Multi-objective optimization of steam system based on GPU acceleration

Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Processing Proceedings, Processing 5th Proceedings, 5th IFAC IFAC Workshop Workshop on on Mining, Mining, Mineral Mineral and and Metal Metal Shanghai, China, August 23-25, 2018 Available online at www.sciencedirect.com Processing Shanghai, China, August 23-25, 2018 Processing Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Shanghai, China, August 23-25, 2018 Shanghai, ProcessingChina, August 23-25, 2018 Shanghai, China, August 23-25, 2018

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IFAC PapersOnLine 51-21 (2018) 183–188

Multi-objective optimization of steam Multi-objective optimization of steam Multi-objective optimization of Multi-objective optimization of steam steam system based on GPU acceleration system based on GPU acceleration Multi-objective optimization of steam system based on GPU acceleration system based on GPU acceleration Liang Zhao, Ye, Wenli system on GPU Liangbased Zhao, Zhencheng Zhencheng Ye,acceleration Wenli Du* Du*

Liang Liang Zhao, Zhao, Zhencheng Zhencheng Ye, Ye, Wenli Wenli Du* Du* Key Laboratory of Advanced Control and Optimization for Chemical Chemical Liang Zhao, Zhencheng Ye, Wenli Du*for Key Laboratory of Advanced Control and Optimization Key Laboratory of Advanced Control and Optimization for Chemical Processes, East China University of Science and Technology, Shanghai Key Laboratory of Advanced Control and Optimization for Chemical Processes, East China University of Science and Technology, Shanghai Processes, East China University of Science and Technology, Shanghai 200237, China (e-mail: [email protected]). Processes, East China University of Science and Technology, Shanghai Key Laboratory of Advanced Control and Optimization for Chemical 200237, China (e-mail: [email protected]). 200237, China (e-mail: [email protected]). 200237, (e-mail: [email protected]). Processes, East ChinaChina University of Science and Technology, Shanghai 200237, an China (e-mail:part [email protected]). Abstract: Abstract: The The steam steam system system is is an important important part of of the the utility utility systems systems in in process process industry. industry. Abstract: The steam system is an important part of the utility utility systems in process processdue industry. The energy consumption and operation cost of the existing plant were increased to Abstract: The steam system is an important part of the systems in industry. The energy consumption and operation cost of the existing plant were increased due to the the The energy consumption and operation cost of the existing plant were increased due to inefficient configuration of the steam system. Meanwhile, the fossil fuels such as coal and oil The energyconfiguration consumption cost of the of existing plant were due to the the Abstract: The steam system issteam an important part the the utility systems in process industry. inefficient ofand the operation system. Meanwhile, fossil fuels increased such as coal and oil inefficient configuration of the steam system. Meanwhile, the fossil fuels such as coal and oil were used to produce steam for the process industry, and the poisonous gases released from the inefficient configuration ofand the steam system. Meanwhile, thepoisonous fossil were fuels such as coal and oil The consumption cost of the and existing plant increased due to the were energy used to produce steam foroperation the process industry, the gases released from were usedprocess to produce steam for the process industry, and gases released from the burning caused a of damage to environments. Therefore, it is great were used to produce steam for the process industry, and the the poisonous gases released from inefficient configuration the system. Meanwhile, thepoisonous fossil fuels as coalpractical and the oil burning process caused aoflot lot of steam damage to the the environments. Therefore, itsuch is of of great practical burning process caused lot of the damage to the the environments. Therefore, it is is of of great practical significance reduce the operation cost pollutant simultaneously. This paper burning caused aa lot of damage environments. Therefore, it great practical were usedprocess toto produce steam for process industry, and emissions the poisonous gases released from the significance to reduce the operation costtoand and pollutant emissions simultaneously. This paper significance to reduce the operation costtoand and pollutant emissions simultaneously. This paper proposes an evolutionary multi-objective optimization (EMOO) algorithm deal with this significance reduce operation cost emissions simultaneously. paper burning causedthe a lot of damage the pollutant environments. Therefore, it is to of great practical proposesprocess an to evolutionary multi-objective optimization (EMOO) algorithm to dealThis with this proposes an evolutionary multi-objective optimization (EMOO) algorithm to deal with this problems. But because of the