Mathematical programming model mining: A systematic field survey

Abstract

Mathematical Programming (MP) is a well-established framework for formulating optimization problems using variables, constraints, and an objective function. The task of developing an MP model involves addressing subproblems such as discovering an MP model from domain knowledge, conformance checking of a candidate MP model with domain knowledge, and enhancing an invalid MP model based on domain knowledge. Traditionally, experts manually perform these tasks, leading to iterative processes that are both labor-intensive and error-prone. Recent literature highlights an emerging field of algorithms focused on automating MP model development using domain knowledge artifacts, which we jointly term MP model mining and divide into discovery, conformance checking, and enhancement problems. This study organizes and analyzes existing knowledge on MP model mining, aiming to elucidate the state of the art and pinpoint current gaps and challenges. Through a systematic review via an acknowledged literature search engine, we address 29 research questions concerning various dimensions, identify 15 knowledge gaps, and propose a future research agenda.