The determination of crop production functions which describe the relationship between irrigation water and crop yield under the assumption of optimal irrigation scheduling is a major building block for a more efficient and sustainable water management. In this paper we introduce a methodology to determine the entire crop production function for a given scenario within a single run of a multi-objective evolutionary algorithm. Further we compare the performance of four major algorithms (NSGA-II, NSDE, DEMO, and MO-CMA-ES), and a single-objective approach based on differential evolution on three different scenarios and two different population initialization methods on this problem. We show that the combination of a problem specific initialization with MO-CMA-ES is able to determine crop production functions which are extremely close to actual ones.