complexity, higher dimension and rigid constraint conditions of proposes evolutionary multi-objective optimization (EMOO) algorithm to deal withpaper this significance to reduce the operation cost and pollutant emissions simultaneously. This problems.an But because of the complexity, higher dimension and rigid constraint conditions of problems. But because of the complexity, higher dimension and rigid constraint conditions of the process industry, the computation time of EMOO algorithm can not meet the requirements problems. But because of the complexity, higher dimension and rigid constraint conditions of proposes anindustry, evolutionary multi-objective (EMOO)can algorithm with this the process the computation timeoptimization of EMOO algorithm not meetto thedeal requirements the processBut industry, theofcomputation computation time of EMOO EMOO algorithm can notconstraint meetwhich the conditions requirements of optimization. Thus, Graphics Processing Unit (GPU) computing, was the process industry, the time of algorithm not meet the requirements problems. because the complexity, higher dimension andcan rigid of of real-time real-time optimization. Thus, Graphics Processing Unit (GPU) computing, which was running running of real-time optimization. Thus, Graphics Processing Unit (GPU) computing, which was running on the CUDA platform was introduced to shorten the running time of the algorithm. A constraint of optimization. Thus, Graphics Processing (GPU) computing, was running the process industry, the computation time of EMOO algorithm notalgorithm. meetwhich the requirements onreal-time the CUDA platform was introduced to shorten the Unit running timecan of the A constraint on the CUDA CUDA platform was introduced to shorten shorten the running time of the the algorithm. A constraint handling mechanism was presented to the performance of the algorithm. The case study on the platform was introduced to running time of algorithm. A constraint of real-time optimization. Thus, Graphics Processing Unit (GPU) which was running handling mechanism was presented to improve improve thethe performance ofcomputing, the algorithm. The case study handling mechanism was presented to improve the performance of the algorithm. The case study indicates that the proposed GPU-based EMOO algorithm can obtain the Pareto optimal solution handling mechanism was presented to improve the performance of the algorithm. The case study on the CUDA was introduced shorten the running of the Pareto algorithm. A constraint indicates that platform the proposed GPU-basedto EMOO algorithm can time obtain optimal solution indicates that the proposed GPU-based EMOO algorithm can obtain the Pareto optimal solution of the steam system in a minute-level time. indicates thatsystem the proposed GPU-based EMOOthe algorithm can obtain Pareto optimal solution handling mechanism wasa presented to improve performance of thethe algorithm. The case study of the steam in minute-level time. of the steam steam system in aa minute-level minute-level time. of the system in time. indicates that the proposed GPU-based EMOO algorithm can obtain the Pareto optimal solution © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Steam system; Multi-objective of the steam system in a minute-level time.optimization; Keywords: Steam system; Multi-objective optimization; GPU GPU acceleration; acceleration; Constraint Constraint Keywords: Steam Steam system; system; Multi-objective Multi-objective optimization; optimization; GPU GPU acceleration; acceleration; Constraint Constraint processing; Keywords: processing; CUDA. CUDA. processing; CUDA. processing; CUDA.system; Multi-objective optimization; GPU acceleration; Constraint Keywords: Steam 1. INTRODUCTION the processing; CUDA. 1. INTRODUCTION the progress progress is is to to achieve achieve the the optimal optimal system system operation, operation, 1. INTRODUCTION INTRODUCTION the progress is to achieve the system operation, mainly based mathematical modeling, inte1. the progress achieve the optimal optimal systemsystem operation, mainly based ison ontothe the mathematical modeling, system intemainly based on the mathematical modeling, system integration and other methods, Aguilar et al. (2007). Energy is the basis of human development, so every mainly based on the mathematical modeling, system inte1. INTRODUCTION the progress is to achieve the optimal system operation, gration and other methods, Aguilar et al. (2007). Energy is the basis of human development, so every gration and other methods, Aguilar et al. (2007). Energy is the basis of human development, so every change of energy use is accompanied by tremendous social gration and other methods, Aguilargetting et al. (2007). based on the mathematical modeling, system inteEnergy the basis human development, so social every mainly With the environmental problems more and more change ofisenergy use isof accompanied by tremendous With the environmental problems more and more change ofisAs energy use is isof accompanied by steam tremendous