Evolutionary multi-objective algorithms for feed resource allocation in dairy systems

In grassland-based dairy systems, determining how to rotate the cows among fields for grazing, how much concentrate to supply and the correct stocking rate to be used are important decisions that impact on the efficiency of the system. Considering the presence of conflictive objectives, a multi-objective approach is therefore the natural way of facing the problem. Due to the computational difficulty of finding the full solution set (the Pareto front) of multi-objective models, it is usually necessary to employ algorithms giving a good approximation of this set. In particular, a number of multi-objective evolutionary algorithms with different characteristics have been proposed in the general optimization literature; but there is no current study of which is the most appropriate one for feed resource allocation in dairy systems. In this work, we present the performance evaluation of four multi-objective evolutionary algorithms to generate an approximation of the Pareto front of the feed resource allocation problem in dairy systems. Two classical genetic algorithms (NSGA-II and SPEA-2) and two differential evolution (DE) algorithms (GDE-3 and a Pareto-based DE) were used. To evaluate the algorithms, two experiments based on scenarios constructed from real data were performed. The comparison took into account running times, objective function values attained, Pareto front comparisons, and approximation quality measures based on four different metrics. From the results we conclude that the SPEA-2 is the algorithm that obtains the best quality performance for the problem under study, but also the slowest one, opening a future work opportunity of improving its computational performance.