Knowledge engineering mixed-integer linear programming: constraint typology
This work addresses the problem of knowledge representation for MILP formulations to facilitate automated modelling in various industry sectors, but it appears incremental as it builds on existing MILP concepts without introducing a new paradigm.
The paper tackles the challenge of representing mixed-integer linear programming (MILP) constraints by proposing an optimization modelling tree based on an MILP ontology, aiming to guide automated systems in eliciting MILP models from end-users for combinatorial business optimization problems.
In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, timetabling optimization problems, providing optimized business solutions for industry sectors such as: manufacturing, agriculture, defence, healthcare, medicine, energy, finance, and transportation. Despite the numerous real-life Combinatorial Optimization Problems found and solved, and millions yet to be discovered and formulated, the number of types of constraints, the building blocks of a MILP, is relatively much smaller. In the search of a suitable machine readable knowledge representation for MILPs, we propose an optimization modelling tree built based upon an MILP ontology that can be used as a guidance for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems.