Optimization of Sustainable Process Systems
Description
Presents a systematic review of optimizing sustainable process systems through multiscale modeling and uncertainty analysis
The global pursuit of net-zero carbon emissions has created an urgent need for chemical engineers and energy researchers to design systems that are both sustainable and resilient. While renewable energy sources such as solar and wind offer great potential, their variability introduces significant challenges that must be addressed through advanced optimization techniques. Optimization of Sustainable Process Systems: Multiscale Models and Uncertainties connects optimization fundamentals with their applications in sustainable energy systems with a particular emphasis on the challenges posed by uncertainty.
Divided into two parts, the book first introduces the core mathematical frameworks and methods needed to model and optimize uncertain systems, including stochastic programming, robust optimization, reinforcement learning, and multiscale algorithms. The authors clearly explain these state-of-the-art tools with attention to both theory and computational practice. The second part shifts to applications, demonstrating how these techniques are applied in real-world contexts such as renewable-based hydrogen, methanol, and ammonia production; carbon capture; shale gas systems; biomass integration; and power system optimization. Throughout the text, the authors emphasize the integration of renewables with chemical industries while highlighting strategies to manage variability, strengthen supply chains, and improve system-wide efficiency.
Combining rigorous fundamentals with cutting-edge applications through a tutorial-style approach, Optimization of Sustainable Process Systems: Multiscale Models and Uncertainties:
- Provides the foundation and tools needed to design resilient, optimized, and sustainable energy systems
- Addresses optimization methods under uncertainty tailored to energy and process systems
- Presents a unified treatment of stochastic programming, robust optimization, and reinforcement learning techniques
- Integrates renewable-based systems with chemical industry supply chain design and operation
- Addresses computational challenges in large-scale optimization of energy systems
Both a theoretical resource and a practical guide for applied problem-solving, Optimization of Sustainable Process Systems: Multiscale Models and Uncertainties is ideal for graduate-level courses in chemical engineering, process systems engineering, energy systems optimization, and operations research. It is also a valuable reference for industrial researchers, system modelers, and developers working on sustainable process design and energy transition strategies.
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CAN LI, PHD, is an Assistant Professor in the Davidson School of Chemical Engineering at Purdue University. His research group focuses on optimization, machine learning, and applications to sustainable process systems. His research has been recognized by the NSF CAREER Award, ACS PRF Doctoral New Investigator Award, and the Amazon Research Award on Sustainability.
Content
List of Contributors xiii
Preface xvii
1 An Introduction to Bilevel Optimization and Its Application to Sustainable Systems Engineering 1
Rishabh Gupta, Jnana S. Jagana, Tushar Rathi, and Qi Zhang
1.1 Introduction 1
1.2 Fundamentals of Bilevel Optimization 2
1.2.1 Mathematical Formulation 2
1.2.1.1 Optimistic Versus Pessimistic Bilevel Optimization 3
1.2.1.2 High-Point Relaxation 4
1.2.1.3 When to Not Use Bilevel Optimization 4
1.2.2 KKT Reformulation 6
1.2.2.1 "Naive" KKT Reformulation 6
1.2.2.2 Mixed-Integer Programming Reformulation 6
1.2.2.3 Branching on Complementarity Constraints 7
1.2.2.4 Penalty-Based Reformulation 8
1.2.3 Value-Function Reformulation 8
1.2.3.1 Reformulation Using the Optimal-Value Function 9
1.2.3.2 Kth-Best Algorithm 9
1.2.3.3 Cutting-Plane Approach 11
1.3 Some Applications in Sustainable Systems Engineering 12
1.4 Bilevel Optimization for Machine Learning 14