social progress. an efficient clean has wide and other methods, Aguilargetting etpollutant al. (2007). change of energy use accompanied by tremendous With the environmental problems getting more and more Energy the humanenergy, development, every serious in the world, the influence of discharge progress. As an basis efficient clean energy, steam hassoaasocial wide gration With the more and more in environmental the world, theproblems influencegetting of pollutant discharge progress. As an efficient efficient clean industries. energy, steam has aayears, wide serious range in process In progress. As an clean energy, has wide serious in the world, the influence of discharge change energy use is by steam tremendous social has attracted more interests in steam system range of ofofapplications applications in accompanied process industries. In recent recent years, serious in environmental the more world,and theproblems influence of pollutant pollutant discharge With the getting and more has attracted more and more interests inmore steam system range of applications in process industries. In recent years, with the trend of large-scale chemical plants development range of applications in process industries. In development recent attracted more and more interests in steam system progress. As anofefficient clean energy,plants steam has ayears, wide has optimization, et al. (2012); Oliveira and with the trend large-scale chemical has attracted more interests in Francisco steam system serious in the Luo world, the influence of pollutant discharge optimization, Luo etand al. more (2012); Oliveira Francisco and with the trend of large-scale chemical plants development in China, the energy consumption has become one of with the trend large-scale chemical plants optimization, Luo et al. (2012); Oliveira Francisco and range of applications in consumption process industries. In development recentone years, (2004). Incorporating environmental factors into in China, the of energy has become of Matos optimization, Luo et al. (2012); Oliveira Francisco and has attracted more and more interests in steam system Matos (2004). Incorporating environmental factors into in China, the energy consumption has become one of the important operational indexes, Li et al. (2014). Most in the operational energy consumption become one of the Matos (2004). Incorporating environmental factors into with the trend of large-scale chemical plants development optimization objectives has become a new area of theChina, important indexes, Lihas et al. (2014). Most Matos (2004). Incorporating environmental factors into optimization, Luo et al. (2012); Oliveira Francisco and the optimization objectives has become a new area of the important operational indexes, Li et al. (2014). Most of fuels consumed in the production process the important operational Lihas et al. (2014). Most the optimization objectives has become a new area of in China, energy consumption become one of steam system optimization, Wu et al. (2016). In chemof the the fuelsthe consumed in indexes, the steam steam production process the optimization objectives Wu has become a new of Matos (2004). optimization, Incorporating environmental factors into steam system et al. (2016). Inarea chemof the fuels consumed in the steam production process will discharge a large amount of polluting gas from the of fuels consumed in indexes, the steam process steam system optimization, Wu et al. (2016). In chemthe important Li production et al. gas (2014). Most process, the optimization variables are constrained willthe discharge aoperational large amount of polluting from the ical steam system optimization, Wu et al. (2016). In chemthe optimization objectives has become a new area of ical process, the optimization variables are constrained will discharge a large amount of polluting gas from the untreated fossil fuels, Luo et al. (2012). The energy saving will discharge afuels, largeLuo amount of polluting gas from the by ical process, the optimization variables are constrained of the fuels consumed in etthe production process various conditions. Compared with the feasible region untreated fossil al. steam (2012). The energy saving ical process, the optimization variables are constrained steam system optimization, Wu et al. (2016). In chemby various conditions. Compared with the feasible region untreated fossilafuels, fuels, Luo et al. al. (2012). Theaenergy energy saving and protection have become new research untreated fossil Luo et (2012). The saving by various conditions. Compared with the feasible region will discharge large amount of polluting the of decision the of the multiand environmental environmental protection have become a gas newfrom research by various conditions. Compared withspace theare feasible ical process, thevariables, optimization variables of the the decision variables, the vector vector space ofconstrained the region multiand environmental protection have become a new research focus for the steam system as an energy supply. and environmental protection