Microplates are indispensable in large-scale biological experiments but the layout of samples and controls can have a large effect on results. Here we introduce an artificial intelligence based method for designing microplate layouts that reduces unwanted bias and limits the impact of batch effects, leading to more accurate and reliable experimental results. The method relies on constraint programming, and produces effective multiplate layouts for different experimental settings, while at the same time remaining flexible and modifiable to take into account particular laboratory settings. First we discuss the desired properties of effective microplate layouts, which we then implement as a constraint model. We show that our method produces layouts that lead to smaller errors in dose response experiments when estimating EC50/IC50 values, to the point of frequently obtaining smaller errors even when using fewer doses or replicates. We also show how effective layouts lead to more robust results in high-throughput screening experiments. Finally, we make our method easily accessible by providing a suite of tools, an online service (PLAID), a data format to enable automated construction of designs programmatically, and notebooks to evaluate and compare designs aiding decisions on the number of doses and replicates when planning microplate experiments.