1.4.1 Data-Driven Inverse Optimization 14
1.4.2 Hyperparameter Tuning 17
1.4.3 Algorithms for Large-Scale Bilevel Optimization 20
1.4.3.1 Implicit Estimation 21
1.4.3.2 Explicit Estimation 22
1.5 Robust Optimization 25
1.5.1 Mathematical Formulation 26
1.5.1.1 Reformulation 27
1.5.1.2 Cutting-Plane Approach 28
1.5.2 Adjustable Robust Optimization 28
1.5.3 Applications 29
1.5.4 Case Study 30
1.6 Conclusions 33
References 34
2 Exploiting the Multiscale Structure of Sustainable Engineering Problems via Network-Based Decomposition 43
Ilias Mitrai and Prodromos Daoutidis
2.1 Introduction 43
2.2 Learning the Structure of Optimization Problems 45
2.2.1 Optimization Problems as Graphs 45
2.2.2 Learning the Structure via Stochastic Blockmodeling 46
2.3 Network-Based Decomposition of Optimization Problems 48
2.3.1 Benders Decomposition Based on the Variable Graph 48
2.3.2 Lagrangean Decomposition Based on the Structure of the Constraint Graph 50
2.4 Case Study: Transition to Green Ammonia Supply Chain Networks 52
2.4.1 Two-Stage Stochastic Programming Problem Formulation 52
2.4.2 Structure of the Optimization Problem 53
2.4.3 Numerical Results 57
2.5 Conclusions 57
References 58
3 Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs 63
Akshay Kudva, Wei-Ting Tang, and Joel A. Paulson
3.1 Introduction 63
3.2 Problem Formulation 66
3.3 Multi-Objective Bayesian Optimization Over Network Systems 68
3.3.1 Statistical Surrogate Model 69
3.3.2 Multi-Objective Thompson Sampling for Function Networks 70
3.3.3 Practical Considerations in MOBONS 71
3.3.3.1 GP Kernel Selection and Tuning 71
3.3.3.2 Thompson Sampling 73
3.3.3.3 Approximating the Pareto Optimal Set 73
3.3.3.4 Selection Function 74
3.3.4 Handling Parallel Evaluations and Constrained Problems 74
3.4 Case Studies 75
3.4.1 Baseline Methods for Comparison 75
3.4.2 Synthetic Test Problem: ZDT4 Benchmark 76
3.4.3 Design of Sustainable Bioethanol Process 79
3.4.3.1 Process Description and Implementation 79
3.4.3.2 Problem Formulation and Function Network Representation 79
3.4.3.3 Optimization Performance and Hypervolume Analysis 81
3.4.3.4 Local Sensitivity Analysis 82
3.5 Conclusion 84
References 85
4 A Tutorial on Multi-time Scale Optimization Models and Algorithms 91
Asha Ramanujam and Can li
4.1 Introduction 91
4.2 Multi-time Scale Optimization Models 92
4.3 Value of the Multi-scale Model (VMM) 94
4.4 Algorithms to Solve Multi-time Scale Optimization Models 96
4.4.1 Full-Space Methods 96
4.4.2 Decomposition Algorithms 97
4.4.2.1 Bi-level Decomposition 98
4.4.2.2 Dual-Based Decomposition Algorithms 100
4.4.2.3 Limitations of Decomposition Algorithms 113
4.4.3 Metaheuristic Algorithms 113
4.4.4 Matheuristic Algorithms 114
4.4.5 Data-Driven Methods 115
4.4.6 Pamso 117
4.5 Illustrative Example 119
4.5.1 Problem Statement 119
4.5.2 Integrated Model 119
4.5.2.1 Indices and Sets 119
4.5.2.2 Variables 119
4.5.2.3 Parameters 120
4.5.2.4 Constraints 120
4.5.2.5 Objective 120
4.5.2.6 Optimization Model 120
4.5.3 Solving the Problem 121
4.5.3.1 Using Full-Space Method 121
4.5.3.2 Using Benders Decomposition 121
4.5.3.3 Using Lagrangian Decomposition 122
4.5.3.4 Using Dantzig-Wolfe Decomposition 124
4.5.3.5 Using PAMSO 126
4.5.4 Vmm 128
4.6 Conclusion 129
References 129
5 Many Objective Optimization Tools for Sustainable Decision-Making 135
Andrew Allman and Hongxuan Wang
5.1 Introduction 135
5.2 Sustainability Objectives 136
5.3 MOP Solution Methods 138
5.4 Objective Dimensionality Reduction for MaOPs 141
5.5 Case Study: Cost Versus Emissions-Driven Demand Response 144
5.6 Case Study: Analysis of Planetary Boundary Objectives 147
5.7 Conclusion and Future Perspectives 150
References 151
6 Optimization Models and Algorithms for Design and Planning of Sustainable Processes and Energy Systems 155
Seolhee Cho and Ignacio E. Grossmann
6.1 Introduction 155
6.2 Optimization Models 156
6.2.1 Continuous Optimization 157
6.2.2 Discrete Optimization 157
6.2.3 Logic-Based Optimization 158
6.2.4 Optimization Under Uncertainty 159
6.3 Solution Strategies 160
6.3.1 Benders Decomposition 160
