A decision-making framework for the optimal design of renewable energy systems under energy-water-land nexus considerations.

The optimal allocation of land for energy generation is of emergent concern due to an increasing demand for renewable power capacity, land scarcity, and the diminishing supply of water. Therefore, economically, socially and environmentally optimal design of new energy infrastructure systems require the holistic consideration of water, food and land resources. Despite huge efforts on the modeling and optimization of renewable energy systems, studies navigating the multi-faceted and interconnected food-energy-water-land nexus space, identifying opportunities for beneficial improvement, and systematically exploring interactions and trade-offs are still limited. In this work we present the foundations of a systems engineering decision-making framework for the trade-off analysis and optimization of water and land stressed renewable energy systems. The developed framework combines mathematical modeling, optimization, and data analytics to capture the interdependencies of the nexus elements and therefore facilitate informed decision making. The proposed framework has been adopted for a water-stressed region in south-central Texas. The optimal solutions of this case study highlight the significance of geographic factors and resource availability on the transition towards renewable energy generation.

A Neural Network Based Superstructure Optimization Approach to Reverse Osmosis Desalination Plants.

An ever-growing population together with globally depleting water resources pose immense stresses for water supply systems. Desalination technologies can reduce these stresses by generating fresh water from saline water sources. Reverse osmosis (RO), as the industry leading desalination technology, typically involves a complex network of membrane modules that separate unwanted particles from water. The optimal design and operation of these complex RO systems can be computationally expensive. In this work, we present a modeling and optimization strategy for addressing the optimal operation of an industrial-scale RO plant. We employ a feed-forward artificial neural network (ANN) surrogate modeling representation with rectified linear units as activation functions to capture the membrane behavior accurately. Several ANN set-ups and surrogate models are presented and evaluated, based on collected data from the H2Oaks RO desalination plant in South-Central Texas. The developed ANN is then transformed into a mixed-integer linear programming formulation for the purpose of minimizing energy consumption while maximizing water utilization. Trade-offs between the two competing objectives are visualized in a Pareto front, where indirect savings can be uncovered by comparing energy consumption for an array of water recoveries and feed flows.

Data-Driven Optimization of Mixed-integer Bi-level Multi-follower Integrated Planning and Scheduling Problems Under Demand Uncertainty.

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. In this paper, we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

Bi-level Mixed-Integer Data-Driven Optimization of Integrated Planning and Scheduling Problems.

Supply chain management is an interconnected problem that requires the coordination of various decisions and elements across long-term (i.e., supply chain structure), medium-term (i.e., production planning), and short-term (i.e., production scheduling) operations. Traditionally, decision-making strategies for such problems follow a sequential approach where longer-term decisions are made first and implemented at lower levels, accordingly. However, there are shared variables across different decision layers of the supply chain that are dictating the feasibility and optimality of the overall supply chain performance. Multi-level programming offers a holistic approach that explicitly accounts for this inherent hierarchy and interconnectivity between supply chain elements, however, requires more rigorous solution strategies as they are strongly NP-hard. In this work, we use the DOMINO framework, a data-driven optimization algorithm initially developed to solve single-leader single-follower bi-level mixed-integer optimization problems, and further develop it to address integrated planning and scheduling formulations with multiple follower lower-level problems, which has not received extensive attention in the open literature. By sampling for the production targets over a pre-specified planning horizon, DOMINO deterministically solves the scheduling problem at each planning period per sample, while accounting for the total cost of planning, inventories, and demand satisfaction. This input-output data is then passed onto a data-driven optimizer to recover a guaranteed feasible, near-optimal solution to the integrated planning and scheduling problem. We show the applicability of the proposed approach for the solution of a two-product planning and scheduling case study.

Multiobjective Optimization of Mixed-Integer Linear Programming Problems: A Multiparametric Optimization Approach.

