###### Abstract
However, only a few general recommendations can be extracted from the literature, especially considering the batch querying AP which is usually problem-dependent. In addition, the main potential for exploiting parallel computing lies in the batch-parallel evaluation of the candidates. Therefore, the AP must be able to provide a batch of valuable candidates. Various approaches are presented in [PERSON] et al. [6], however, batch selection remains a challenging question, especially for large batch sizes and small amounts of time. Indeed, the computational overhead of surrogate-related algorithm components is rarely considered and usually judged as negligible with respect to simulation time [7]. Furthermore, the efficiency of large batches of candidates is often lesser than that of the same number of candidates taken sequentially [8]. In this paper, we investigate several parallel batch-based algorithms using different APs, and we compare the optimized average profit: \(q\)-Efficient Global Optimization with Kriging Believer (KB) heuristic (KB-\(q\)-EGO) from [PERSON], [PERSON] and [PERSON] [9] (2008) and a revisited version allowing multi-infill criteria sampling (mic-\(q\)-EGO) inspired by [PERSON] et al. [10] and [PERSON] et al. [11]; Monte Carlo-based \(q\)-EGO (MC-based \(q\)-EGO) from [PERSON] et al. [12] (2020); Binary Space Partitioning EGO (BSP-EGO) from [PERSON] et al. [13] (2020); and TrUst Region BO (TuRBO) from [PERSON] et al. [14] (2019). Experiments are conducted with different batch sizes to evaluate and compare the scalability of the approaches. A thorough investigation of the different approaches is required to identify the most suitable algorithm that responds to the specificities of the UPHES optimization problem. Indeed, the optimization must be conducted in a restricted time and, contrary to common assumption, the acquisition time is not negligible compared to the simulation time. Consequently, the acquisition time needs to be taken into account in order to perform an efficient optimization. Hence, the main contribution of this paper is the comparison of several PBO approaches in view of their application to a current concern in energy production. The conducted study reveals that all investigated BO algorithms have poor scalability regarding parallel efficiency. Indeed, increasing the batch sizes obviously comes with the management of a larger data set. Consequently, a decrease in the number of performed cycles in a restricted time is expected, since the sequential part grows larger. Ideally, for an equivalent number of simulations, whatever the batch size, the final outcomes would be comparable. However, and despite the potentially larger number of simulations gained by parallelization, the final outcome of the algorithms is often worse with high batch sizes (8 or 16 compared to 2 or 4) within a fixed time budget. In Section 2.1, a detailed explanation of the complex UPHES operation is provided along with a mathematical formulation of the resulting optimization problem. In Section 2.2, the PBO algorithms designed to optimize UPHES station management are presented with a focus on their specificities. Section 3 is dedicated to experiments and results, where the outcomes from different algorithms are compared. In Section 4, we discuss the experimental results. Finally, conclusions are drawn in Section 5 and we outline possible future research directions to overcome the observed limitations of PBO.