6.3.2 Lagrangean Decomposition 161
6.3.3 Bilevel Decomposition 162
6.4 Algebraic Modeling Languages 162
6.5 Applications in Sustainable Process and Energy Systems 164
6.5.1 Hydrogen 164
6.5.2 Biomass 165
6.5.3 Methanol 166
6.5.4 Power Systems 167
6.6 Conclusions 169
References 169
7 Multiscale Modeling and Optimization of Carbon Capture Processes 179
Kyeongjun Seo, Mark A. Stadtherr, and Michael Baldea
7.1 Introduction 179
7.2 Modeling of Carbon Capture Processes 180
7.2.1 Process Structure and Operation 180
7.2.2 Mathematical Modeling 183
7.2.3 Multiscale Optimization 185
7.3 Multiscale Modeling and Optimization Results 187
7.4 Conclusions 193
Acknowledgments 194
Disclaimer 194
References 195
8 Integrated Design and Operability Optimization of Sustainable Process Intensification Systems 199
Yuhe Tian, Rahul Bindlish, and Efstratios N. Pistikopoulos
8.1 Introduction 199
8.2 Methodology Framework 202
8.2.1 Prelude: Phenomena-Based Process Synthesis 202
8.2.2 Generalized Modular Representation Framework 203
8.2.3 Integrated Synthesis and Operability Optimization 205
8.2.3.1 Safety Considerations via Risk Analysis 205
8.2.3.2 Design Under Uncertainty via Flexibility Analysis 208
8.3 Case Studies 210
8.3.1 MMA Purification 210
8.3.1.1 Process Description 210
8.3.1.2 GMF Simulation of Base Case Design 211
8.3.1.3 GMF Synthesis for Grassroots Design 212
8.3.2 MTBE Production 214
8.3.2.1 Process Description 214
8.3.2.2 Integrated GMF Synthesis and Operability Optimization 215
8.4 Concluding Remarks 218
Acknowledgment 218
References 218
9 Circular Economy Assessment Tools for Process Systems 223
Paola Munoz-Briones, Kenneth Martinez, Javiera Vergara-Zambrano, and Styliani Avraamidou
9.1 Introduction 223
9.2 Circular Economy Assessment in the Food Sector 226
9.2.1 Example: CE Assessment for Food Packaging Waste Management Technologies 230
9.3 Circular Economy Assessment in the Chemical Industry 232
9.3.1 Example: Circular Economy Assessment of Viable for Fuels for Mobility 235
9.4 Circular Economy Metrics for Energy Systems 237
References 240
10 Decarbonization of Steam Cracking for Clean Olefins Production: Optimal Microgrid Scheduling 251
Saba Ghasemi Naraghi, Tylee Kareck, Lingyun Xiao, Richard Reed, Paritosh Ramanan, and Zheyu Jiang
10.1 Introduction 251
10.2 Dynamic Optimization of Steam Cracking Process 254
10.3 Scenario-Based Optimal Microgrid Scheduling Problem 258
10.4 Illustrative Case Studies 265
10.4.1 Problem Setting 265
10.4.2 Grid-Connected Mode 267
10.4.3 Islanded Mode 272
10.5 Conclusion 275
Acknowledgments 275
References 276
11 Multiscale Strategies for the Use of Chemicals as Energy Storage Systems 279
Diego Santamaría, Antonio Sánchez, and Mariano Martín
11.1 Introduction 279
11.2 Methodology 279
11.2.1 Process Design 280
11.2.2 Process Scale Up/Down 282
11.2.3 Enterprise-Wide Level 283
11.3 Cases of Study 285
11.3.1 Hydrogen 285
11.3.2 Methane 291
11.3.3 Methanol 295
11.3.4 Ammonia 298
11.4 Conclusions 304
Acknowledgment 304
References 304
12 Repurposing a Conventional Oil Refinery for Biomass Processing to Aviation Fuel: Process Design and Techno-Environmental Evaluation for a Real Operating Plant 317
Valeria González, Alejandro Pedezert, Soledad Gutiérrez, Roberto Kreimerman, Lucia Pittaluga, and Ana I. Torres
12.1 Introduction 317
12.2 Overview of Feed Options, Processing Pathways and Current Infrastructure 319
12.3 Sustainable Aviation Fuel Process Design 321
12.3.1 Base Process Overview 322
12.3.2 Modeling 323
12.3.2.1 Feedstock 323
12.3.2.2 Hydrotreating Reactor (R-100) 323
12.3.2.3 Area 200: Separation 329
12.3.2.4 Area 300: Hydrocracking and Hydroisomerization 331
12.3.2.5 Area 400: Products Separation 331
12.3.3 Simulation Results 331
12.4 Sustainable Aviation Fuel Process Design: Adjustments in Design to Match Current Operations in the Refinery 333
12.4.1 Simulation Results 337
12.5 Environmental Assessment Using GREENSCOPE 337
12.5.1 Overview of Selected Indicators 338
12.5.1.1 Dangerous Materials 338
12.5.1.2 Chemical Exposure Index (CEI) 339
12.5.1.3 Health Hazards in the Workplace 339