have become a new research of the decision variables, the vector space of the multiuntreated fossil fuels,system Luo etasal.an(2012). energy saving of objective feasible solution of the steam system is often very focus for the steam energyThe supply. the decision variables, the vector space of the multiby variousfeasible conditions. Compared withsystem the feasible region objective solution of the steam is often very focus for the steam system as an energy supply. focus for the steam system as an energy supply. objective feasible solution of the steam system is often very and environmental protection have become a neware research small, which makes the optimization problem hard to be The researches of the steam system optimization mainobjective feasible solution of the steam system is often very of the decision variables, the vector space of the multismall, which makes the optimization problem hard to be The researches of the steam system optimization are mainsmall, which makes the optimization problem hard to be focus for the steam system as an energy supply. solved, Gao et al. (2008). Moreover, the high-dimension of The researches of the steam system optimization are mainly in the following three aspects. First, from the viewsmall, which makes the optimization problem hard to be objective feasible solution of the steam system is often very solved, Gao et al. (2008). Moreover, the high-dimension of The researches of the steam system optimization are mainly in the following three aspects. First, from the view- the solved, Gao et al. (2008). Moreover, the high-dimension of variables and optimization mechanism of evolutionary ly in the following three aspects. First, from the viewpoint of research contents, the progress is divided into solved, Gao etand al. optimization (2008). Moreover, the high-dimension of which makes the optimization problem hard to be the variables mechanism of evolutionary ly inresearches the following three First, from the viewThe of the steamaspects. system optimization are mainpoint of research contents, the progress is divided into small, the variables and optimization mechanism of evolutionary multi-objective optimization (EMOO) algorithm also inpoint of research contents, the progress is divided into parameters optimization, Varbanov et al. (2004), structure the variables and optimization mechanism of evolutionary Gao et al. (2008). Moreover, the algorithm high-dimension of multi-objective optimization (EMOO) also inpoint of research contents, the progress is divided into solved, ly in the following threeVarbanov aspects. First, from the viewparameters optimization, et al. (2004), structure multi-objective (EMOO) algorithm also increase the cost, Deb (2002). So, parameters optimization, Varbanov et al. al. (2004), (2004), structure optimization, Papoulias and Grossmann (1983) and commulti-objective optimization algorithm alsohow invariables andoptimization optimization mechanism of evolutionary crease the computational computational cost,(EMOO) Deb et et al. al. (2002). So, how parameters optimization, Varbanov et structure point of research contents, the progress is divided into the optimization, Papoulias and Grossmann (1983) and comcrease the computational cost, Deb (2002). So, with the constraints properly and accelerate the optimization, Papoulias and Grossmann (1983) and com- to bined with both parameters and crease computational cost,(EMOO) Deb et et al. al. (2002). So, how multi-objective algorithm alsohow into deal dealthe with theoptimization constraints properly and accelerate the optimization, Papoulias (1983) and comparameters optimization, Varbanov et al. (2004), structure bined optimization optimization withand bothGrossmann parameters and structure, structure, to deal with the constraints properly and accelerate the solution process has to be settled urgently in the multibined optimization with both parameters and structure, Chen and Lin (2011). Second, from the viewpoint of optito dealthe with the has constraints properly and(2002). accelerate the computational Deburgently et al. how solution process to becost, settled in theSo, multibined optimization with bothGrossmann parameters and structure, optimization, and (1983) and Chen and Lin Papoulias (2011). Second, from the viewpoint of comopti- crease process to be urgently in objective optimization of system. Chen and Lin (2011). (2011). Second, from the viewpoint of optiopti- solution mization operation, the progress is develop optimal solution process has toprocess be settled settled urgently in the the multimultito deal with the has constraints properly and accelerate the objective optimization process of steam steam system. Chen and Lin Second, the viewpoint of bined optimization with both from parameters andthe structure, mization operation, the progress is to to develop the optimal objective optimization process of steam system. mization operation, the progress is to develop the optimal operation strategies, mainly for the overall optimization objective optimization process