DeepAI
Log In Sign Up

A Knowledge Representation Approach to Automated Mathematical Modelling

11/12/2020
by   Bahadorreza Ofoghi, et al.
0

Mathematicians formulate complex mathematical models based on user requirements to solve a diverse range of problems in different domains. These models are, in most cases, represented through several mathematical equations and constraints. This modelling task comprises several time-intensive processes that require both mathematical expertise and (problem) domain knowledge. In an attempt to automate these processes, we have developed an ontology for Mixed Integer Linear Programming (MILP) problems to formulate expert mathematician knowledge and in this paper, we show how this new ontology can be utilized for modelling a relatively straightforward MILP problem, a Machine Scheduling example. We also show that more complex MILP problems, such as the Asymmetric Travelling Salesman Problem (ATSP), however, are not readily amenable to simple elicitation of user requirements and the utilization of the proposed mathematical model ontology. Therefore, an automatic mathematical modelling framework is proposed for such complex MILP problems, which includes a problem (requirement) elicitation module connected to a model extraction module through a translation engine that bridges between the non-expert problem domain and the expert mathematical model domain. This framework is argued to have the necessary components to effectively tackle the automation of modelling task of the more intricate MILP problems such as the ATSP.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/20/2021

Knowledge engineering mixed-integer linear programming: constraint typology

In this paper, we investigate the constraint typology of mixed-integer l...
08/28/2014

Mathematical Knowledge Representation: Semantic Models and Formalisms

The paper provides a survey of semantic methods for solution of fundamen...
05/04/2022

BilevelJuMP.jl: Modeling and Solving Bilevel Optimization in Julia

In this paper we present BilevelJuMP, a new Julia package to support bil...
11/20/2020

OAK: Ontology-Based Knowledge Map Model for Digital Agriculture

Nowadays, a huge amount of knowledge has been amassed in digital agricul...
02/10/2010

Dire n'est pas concevoir

The conceptual modelling built from text is rarely an ontology. As a mat...
04/22/2022

Ontology-based system to support industrial system design for aircraft assembly

The development of an aircraft industrial system is a complex process wh...
03/26/2019

Interoperability and machine-to-machine translation model with mappings to machine learning tasks

Modern large-scale automation systems integrate thousands to hundreds of...