12.5.1.4 Safety Hazards 339
12.5.1.5 Substance Toxicity 340
12.5.1.6 Enviromental Hazard 340
12.5.1.7 Indicators from Potency Factors: Global Warming, Smog, Acidification, Ozone Depletion, and Cancer 341
12.5.1.8 Liquid Emissions 341
12.5.2 Results 341
12.6 Summary and Final Remarks 343
Acknowledgments 344
References 344
13 Uncertainty Quantification of Solid Sorbent-Based CO 2 Capture Processes 349
Ana Flávia Monteiro and Debangsu Bhattacharyya
13.1 Introduction 349
13.2 Methodology 352
13.2.1 UQ of Model Parameters 352
13.2.2 UQ of Model Form Discrepancy 354
13.3 Example-UQ of a Solid-Based CO 2 Capture System in a Fixed Bed 356
13.3.1 UQ of the Isotherm Model 356
13.3.2 Uncertainty Propagation 359
13.3.2.1 Lab-Scale Axial Flow-Fixed Bed 360
13.3.2.2 Commercial-Scale Radial Flow-Fixed Bed 361
13.4 Concluding Remarks 363
References 366
Index 371
1
An Introduction to Bilevel Optimization and Its Application to Sustainable Systems Engineering
Rishabh Gupta, Jnana S. Jagana, Tushar Rathi, and Qi Zhang
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA
1.1 Introduction
Bilevel optimization refers to a class of optimization problems that involves a hierarchy of two interdependent decision-making levels. At the upper level, the "leader" makes decisions while anticipating the reaction of the "follower," who solves their own optimization problem at the lower level based on the leader's decisions. The leader's problem can then be formulated as a bilevel optimization problem (also called a bilevel program), which considers the follower's optimization problem in its constraints.
The leader-follower terminology originates from the leader-follower game conceptualized by von Stackelberg [1, 2]. Also known as the Stackelberg game, it is a strategic sequential game in which one player, the leader, makes the first move, followed by the move made by the second player, the follower. The two players are assumed to be noncooperative, that is, they both try to maximize their own utilities. Bracken and McGill [3] were the first to formulate such a Stackelberg game, in their case for a military application, as an optimization problem, which marked the beginning of bilevel optimization.
Many problems can be interpreted as Stackelberg games and hence be modeled as bilevel optimization problems. This is especially true in sustainable systems engineering as these systems often involve conflicts between upper-level policy goals, for example, sustainability and equity, and lower-level goals of individual stakeholders, who typically focus on economic performance. For example, a city government may want to assign tolls to some roads in an effort to reduce traffic, and thereby air pollution, in certain parts of the city [4]. With a toll in place, a driver now has to consider not only the travel time but also the toll amount when choosing their route; here, the driver's route choice will only be different from the case with no tolls if the imposed toll is sufficiently high. In this setting, the city government is the leader and each driver is a follower. To design effective tolls, the city government needs to anticipate the paths the drivers take as a function of the toll amount. Assuming that drivers make their decisions by solving an optimization problem (e.g. the shortest-path problem), the city government's toll design problem can be formulated as a bilevel program.
In this chapter, we provide an introductory overview of bilevel optimization and its applications. In Section 1.2, the fundamentals of bilevel optimization are presented, including its formal mathematical formulation and the most commonly applied solution approaches. Section 1.3 provides a brief overview of common bilevel optimization problems in sustainable systems engineering. In Sections 1.4 and 1.5, we discuss the use of bilevel optimization in machine learning and robust optimization, respectively, two more general areas that have gained significant relevance in sustainable systems engineering. Finally, we close with some concluding remarks in Section 1.6.
