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

Abstract

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

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

“…U is an uncertainty set that characterizes the region of uncertainty realizations. ARO approaches could be applied to address uncertainty in a variety of applications, including process design [99][100][101], process scheduling [102], supply chain optimization [101,103], among others.…”

Resilient supply chain design and operations with decision‐dependent uncertainty using a data‐driven robust optimization approach

“…Next, to overcome the challenge resulting from the fractional objective function, we adopt a parametric algorithm . The static robust mixed‐integer fractional programming problem with decision‐dependent uncertainty set is first transformed into an equivalent auxiliary static robust mixed‐integer linear programming problem with decision‐dependent set, which has the same constraints as the original problem and a new objective function given as the difference between the numerator and the denominator of the original fractional objective function multiplied by a parameter p . The parametric function G ( p ) has such an important property that when G ( p ) = 0, the reformulated problem has a unique optimal solution that is identical to that of the original problem with fractional objective function.…”

Data-driven stochastic robust optimization: General computational framework and algorithm leveraging machine learning for optimization under uncertainty in the big data era

“…To this end, a plethora of mathematical programming techniques, such as stochastic programming and robust optimization [23][24][25], have been proposed for decision making under uncertainty. These techniques have their respective strengths and weaknesses, which lead to different application scopes [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Stochastic programming focuses on the expected performance of a solution by leveraging the scenarios of uncertainty realization and their probability distribution [42][43][44].…”

“…-(21), production level constraint(22), mass balance constraint (23), supply and demand constraints (24)-(25), non-negativity constraints (26)-(27), and integrity constraint(28). A list of indices/sets, parameters and variables is given in Nomenclature, where all the parameters are in lower-case symbols, and all the variables are denoted in upper-case symbols.…”