A Knowledge Representation Approach to Automated Mathematical Modelling

TL;DR

This paper introduces a new ontology and constraint typology for MILP models, aiming to facilitate automated mathematical modeling from natural language descriptions of optimization problems.

Contribution

It proposes a novel MILP model ontology and an optimization modeling tree to enable automated, machine-readable representations of MILP models from user descriptions.

Findings

Developed a MILP model ontology and constraint typology.

Created an optimization modeling tree for automated model elicitation.

Aimed to bridge natural language and formal MILP specifications.

Abstract

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning, resource allocation, and 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 small. In the search for a suitable machine-readable knowledge representation structure for MILPs, we propose an optimization modelling tree built based upon an MILP model ontology that can be used as a guide for automated systems to elicit an MILP model from end-users on their combinatorial business optimization problems. Our ultimate aim is to develop a machine-readable knowledge representation for MILP that allows us to map an end-user's natural language description of the business optimization problem to an MILP formal specification as a first step towards automated mathematical modelling.