1.2 Fundamentals of Bilevel Optimization
In the following, we provide an introduction to the mathematical fundamentals of bilevel optimization. For a more comprehensive and in-depth discussion, we refer the reader to the book by Dempe et al. [5]. For a "gentle" (but perhaps not as gentle as this book chapter) introduction to the topic, we recommend the lecture notes from Beck and Schmidt [6]. Recent review papers on bilevel optimization include Colson et al. [7], Kleinert et al. [8], and Beck et al. [9].
1.2.1 Mathematical Formulation
Let and denote the leader's and the follower's decision variables, respectively. Given the leader's decision , the follower's problem is as follows:
(1.1)where , and the objective function and the constraint functions generally depend on both and . Now let denote the set of optimal solutions to problem (1.1), also referred to as the rational reaction set, that is,
(1.2)Then, the leader's problem, which is the bilevel program, can be formulated as follows:
(1.3)where , and and can similarly be functions of both and . Note that the last constraint forces to be an optimal solution to the follower's optimization problem (1.1), which is what makes problem (1.3) a bilevel program. Acknowledging the given bilevel decision-making hierarchy, problems (1.1) and (1.3) are also referred to as the lower- and upper-level problems, respectively.
1.2.1.1 Optimistic Versus Pessimistic Bilevel Optimization
When is a singleton, that is, the follower's problem has a unique optimal solution given any feasible , there is no ambiguity in the definition of the bilevel optimization problem. If, however, there are multiple optimal solutions to the follower's problem, it is not always clear which one the follower will choose. In that case, the leader needs to make some assumptions in terms of how they expect the follower to react.
One option is to assume that the follower is "leader-friendly," that is, that they will choose among the optimal solutions the one that is best for the leader. This applies if the follower is, for example, a colleague or a friendly neighbor, who still primarily cares about their own objective but is willing to help you out given that it does not negatively affect their own performance. This is the most optimistic assumption from the leader's perspective; hence, the associated bilevel optimization problem is called an optimistic bilevel problem. Indeed, formulation (1.3) does model the optimistic case, where is chosen from such that is minimized.
Another option is to assume that the follower tries to work against the leader by choosing the solution from their rational reaction set that is the least beneficial to the leader. This assumption is more appropriate when the follower is an adversary or competitor. The bilevel optimization problem that considers this worst case for the leader is called a pessimistic bilevel problem and can be formulated as follows:
(1.4)where for a given , is chosen such that is maximized. Implicit in this formulation is the use of the convention that a that violates the constraints leads to a value of of . Alternatively, we apply the following formulation, which explicitly states that the upper-level constraints must be feasible for all :
(1.5)The optimistic and pessimistic bilevel optimization problems represent the two extreme cases; in reality, the solution could also be anywhere in-between, that is, the follower chooses a that satisfies neither of these two assumptions. However, in that case, it is more difficult to clearly define the problem; as a result, the literature mainly considers the optimistic and pessimistic cases. For the remainder of this chapter, we will restrict our discussion to the optimistic bilevel problem, which is the more commonly used one, in part, because it is significantly easier to solve than the pessimistic case.
1.2.1.2 High-Point Relaxation
A straightforward and useful relaxation of the bilevel program (1.3) is the high-point relaxation, which is formulated as follows:
(1.6)where the constraint from the bilevel problem has been replaced with and . This means that in problem (1.6), can be chosen from the set of all feasible instead of only the set of optimal solutions of the lower-level problem; as a result, problem (1.6) is clearly a relaxation of problem (1.3). Importantly, problem (1.6) is a single-level problem and hence much easier to solve than problem (1.3).
1.2.1.3 When to Not Use Bilevel Optimization
There are sometimes problems that have a seemingly bilevel decision-making structure but upon closer inspection, one realizes that their solution does not really require the use of bilevel optimization. In the following, we discuss two such situations.
- The problem does not involve two noncooperative decision-makers. For example, if the two-decision makers are from different parts of the same company but share the same overall business goals, they will be willing to cooperate to achieve the best overall outcome. In that case, instead of a bilevel problem, the problem should be an integrated optimization problem where the decisions of the two decision-makers are optimized jointly, which can be formulated as follows: (1.7) Note that here we assume that the overall objective function is , but it could also be a differently weighted sum of and . An example for such a problem is production planning and scheduling where in practice, the planning and scheduling decisions are often made in a sequential manner, that is, production targets are first determined by solving a long-term planning problem after which short-term scheduling problems are solved to meet these targets. We are often restricted to such a sequential decision-making process due to a stringent hierarchical...
