论文标题
自动数学建模的知识表示方法
A Knowledge Representation Approach to Automated Mathematical Modelling
论文作者
论文摘要
在本文中,我们提出了一种新的混合企业线性编程(MILP)模型本体论和MILP配方的新约束类型。 MILP是一种常用的数学编程技术,用于建模和解决现实生活中的计划,路由,计划,资源分配以及时间表优化问题,为工业领域提供优化的业务解决方案,例如制造,农业,国防,医疗保健,医疗保健,医学,药物,能源,金融,财务和运输。尽管发现和解决了许多现实生活中的组合优化问题以及尚未发现和制定的数百万美元,但约束类型(MILP的构件)的数量相对较小。在搜索MILP的合适的机器可读的知识表示结构时,我们提出了一个基于MILP模型本体论的优化建模树,可以用作自动化系统的指南,以在其组合业务优化问题上引起最终用户的MILP模型。我们的最终目的是为MILP开发一个可读的机器可读知识表示形式,使我们能够将最终用户对业务优化问题的自然语言描述绘制为MILP正式规范,这是迈向自动化数学建模的第一步。
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.