Process to Planet Approach to Sustainable Process Design: Multiple Objectives and Byproducts

While standard life cycle assessment methods exclude fundamental process engineering models in its analysis, sustainable process design (SPD) is plagued by the dilemma of boundary selection that results in consideration of incomplete life cycles and shifting of emissions outside the system boundary. The Process to Planet (P2P) framework bridges this gap by combining sustainable process design with environmentally extended input output analysis. This framework extending across multiple scales provides the capability of working with process variables and designing processes at the equipment scale while considering the entire life cycle through the supply chain and economic scale models. This work expands the P2P framework to account for byproducts originating from any unit within the model. The framework is further modified to incorporate an economic objective function, henceforth developing a multiobjective (MO) optimization problem for optimal design of any generic industrial process. The modified P2P framework is demonstrated by application to a corn ethanol manufacturing process case study. The MO problem is solved using the epsilon constraint method to obtain Pareto optimal frontiers that reveal the trade-off between environmental and economic dimensions of the sustainable process design problem. Comparison between commonly practiced conventional SPD and P2P SPD Pareto curves exposes the chance of choosing non optimal solutions if the former method is employed.     

Sustainable scheduling of batch processes under economic and environmental criteria with MINLP models and algorithms

We address the bi-criterion optimization of batch scheduling problems with economic and environmental concerns. The economic objective is expressed in terms of productivity, which is the profit rate with respect to the makespan. The environmental objective is evaluated by means of environmental impact per functional unit based on the life cycle assessment methodology. The bi-criterion optimization model is solved with the ε-constraint method. Each instance is formulated as a mixed-integer linear fractional program (MILFP), which is a special class of non-convex mixed-integer nonlinear programs. In order to globally optimize the resulting MILFPs effectively, we employ the tailored reformulation-linearization method and Dinkelbach's algorithm. The optimal solutions lead to a Pareto frontier that reveals the tradeoff between productivity and environmental impact per functional unit. To illustrate the application, we present two case studies on the short-term scheduling of multiproduct and multipurpose batch plants.     

Multi-objective optimization of industrial styrene reactor: Adiabatic and pseudo-isothermal operation

Multi-objective differential evolution (MODE) is used to optimize an industrial styrene reactor considering productivity, selectivity and yield as the main objectives. Two reactor configurations (single bed adiabatic operation and steam injected pseudo-isothermal operation) and four combinations of objectives consisting of 5 and 7 variables respectively are considered. Pareto optimal solutions are obtained for all combinations of objective functions for both the configurations. The results are compared with those reported in the literature and an industrial operating point. For all the cases considered, MODE is able to give a Pareto front better (in terms of wider range and a better spread) than that obtained using NSGA for both the configurations. Steam injected reactor configuration is better than the adiabatic reactor configuration in terms of performance. The Pareto optimal solutions obtained from such studies provide a wide range of optimal operating conditions from which an appropriate operating point can be selected based on the requirements of the decision maker.     

Optimization of styrene acrylonitrile random bulk copolymerization reactors

Bulk polymerization of random styrene‐acrylonitrile (SAN) copolymer using AIBN initiator, in nonisothermal batch reactors is optimized using single and multiple objective functions. The objectives are selected from among: minimization of the reaction time, maximization of the overall monomer conversion, and maximization of the number average molecular weight of the product. Constraints are used for the mole fraction of styrene in the copolymer produced (so as to produce copolymer having desired properties), and on the permissible range of temperature in the reactor. Pareto optimal solutions are obtained for some sample 2‐ and 3‐objective optimization problems. The optimization toolbox of MATLAB with genetic algorithm as the solver is used. Different points in the Pareto set are associated with different optimal temperature histories, a few of which are provided. POLYM. ENG. SCI., 55:2377–2387, 2015. © 2015 Society of Plastics Engineers     

A bi‐criterion optimization approach for the design and planning of hydrogen supply chains for vehicle use

In this article, we address the design of hydrogen supply chains for vehicle use with economic and environmental concerns. Given a set of available technologies to produce, store, and deliver hydrogen, the problem consists of determining the optimal design of the production‐distribution network capable of satisfying a predefined hydrogen demand. The design task is formulated as a bi‐criterion mixed‐integer linear programming (MILP) problem, which simultaneously accounts for the minimization of cost and environmental impact. The environmental impact is measured through the contribution to climate change made by the hydrogen network operation. The emissions considered in the analysis are those associated with the entire life cycle of the process, and are quantified according to the principles of Life Cycle Assessment (LCA). To expedite the search of the Pareto solutions of the problem, we introduce a bi‐level algorithm that exploits its specific structure. A case study that addresses the optimal design of the hydrogen infrastructure needed to fulfill the expected hydrogen demand in Great Britain is introduced to illustrate the capabilities of the proposed approach. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with life cycle assessment and input–output analysis