Industrial process systems need to be optimized, simultaneously satisfying financial, quality and safety criteria. To meet all those potentially conflicting optimization objectives, multiobjective optimization formulations can be used to derive optimal trade-off solutions. In this work, we present a framework that provides the exact Pareto front of multiobjective mixed-integer linear optimization problems through multiparametric programming. The original multiobjective optimization program is reformulated through the well-established ϵ-constraint scalarization method, in which the vector of scalarization parameters is treated as a right-hand side uncertainty for the multiparametric program. The algorithmic procedure then derives the optimal solution of the resulting multiparametric mixed-integer linear programming problem as an affine function of the ϵ parameters, which explicitly generates the Pareto front of the multiobjective problem. The solution of a numerical example is analytically presented to exhibit the steps of the approach, while its practicality is shown through a simultaneous process and product design problem case study. Finally, the computational performance is benchmarked with case studies of varying dimensionality with respect to the number of objective functions and decision variables.

A systems engineering framework for the optimization of food supply chains under circular economy considerations.

The current linear "take-make-waste-extractive" model leads to the depletion of natural resources and environmental degradation. Circular Economy (CE) aims to address these impacts by building supply chains that are restorative, regenerative, and environmentally benign. This can be achieved through the re-utilization of products and materials, the extensive usage of renewable energy sources, and ultimately by closing any open material loops. Such a transition towards environmental, economic and social advancements requires analytical tools for quantitative evaluation of the alternative pathways. Here, we present a novel CE system engineering framework and decision-making tool for the modeling and optimization of food supply chains. First, the alternative pathways for the production of the desired product and the valorization of wastes and by-products are identified. Then, a Resource-Task-Network representation that captures all these pathways is utilized, based on which a mixed-integer linear programming model is developed. This approach allows the holistic modeling and optimization of the entire food supply chain, taking into account any of its special characteristics, potential constraints as well as different objectives. Considering that typically CE introduces multiple, often conflicting objectives, we deploy here a multi-objective optimization strategy for trade-off analysis. A representative case study for the supply chain of coffee is discussed, illustrating the steps and the applicability of the framework. Single and multi-objective optimization formulations under five different coffee-product demand scenarios are presented. The production of instant coffee as the only final product is shown to be the least energy and environmental efficient scenario. On the contrary, the production solely of whole beans sets a hypothetical upper bound on the optimal energy and environmental utilization. In both problems presented, the amount of energy generated is significant due to the utilization of waste generated for the production of excess energy.

Integrated Modeling of Transfer Learning and Intelligent Heuristic Optimization for Steam Cracking Process.

The construction and expansion of steam cracking plants and feedstock diversification have resulted in a significant demand for the numerical simulation and optimization of models to achieve molecular refining and intelligent manufacturing. However, the existing models cannot be widely applied in industrial practice because of the high computational expense, time-consumption, and data size requirements. In this paper, a high-performance optimization process, which integrates transfer learning and a heuristic algorithm, is proposed for the optimization of furnaces for various feedstocks. An effective transfer learning structure, based on motif feature of the reaction network, is designed and subsequent product distribution prediction program is compiled. Then a hybrid genetic algorithm and particle swarm optimization method is applied for the coil outlet temperature (COT) curve optimization using the derived prediction model, and the results are obtained for different pricing policies of products. The results are determined based on the weight coefficients of prices for different products, and could be further explained by the yield distribution pattern and reaction mechanism.

DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems.

The Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework is presented for addressing the optimization of bi-level mixed-integer nonlinear programming problems. In this framework, bi-level optimization problems are approximated as single-level optimization problems by collecting samples of the upper-level objective and solving the lower-level problem to global optimality at those sampling points. This process is done through the integration of the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper-level objective, and to consecutively approximate and optimize bi-level mixed-integer nonlinear programming problems that are challenging to solve using exact methods. The performance of DOMINO is assessed through solving numerous bi-level benchmark problems, a land allocation problem in Food-Energy-Water Nexus, and through employing different data-driven optimization methodologies, including both local and global methods. Although this data-driven approach cannot provide a theoretical guarantee to global optimality, we present an algorithmic advancement that can guarantee feasibility to large-scale bi-level optimization problems when the lower-level problem is solved to global optimality at convergence.

