This volume LNCS 12735 constitutes the papers of the 18th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, CPAIOR 2021, which was held in Vienna, Austria, in 2021. Due to the COVID-19 pandemic the conference was held online. The 30 regular papers presented were carefully reviewed and selected from a total of 75 submissions. The conference program included a Master Class on the topic "Explanation and Verification of Machine Learning Models".