Reply to J. Vrugt’s comment on “How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?”

We would like to thank Jasper Vrugt for his comment on our recent paper Tang et al. (2006) in which we compare the Strength Pareto Evolutionary Algorithm 2 (SPEA2), the Multi-objective Shuffled Complex Evolution Metropolis algorithm (MOSCEM-UA), and the Epsilon Dominance Nondominated Sorted Genetic Algorithm II (ε-NSGAII) using a statistical metrics-based approach. To frame our response, we will provide a brief synopsis of the issues of concern discussed in the comment on our paper. Issue 1: Vrugt contends that the exclusion of the recommendation of Vrugt et al. (2003) that a single objective methodology should be used to first find the endpoints of the Pareto set to precondition search for MOSCEM-UA and that our use of initial uniform random sampling for the three algorithms did not accurately portray the performance of MOSCEM-UA. Issue 2: Vrugt contends that our approach in attaining the reference Pareto front in Fig. 5 using the 15 000 000 model simulations from all of the runs from all of the algorithms (i.e., 3 algorithms * 50 random seed trials/algorithm * 100 000 model simulations/random seed trail) is inefficient relative to his assertion that MOSCEM-UA would reliably identify the true reference front in approximately 22,000 model evaluations if we had first used a single objective algorithm to pre-condition MOSCEM-UA’s search. We will address each of these issues individually and then provide some brief concluding remarks.