of steam system. solution process has to be settled urgently in the multimization the progress is to develop the optimal Chen andoperation, Lin (2011). Second, from the viewpoint of opti- In this paper, based on the process mechanism and process operation strategies, mainly for the overall optimization In this paper, based on the process mechanism and process operation strategies, mainly for is the overall optimization objectives, according to the relationship among optimization process of steam system. operation strategies, mainly for the optimization In this based on mechanism and mization operation, to overall develop the optimal information, non-linear model of steam objectives, accordingthe to progress the coupling coupling relationship among objective In this paper, paper, the based on the the process process and process process information, the non-linear modelmechanism of extraction extraction steam objectives, according to the coupling relationship among various parts of the system, Li et al. (2015); Micheletto objectives, according to the coupling relationship among turbine information, the non-linear model of extraction steam operation strategies, mainly for theal.overall is developed. Then, the operational cost model various parts of the system, Li et (2015);optimization Micheletto information, the non-linear model of extraction steam In this paper, based on the process mechanism and process turbine is developed. Then, the operational cost model various parts of the system, Li et al. (2015); Micheletto et al. (2008). Finally, from the aspect of energy analysis, various parts of the system, Li aspect et al. relationship (2015); Micheletto turbine is developed. Then, the operational cost model objectives, according to thethe coupling among of steam system has been developed by incorporating the et al. (2008). Finally, from of energy analysis, turbine is developed. Then, the operational cost model information, the non-linear model of extraction steam of steam system has been developed by incorporating the et al. al. (2008). (2008). Finally, from the the aspect of energy analysis, consumption et from energy analysis, of steam system has been developed by incorporating the various parts Finally, of the system, Li aspect et al. of (2015); Micheletto of coal and natural gas, as well as running or of steamissystem has and been developed by incorporating the turbine developed. Then, thegas, operational cost model consumption of coal natural as well as running or ⋆ This work was supported by Natural Science Foundation of China ⋆ This consumption of coal and natural gas, as well as running or et al. (2008). the aspect energy analysis, standby of the motors and steam turbines. Considering the work wasFinally, supportedfrom by Natural ScienceofFoundation of China consumption of coal and natural gas, as well as running of steam system has been developed by incorporating the ⋆ standby of the motors and steam turbines. Considering or (No. 61590923,61703163, 61503138,61403141) and the Programme This work was supported by Natural Science Foundation of China ⋆ standby of the motors and steam turbines. Considering (No. 61590923,61703163, the Programme This work was supported61503138,61403141) by Natural Science and Foundation of China treatment of various pollutants, the emission model for the standby of of the andnatural steamthe turbines. Considering consumption ofmotors coal and gas,emission as well as running or treatment various pollutants, model for the of Introducing Talents of Discipline to Universities 111 Project) (No. 61590923,61703163, 61503138,61403141) and(the the Programme ⋆ of This Introducing Talents of Discipline to Universities (the Project) (No. 61590923,61703163, 61503138,61403141) the 111 Programme treatment of various pollutants, the emission model for the work was supported by Natural Science and Foundation of China actual consumption of fossil fuels of SO NO CO 2 ,, Considering x and 2 ,, treatment of various pollutants, the emission model for the standby of the motors and steam turbines. under Grant B17017. actual consumption of fossil fuels of SO NO and CO of Introducing Talents of Discipline to Universities (the 111 Project) 2 x 2 under Grant B17017. of Introducing Talents of Discipline to Universities Project) (No. 61590923,61703163, 61503138,61403141) and(the the 111 Programme actual consumption of fossil fuels of SO , NO and CO 2 x 2 ,, under Grant B17017. actual consumption of fossil fuels of SO , NO and CO treatment of various pollutants, the emission model for the 2 x 2 under Grant B17017. of Introducing Talents of Discipline to Universities (the 111 Project) actual consumption of fossil fuels of SO , NO and CO 2 x 2, Copyright © 2018 IFAC 183 under Grant B17017. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 183Hosting by Elsevier Ltd. All rights reserved. Copyright 2018 IFAC 183 Peer review© of International Federation of Automatic Copyright ©under 2018 responsibility IFAC 183Control. 10.1016/j.ifacol.2018.09.415 Copyright © 2018 IFAC 183

