This paper presents and analyses an engineered expected hypervolume improvement (EHVI) algorithm for solving the problem of PID parameter tuning and the optimization problem of controlling the substrate feed of a biogas plant. The EHVI is the expected value of the increment of the hypervolume indicator given a Pareto front approximation and a predictive multivariate Gaussian distribution of a new point. To solve this problem, S-metric selection-based efficient global optimization (SMS-EGO), EHVI based efficient global optimization (EHVIEGO) and SMS-EMOA are used and compared in both the PID parameter tuning problem and for biogas plant feed optimization. The results of the experiments show that surrogate model based algorithms perform better than SMS-EMOA, and the performance of EHVI-EGO is slightly better than SMS-EGO.