRamel is to rely on stochastic rules while also allowing more “local” mechanisms, such as the extrapolation along vectors in the parameter space. The caRamel algorithm is a hybrid of the multi-objective evolutionary annealing simplex (MEAS) method and the non-dominated sorting genetic algorithm II ( e -NSGA-II). It was initially developed for calibrating hydrological models but can be used for any environmental model. The caRamel algorithm is well adapted to complex modelling. The comparison with other optimizers in hydrological case studies (i.e. NSGA-II and MEAS) confirms the quality of the algorithm. An R package, caRamel , has been designed to easily implement this multi-objective algorithm optimizer in the R environment.