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2.2 The environmental impact and operation cost models 



     

 

The steam system mainly consumes coal and natural gas to produce SS. The price of coal is relatively cheap, but the combustion process will produce more polluted environment of SO2 , NOx , CO2 and other harmful gases, Resnik et al. (2004). The price of natural gas is higher, but the combustion process will produce less harmful gases.









 







   

Fig. 1. The general structure of steam system. which are the main pollutants, is established based on the thermodynamic principles. The environmental impact model for steam system is developed to eliminate the fossil fuels with the two objectives of economic benefits and environmental protection. The EMOO algorithm is used to optimize the operating cost and environmental impact models. An improved strategy is proposed to improve the convergence rate of the proposed algorithm. The GPUbased parallel computation framework is introduced to accelerate the optimization process to satisfy the industrial needs. Finally, the validity and necessity of multi-objective optimization of steam system are verified by a real-world case study. The remainder of this paper is organized as follows: Section 2 describes the multi-objective models of steam system. The EMOO algorithm and GPU acceleration strategy are provided in Section 3. Section 4 presents the case study from the ethylene plant and conclusions are drawn in section 5.

In this paper, considering the total consumption of SS, the consumption of fuel and the emissions of harmful gases can be calculated by using thermodynamic and chemical equations. Depending on the impact of different polluting gases on the environment, various pollutants are weighted. In the optimization design of emission reduction of the steam system, there are two mature emission reduction technologies employed to treat SO2 and NOx : wet flue gas desulfurization and catalytic reduction denitrification. Finally, the pollutant emission model with reducing treatment is established by combining with the consumptions of natural gas and coal. The operating cost model includes the cost of steam, electricity and pollution treatment. The decision variables of the optimization models include the extraction steam flow rates of steam turbine, the consumptionss of coal and natural gas, as well as the binary variables that denote running or standby of motors and steam turbine. Environmental impact model. The impact factors of different pollutants such as SO2 , NOx , CO2 are given in Tab.1. Table 1. Potency factors of different pollutants.

CO2 SO2 NOx

Atmospheric acidification 1 0.7

Global warming 1 40

Photochemical ozone formation 0.048 0.028

The environmental impact model is shown as Equ.1. f1 = 1 × mCO2 + 1.048 × mSO2 + 40.728 × mN Ox , (1) where mCO2 ,mSO2 , and mN Ox are the emissions of CO2 , SO2 and NOx respectively.

2. MULTI-OBJECTIVE MODELS OF STEAM SYSTEM 2.1 Overview of steam system Steam system of industrial process usually consists of steam production, transportation, monitoring, control, consumption and the other components. The main approaches of energy optimization for steam system are reducing the consumption of steam in the transmission and consumption processes, Li et al. (2014, 2015). The loss in the transmission process is related to heat preservation and pressure drop, which can only be realized by improving the performance of pipelines and devices. Therefore, this paper focuses on the optimization in the steam consumption process. The general structure of the steam system of petrochemical plant is shown in Fig. 1, which contains four steam grades: Super-high-pressure Steam (SS), High-pressure Steam (HS), Medium-pressure Steam (MS), and Lowpressure Steam (LS). There are five kinds of devices: boilers, compressor turbines, heat exchangers, pump turbines and let-down station. 184

