Grassland: A Rapid Algebraic Modeling System for Million-variable Optimization
Grassland: 백만 변수 최적화를 위한 신속한 대수 모델링 시스템
Grassland: un sistema de modelado algebraico rápido para optimización de millones de variables
Grassland : un système de modélisation algébrique rapide pour une optimisation à millions de variables
Grassland: система быстрого алгебраического моделирования для оптимизации с миллионами переменных
Xihan Li ¹, Xiongwei Han 韩雄威 ², Zhishuo Zhou ³, Mingxuan Yuan ², Jia Zeng ², Jun Wang ¹
¹ University College London, The United Kingdom
² Huawei Noah's Ark Lab 华为 诺亚方舟实验室
³ Fudan University 复旦大学
arXiv, 10 August 2021

An algebraic modeling system (AMS) is a type of mathematical software for optimization problems, which allows users to define symbolic mathematical models in a specific language, instantiate them with given source of data, and solve them with the aid of external solver engines. With the bursting scale of business models and increasing need for timeliness, traditional AMSs are not sufficient to meet the following industry needs: 1) million-variable models need to be instantiated from raw data very efficiently; 2) Strictly feasible solution of million-variable models need to be delivered in a rapid manner to make up-to-date decisions against highly dynamic environments.

Grassland is a rapid AMS that provides an end-to-end solution to tackle these emerged new challenges. It integrates a parallelized instantiation scheme for large-scale linear constraints, and a sequential decomposition method that accelerates model solving exponentially with an acceptable loss of optimality. Extensive benchmarks on both classical models and real enterprise scenario demonstrate 6 ~ 10x speedup of Grassland over state-of-the-art solutions on model instantiation.

Our proposed system has been deployed in the large-scale real production planning scenario of Huawei. With the aid of our decomposition method, Grassland successfully accelerated Huawei's million-variable production planning simulation pipeline from hours to 3 ~ 5 minutes, supporting near-real-time production plan decision making against highly dynamic supply-demand environment.
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