This article addresses the optimal design and planning of cellulosic ethanol supply chains under economic, environmental, and social objectives. The economic objective is measured by the total annualized cost, the environmental objective is measured by the life cycle greenhouse gas emissions, and the social objective is measured by the number of accrued local jobs. A multiobjective mixed‐integer linear programming (mo‐MILP) model is developed that accounts for major characteristics of cellulosic ethanol supply chains, including supply seasonality and geographical diversity, biomass degradation, feedstock density, diverse conversion pathways and byproducts, infrastructure compatibility, demand distribution, regional economy, and government incentives. Aspen Plus models for biorefineries with different feedstocks and conversion pathways are built to provide detailed techno‐economic and emission analysis results for the mo‐MILP model, which simultaneously predicts the optimal network design, facility location, technology selection, capital investment, production planning, inventory control, and logistics management decisions. The mo‐MILP problem is solved with an ε‐constraint method; and the resulting Pareto‐optimal curves reveal the tradeoff between the economic, environmental, and social dimensions of the sustainable biofuel supply chains. The proposed approach is illustrated through two case studies for the state of Illinois. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Optimal planning for the reuse of municipal solid waste considering economic,environmental, and safety objectives

A mathematical programming model is presente for the optimal planning of the reuse of municipal solid waste (MSW) to maximize the economic benefit while simultaneously considering sustainability and safety criteria. The proposed methodology considers several phases of the supply chain including waste separation, distribution to processing facilities, processing to obtain useful products, and distribution of products to consumers. Additionally, the safety criteria are based on the potential fatalities associated with waste management. The proposed optimization model is formulated as a multiobjective optimization problem, which considers three different objectives including the maximization of the net annual profit, the maximization of the amount of reused MSW, and the minimization of the social risk associated with the supply chain. The proposed model is applied to a case study in the central‐west region of Mexico. The results show the tradeoff between the social risk and the economic and environmental criteria. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1881–1899, 2015     

考虑环境影响的间歇过程多目标最优化设计

同时考虑费用和环境影响的间歇化工过程多目标最优化设计问题的求解,通常的做法是使用权重系数法,将其转变成单一目标来优化。但大多数情况下,这种权重系数很难确知。因此,有必要提供多个解以便于设计者作出合理的最终选择。采用多目标遗传算法和线性规划相结合的方法求解出间歇化工过程优化设计模型的非劣解集,并与不同权重系数下的单目标算例进行了比较。结果表明,用多目标遗传算法求解间歇化工过程是有效的。这为设计者在间歇化工过程最优化研究考虑环境因素的决策提供了更多的选择。     

反应器网络多目标综合优化

通过反应系统综合优化获得经济效益好、对环境友好的反应系统是大多化工厂提高全流程整体经济和环境性能的重要手段。反应器网络综合优化方法主要包括可得区法、导数分析法、超结构优化法、目标类法、经验推断法和分布参数法等,然而却很少有文献报道对反应器网络进行多目标综合优化。由于过程中往往存在多个相互冲突的目标函数,所以仅仅依靠单目标对反应器网络进行综合优化已显得不合适。本文采用分布参数法建立多目标优化模型,目标函数为经济最大化和环境影响最小,并采用非支配排序基因算法(NSGA-Ⅱ)进行优化得到Pareto最优解集。     

Optimal design and planning of sustainable chemical supply chains under uncertainty

This article addresses the design of sustainable chemical supply chains in the presence of uncertainty in the life cycle inventory associated with the network operation. The design task is mathematically formulated as a bi‐criterion stochastic mixed‐integer nonlinear program (MINLP) that simultaneously accounts for the maximization of the net present value and the minimization of the environmental impact for a given probability level. The environmental performance is measured through the Eco‐indicator 99, which incorporates the recent advances made in Life Cycle Assessment. The stochastic model is converted into its deterministic equivalent by reformulating the probabilistic constraint required to calculate the environmental impact in the space of uncertain parameters. The resulting deterministic bi‐criterion MINLP problem is further reformulated as a parametric MINLP, which is solved by decomposing it into two sub‐problems and iterating between them. The capabilities of the proposed model and solution procedure are illustrated through two case studies for which the set of Pareto optimal, or efficient solutions that trade‐off environmental impact and profit, are calculated. These solutions provide valuable insights into the design problem and are intended to guide the decision maker towards the adoption of more sustainable design alternatives. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Teaching mathematical modeling software for multiobjective optimization in chemical engineering courses