Operational cost model. The operational cost model is given in Equ.2. f2 = Pf uel × mf uel + Pe × E + Pnh3 × mnh3 , (2) where Pf uel , Pe , and Pnh3 are the prices of fuel, electricity, the absorbent of desulfurization and denitrification respectively. mf uel , E, and mnh3 are the consumptions of the three material. The calculation process of the related parameters for the environmental impacts and operating cost models are listed as follows. • Fuel consumption. All grades of steam are directly or indirectly derived from SS, which produces by fuel combustion. Equ.3 indicates that the energy in steam system is generated from the combustion of fuel. mgas × Qgas × δ1 + mcoal × Qcoal × δ2 n ∑ (3) = mss i × (Hss − Hbf w ), i=1

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•

•

•

•

•

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where mgas is the consumption of natural gas , Qgas is the calorific value of natural gas, δ1 is the efficiency of the gas boiler, mcoal is the consumption of coal, Qcoal is∑ the calorific value of coal, δ2 the efficiency of n boiler, i=1 mss i is the requirement of SS, Hss and Hbf w are the enthalpy of SS boiler feed water. NOx emission model. In the optimization design, the NOx is mixed with a certain concentration of ammonia. After catalytic reduction, the NOx is converted to N2 which do no harm to the environment, Forzatti et al. (2010). Equ.4 is the emission model of NOx . mN Ox = 1.63×mcoal ×(Nar ×β1 +0.000938)×(1−µN ), (4) where Nar is the N content in coal, β1 is the ratio of N converting to NOx in the combustion process, and µN is the efficiency of NOx removal. SO2 emission model. In the wet flue gas desulfurization technology, SO2 is mixed with the desulfurizer CaCO3 to generate non-polluting substances CaSO4 and CO2 . Equ. 5 gives the emission model of SO2 . (5) mSO2 = 1.6 × mcoal × Sbn × (1 − µS ), where Sbn is sulfur content in coal, and µS is the sulfur removal efficiency of wet desulfurization. CO2 emission model. CO2 is derived from fuel combustion and wet desulfurization reactions. Equ.6 presents the emission model of CO2 . mCO2 = 3.667 × mcoal × Ccoal + 2.75 × mgas (6) ×Cgas + 0.44 × mCaCO3 × CCaCO3 , where Ccoal and Cgas are carbon contents in the coal and natural gas, mCaCo3 is the consumption of desulfurizer, and CCaCo3 is the concentration of desulfurizer. Denitration agent consumption model. In the pollution discharge process, the denitrfying agent is the ammonia with a certain concentration, and its consumption model is given in Equ.7. mN H3 = mN OX × (µN ÷ (1 − µN ))× (7) (0.567 × γ1 + 0.739 × γ2 ) ÷ CN H3 , where mN H3 is the mass of denitration agent, γ1 is the proportion of NO in the exhaust gas, γ2 is the proportion of NO2 in the exhaust gas, and CN H3 is the concentration of denitrification agent. Desulfurization agent consumption model. In the pollution discharge process, the desulfurization agent is MCaCO3 , and its consumption model is given in Equ.8. Ca µS , (8) × mCaCO3 = 1.5625 × mSO2 × 1 − µS S where mCaCO3 is the mass of desulfurization agent, and Ca S is the molar ratio of calcium and sulfur.

