Global optimization of large‐scale mixed‐integer linear fractional programming problems: A reformulation‐linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013     

A superstructure‐based mixed‐integer programming approach to optimal design of pipeline network for large‐scale CO2 transport

Pipeline transport is the major means for large‐scale and long‐distance CO₂ transport in a CO₂ capture and sequestration (CCS) project. But optimal design of the pipeline network remains a challenging problem, especially when considering allocation of intermediate sites, like pump stations, and selection of pipeline routes. A superstructure‐based mixed‐integer programming approach for optimal design of the pipeline network, targeting on minimizing the overall cost in a CCS project is presented. A decomposition algorithm to solve the computational difficulty caused by the large size and nonlinear nature of a real‐life design problem is also presented. To illustrate the capability of our models. A real‐life case study in North China, with 45 emissions sources and four storage sinks, is provided. The result shows that our model and decomposition algorithm is a practical and cost‐effective method for pipeline networks design. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2442–2461, 2014     

Tactical capacity planning for semiconductor manufacturing: MILP models and scalable distributed parallel algorithms

A multiperiod stochastic mixed‐integer linear programming model is developed to address the tactical capacity planning of semiconductor manufacturing with considerations of complex routing of material flows, in‐process inventory, demand and capacity variability, multisite production, capacity utilization rate, and downside risk management. Both planning level decisions (i.e., capacity allocation and customer service level decisions) as well as operational level decisions (i.e., production, inventory, and shipment decisions) can be simultaneously determined based on the two proposed multiobjective optimization models. To address the huge number of scenarios needed to characterize the uncertainty and the large number of first‐stage integer variables in industrial scale applications, two novel scalable distributed parallel optimization algorithms are developed to mitigate the computational burden. The proposed mathematical models and algorithms are illustrated through two case studies from a major US semiconductor manufacturer. Results from these case studies provide key decision support for capacity expansion in semiconductor industry. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3930–3946, 2016     

Optimal processing network design under uncertainty for producing fuels and value‐added bioproducts from microalgae: Two‐stage adaptive robust mixed integer fractional programming model and computationally efficient solution algorithm

Fractional metrics, such as return on investment (ROI), are widely used for performance evaluation, but uncertainty in the real market may unfortunately diminish the results that are based on nominal parameters. This article addresses the optimal design of a large‐scale processing network for producing a variety of algae‐based fuels and value‐added bioproducts under uncertainty. We develop by far the most comprehensive processing network with 46,704 alternative processing pathways. Based on the superstructure, a two‐stage adaptive robust mixed integer fractional programming model is proposed to tackle the uncertainty and select the robust optimal processing pathway with the highest ROI. Since the proposed problem cannot be solved directly by any off‐the‐shelf solver, we develop an efficient tailored solution method that integrates a parametric algorithm with a column‐and‐constraint generation algorithm. The resulting robust optimal processing pathway selects biodiesel and poly‐3‐hydroxybutyrate as the final fuel and bioproduct, respectively. © 2016 American Institute of Chemical Engineers AIChE J, 63: 582–600, 2017     

多杂质用水网络最优化设计——水质分析及数学规划法

在多杂质用水系统中,各操作出水水质会以不同杂质为主要因素,难以直接比较水质优劣,本文提出了水质分析与数学规划法相结合的用水网络最优化设计方法,对进出口水的极限数据进行分析得出水质状况并对它们按优劣进行排序,优先将排在前面的、节水效果好的操作作为供水源,在水量足够的情况下,对后面的操作不予考虑,以此来简化用水网络超结构模型,然后利用GAMS软件对经过简化后的超结构进行非线性规划并求解,通过两个例子的分析,证明了本方法的有效性。     

Optimal design and operations of supply chain networks for water management in shale gas production: MILFP model and algorithms for the water‐energy nexus

The optimal design and operations of water supply chain networks for shale gas production is addressed. A mixed‐integer linear fractional programming (MILFP) model is developed with the objective to maximize profit per unit freshwater consumption, such that both economic performance and water‐use efficiency are optimized. The model simultaneously accounts for the design and operational decisions for freshwater source selection, multiple transportation modes, and water management options. Water management options include disposal, commercial centralized wastewater treatment, and onsite treatment (filtration, lime softening, thermal distillation). To globally optimize the resulting MILFP problem efficiently, three tailored solution algorithms are presented: a parametric approach, a reformulation‐linearization method, and a novel Branch‐and‐Bound and Charnes–Cooper transformation method. The proposed models and algorithms are illustrated through two case studies based on Marcellus shale play, in which onsite treatment shows its superiority in improving freshwater conservancy, maintaining a stable water flow, and reducing transportation burden. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1184–1208, 2015     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016