This paper expects to give undergraduate students some guidelines about how to incorporate environmental considerations in a chemical supply chain and how the introduction of these concerns have an important effect on the results obtained in the multiobjective optimization problem where both economic and environmental aspects are considered simultaneously.To extend the economic and environmental assessment outside the chemical plant and to identify the tradeoffs associated with the reality of chemical and petrochemical industries, a simplified problem of a chemical supply chain is proposed as a case study.The inclusion of environmental concerns to this economic problem make this new case study a good example for undergraduate students interested in implementing simultaneous economic and environmental considerations in the chemical process design incorporating mathematical modeling software for solving this multiobjective problem.Thus, the final objective of this paper is to show to undergraduate students how environmental together with economic considerations could have an important impact in the logistics of a supply chain and how multiobjective optimization could be used to make better decisions in the design of chemical processes including its supply chain.To reach our purpose, the Pareto curve of the supply chain is obtained using the ?-constraint method. In addition, the tradeoffs of this multiobjective optimization have been identified and analyzed and ultimately a good decision based on the set of ‘equivalent’ optimal solutions for this chemical supply chain problem determined.     

Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

A wide range of problems arising from real world applications present multiple and conflicting objectives to be simultaneously optimized. However, this multi-objective nature is too often neglected. Multi-objective optimization proved to be a powerful tool to correctly describe the trade-offs among conflicting objectives in a set of optimal solutions known as the Pareto set. This paper introduces an interactive method to solve multi-objective problems based on geometric considerations. The method returns a wider Pareto set, at a negligible computational cost, when compared to existing methods. The interactivity also allows the decision-maker to explore only relevant parts of the Pareto set. The extreme solutions yield insightful considerations on the generation of the scalarization parameters for the Normal Boundary Intersection and the Enhanced Normalized Normal Constraints methods. The proposed method is applied to: (i) three scalar multi-objective problems and (ii) the multi-objective optimal control of a tubular and a fed-batch reactor.     

多期生物燃料供应链网络建模与多目标优化

建立了一个基于多目标优化以及生命周期评价（LCA）的多期生物燃料供应链模型。该模型的3个目标函数分别为总折现利润、平均单位能量生物燃料的温室气体排放和化石能源投入（economic,energy,environmental,3E）。为了将生物质生产的季节性以及库存等问题引入模型中,需要对每年进行多期划分。考虑到需要进一步引入供应链的扩张,模型的时间跨度设定为3年。此外,该模型还考虑了生物质产地、工厂,生物燃料市场的选址以及各节点间的物流流量等问题。通过将非线性的后两个目标函数利用ε-constraint法转化为线性约束条件,该模型最终被转化为混合整数线性规划（MILP）问题并得以求解。对解得的非劣解在三维坐标系上线性插值可得非劣解所在曲面,它揭示了3E目标之间的权衡取舍关系。还使用了一个基于中国国情的数据的案例对该模型进行检验。     

A LCA Based Biofuel Supply Chain Analysis Framework

This paper presents a life cycle assessment （LCA） based biofuel supply chain （SC） analysis framework which enables the study of economic, energy and environmental （3E） performances by using multi-objective opti-mization. The economic objective is measured by the total annual profit, the energy objective is measured by the average fossil energy （FE） inputs per MJ biofuel and the environmental objective is measured by greenhouse gas （GHG） emissions per MJ biofuel. A multi-objective linear fractional programming （MOLFP） model with multi-conversion pathways is formulated based on the framework and is solved by using theε-constraint method. The MOLFP prob-lem is turned into a mixed integer linear programming （MILP） problem by setting up the total annual profit as the optimization objective and the average FE inputs per MJ biofuel and GHG emissions per MJ biofuel as constraints. In the case study, this model is used to design an experimental biofuel supply chain in China. A set of the weekly Pareto optimal solutions is obtained. Each non-inferior solution indicates the optimal locations and the amount of biomass produced, locations and capacities of conversion factories, locations and amount of biofuel being supplied in final markets and the flow of mass through the supply chain network （SCN）. As the model reveals trade-offs among 3E criteria, we think the framework can be a good support tool of decision for the design of biofuel SC.     