A Food-Energy-Water Nexus approach for land use optimization.

Allocation and management of agricultural land is of emergent concern due to land scarcity, diminishing supply of energy and water, and the increasing demand of food globally. To achieve social, economic and environmental goals in a specific agricultural land area, people and society must make decisions subject to the demand and supply of food, energy and water (FEW). Interdependence among these three elements, the Food-Energy-Water Nexus (FEW-N), requires that they be addressed concertedly. Despite global efforts on data, models and techniques, studies navigating the multi-faceted FEW-N space, identifying opportunities for synergistic benefits, and exploring interactions and trade-offs in agricultural land use system are still limited. Taking an experimental station in China as a model system, we present the foundations of a systematic engineering framework and quantitative decision-making tools for the trade-off analysis and optimization of stressed interconnected FEW-N networks. The framework combines data analytics and mixed-integer nonlinear modeling and optimization methods establishing the interdependencies and potentially competing interests among the FEW elements in the system, along with policy, sustainability, and feedback from various stakeholders. A multi-objective optimization strategy is followed for the trade-off analysis empowered by the introduction of composite FEW-N metrics as means to facilitate decision-making and compare alternative process and technological options. We found the framework works effectively to balance multiple objectives and benchmark the competitions for systematic decisions. The optimal solutions tend to promote the food production with reduced consumption of water and energy, and have a robust performance with alternative pathways under different climate scenarios.

A hierarchical Food-Energy-Water Nexus (FEW-N) decision-making approach for Land Use Optimization.

The land use allocation problem is an important issue for a sustainable development. Land use optimization can have a profound influence on the provisions of interconnected elements that strongly rely on the same land resources, such as food, energy, and water. However, a major challenge in land use optimization arises from the multiple stakeholders and their differing, and often conflicting, objectives. Industries, agricultural producers and developers are mainly concerned with profits and costs, while government agents are concerned with a host of economic, environmental and sustainability factors. In this work, we developed a hierarchical FEW-N approach to tackle the problem of land use optimization and facilitate decision making to decrease the competition for resources and significantly contribute to the sustainable development of the land. We formulate the problem as a Stackelberg duopoly game, a sequential game with two players - a leader and a follower (Stackelberg, 2011). The government agents are treated as the leader (with the objective to minimize the competition between the FEW-N), and the agricultural producers and land developers as the followers (with the objective to maximize their profit). This formulation results into a bi-level mixed-integer programming problem that is solved using a novel bi-level optimization algorithm through ARGONAUT. ARGONAUT is a hybrid optimization framework which is tailored to solve high- dimensional constrained grey-box optimization problems via connecting surrogate model identification and deterministic global optimization. Results show that our data-driven approach allows us to provide feasible solutions to complex bi-level problems, which are essentially very difficult to solve deterministically.

Towards a Quantitative Food-Energy-Water Nexus Metric to Facilitate Decision Making in Process Systems: A Case Study on a Dairy Production Plant.

While the importance of the Food-Energy-Water Nexus (FEW-N) has been widely accepted, a holistic approach to facilitate decision making in FEW-N systems, along with a quantitative index assessing the integrated FEW-N performance is rather lacking. In this work, we propose a FEW-N metric along with a framework to facilitate decision making for FEW-N process systems through a FEW-N integrated approach. The framework and metric are illustrated through a case study on a dairy production and processing plant. The dairy industry is a significant user of water and energy, with water being a top issue for most dairy industries and organizations worldwide. Following the framework, we develop a mixed-integer scheduling model, with alternative pathways, that faithfully replicated the major food, energy, and water aspects of a real cottage-cheese production plant. Using the developed FEW-N metric we were able to optimize the cottage-cheese plant process and observe different trade-offs between the FEW-N elements.