Solving Multi‐objective MILP Problems in Process Synthesis using the Multi‐Criteria Branch and Bound Algorithm

The paper briefly describes the problem of process synthesis in the area of chemical engineering, and suggests its formulation as a Multi‐Objective Programming problem. Process synthesis optimization is usually modeled as Mixed Integer Linear Programming (MILP) or Mixed Integer Non‐Linear Programming (MINLP) with an economic objective function. We claim that incorporating more criteria (e.g., environmental criteria) in this kind of combinatorial optimization problem offers the decision makers the opportunity to refine their final decision by examining more than one solution (a set of efficient or Pareto optimal solutions instead of one optimal solution). For solving the multi‐objective process synthesis problem, an improved version of the Multi‐Criteria Branch and Bound (MCBB) algorithm, which has been developed by the same authors, is used. MCBB is a vector maximization algorithm capable of deriving all efficient points (supported and unsupported), for small and medium sized Multi‐Objective MILP problems. The application of MCBB in two examples from process synthesis is also presented.     

Using NSGA‐II and TOPSIS Methods for Interior Ballistic Optimization Based on One‐Dimensional Two‐Phase Flow Model

In order to meet the design demands of new gun systems or new types of projectiles, the interior ballistic charge design seems especially important. In this paper, a one‐dimensional two‐phase flow model is presented. The model describes the transient combustion of granular propellants in a gun, and pressure waves are considered as an objective. This study adopts a hybrid method to solve the problem. In the first stage, the non‐dominated sorting genetic algorithm (NSGA‐II) with “a “filter” is employed to approximate a set of Pareto‐optimal solutions. In the subsequent stage, a multi‐attribute decision‐making (MADM) approach is adopted to rank these solutions from the best to the worst. The ranking of Pareto‐optimal solutions is based on the technique ordered preference by similarity to ideal solution (TOPSIS) method. In TOPSIS method each objective needs a corresponding weight coefficient, and a practical problem is introduced. Both the entropy method and linear analysis method are adopted to get two sets of weights for the objectives, respectively. The two pairs of final, best compromise solutions are compared for satisfying the designer’s aim. For the analysis of the results, a two‐phase flow interior ballistic model for design optimization is established, and the hybrid approach could get a reasonable design scenario.     

Computer-aided process engineering for environmental efficiency: Industrial drying of biomass

The idea of taking into account environmental impact criteria in the process design becomes a necessity for both the industry and governments, due to increased binding regulations. Moreover, to address the issue of integrating sustainable processes, environmental impact must be weighed and balanced against other concerns, such as economic performance, product quality, and long-term sustainability. Therefore, this study introduces a methodology for environmental impact minimization and optimization of multiple conflicting criteria. A general eco-design method for biomass drying process is proposed. The main target is to develop an assessment computer-aided process engineering tool that compares environmental impacts of different operating conditions and fuel types to support decision-makers for an improved compliance to environmental criterion and sustainability.     

Multiobjective optimization of polymerization reaction of vinyl acetate by genetic algorithm technique with a new replacement criterion

A multiobjective optimization procedure based on genetic algorithm has been developed to determine optimum operational conditions of polymerization reaction. In this article by using a new selection criterion to choose the next generation members with better quality, optimization efficiency is improved and the number of generations to obtain Pareto optimal set reduced. In this proposed method a novel replacement criterion based on ranking level information and proximity of solutions to the Pareto optimal front is used to choose the next generation members. The polymerization of vinyl acetate has been chosen as an example. Two objective functions, which used in this study, are maximization of the weight average molecular weight up to the desired value and minimization of the residual initiator concentration. A Pareto optimal set of objective functions has been obtained by application of a Pareto set filter operator. Furthermore, the influence of genetic algorithm parameters on the efficiency and convergence of genetic algorithm is studied by changing cross over and mutation probabilities. Because of the flexibility and generality of genetic algorithm, this optimization method is a useful technique with lots of potentials in determination of optimum value of operation parameters. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Efficient deterministic multiple objective optimal control of (bio)chemical processes

In practical optimal control problems multiple and conflicting objectives are often present, giving rise to a set of Pareto optimal solutions. Although combining the different objectives into a convex weighted sum and varying the weights is the most common approach to generate the Pareto front (when deterministic optimisation routines are exploited), it suffers from several intrinsic drawbacks. A uniform variation of the weights does not necessarily lead to an even spread on the Pareto front, and points in non-convex parts of the Pareto front cannot be obtained [Das, I., Dennis, J.E., 1997. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optimization 14, 63-69]. Therefore, this paper investigates alternative approaches based on novel methods as normal boundary intersection [Das, I., Dennis, J.E., 1998. Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization 8, 631-657] and normalised normal constraint [Messac, A., Ismail-Yahaya, A., Mattson, C.A., 2003. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 25, 86-98] to mitigate these drawbacks. The resulting multiple objective optimal control procedures are successfully used in (i) the design of a chemical reactor with conflicting conversion and energy costs, and (ii) the control of a bioreactor with a conflict between yield and productivity.