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• Energy balance constraints The mechanical powers generated by steam turbines should satisfy the demands of the process. Equs. 10 and 11 represent the energy constraints of a steam turbine. Wt = mss × (Hss − Hhs ) + (mss − mhs ) × (Hhs − Hsc ) (10) (11) Wt ≥ Wtd where mss and mhs are the initial mass flows of inlet steam and extracted steam, Hss , Hhs and Hsc are the enthalpy of inlet, extracted and exhausted steam respectively, and Wtd is the desired shaft power of the compressor. • Mass balance constraints For each steam grade, the total steam or electricity supply must be greater than or equal to the demands of the process. The mass balance constraint is shown as Equ. 12. n1 n2 ∑ ∑ mi + ej ≥ E d (12) ∑n1

i=1

j=1

∑n2

where i=1 mi and j=1 ej are the sum of steam and electricity produced from each steam grade. E d is the energy demand. 3. GPU-BASED EVOLUTIONARY MULTI-OBJECTIVE ALGORITHM

3.1 Multi-objective evolutionary algorithm The multi-objective optimization problem (MOP) is fundamentally different from the single-objective optimization problem. MOP has no unique solution, but rather performs a trade-off among all the objectives, and finally finds a set of compromise optimization solutions, Miettinen (2012). EMOO is one of the methods to solve MOP, Coello (2006). Non-dominated sorting genetic algorithm-II (NSGA-II) has been used widely to test the performance of new EMOO algorithms. The implement process of NSGA-II is described as follows, Deb et al. (2002). Firstly, a population P with size N is randomly initialized in the feasible region of the decision variables, and then the genetic operation such as selection, crossover and mutation are performed on the population P to generate a new population R. Then, the individuals in set P ∪ R are sorted by the non-dominated method, and each dominating front is sorted according to the crowd distance. The first N individuals after non-dominated sorting are selected as the new population. Finally, the termination criterion is determined. If it is met, the evolution process is ended, else the evolution process is continued. 3.2 Improvement of Constraint Processing Mechanism for EMOO algorithm

2.3 The constraints of steam system model The steam system model includes three kinds of constraints: device capacity constraints, energy balance constraints and mass balance constraints. • Device capacity constraints. For each device, the mass flow rates of steam are limited to a certain bound as given in Equ. 9. mlb ≤ m ≤ mup (9) 185

Most EMOO algorithms can achieve good results when solving unconstrained MOO problems. However, there are always constraints on the engineering optimization problems. Therefore, the constraint processing methods are directly related to the solution of optimization, especially when the feasible region of the decision variable is small and irregular, Michalewicz (1995). In the early years of

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constraint evolutionary algorithm, the constraint-handing methods include penalty functions, decoders, special operators, separation of objective function and constraints, Coello (2002). The use of multi-objective concepts has been considered as a separate category in evolutionary computation community because it is widely used in recent years. The constraint-handing approaches of EMOO can be summarized as feasibility rules, stochastic ranking, εconstrained method, novel penalty functions, novel special operators, multi-objective concepts, and ensemble of constraint-handling techniques, Mezura-Montes and Coello (2011). In the absence of the initial feasible solution, simply dividing the individuals into feasible solutions and infeasible solutions will lead to more difficulties in finding the solution and reduce the reduction the applicability of the algorithms. In this paper, based on the non-domination sorting and the selection mechanism of crowding distance in NSGA-II, the individuals in evolutionary algorithms are divided into feasible solution, 1 degree infeasible solution, 2 degree infeasible solution, · · · , as well as n degree infeasible solution for EMOO with n constraints. The performing process of the proposed method is given as follows. (1) Generate population P with size N within the feasible region of decision variables randomly. (2) Calculate the number i that does not satisfy the constraint conditions for N decision variables, and divide the individuals into different degrees of infeasible solutions according to i. For example, if i equals to 0, it means the solution is feasible; if i equals to 1, it means the individual is 1 degree infeasible solution. When the value of i is higher, the degree of the solution approaching to the feasible region is lower. (3) Evolve the individuals with different feasible degrees by NSGA-II. (4) Sort the individuals according to three priorities such as infeasible degree, non-dominated relations and crowded distance. Select the first N individuals as the population of the next generation. (5) Determine whether the termination conditions is satisfied. If not, jump to step 2. The following test function is employed to verify the effectiveness of the improved algorithm.

minf1 (X) = 18(x0.6 1 + x2 + x3 + x4 ) + 3.6x9 + 670y1 0.25 minf2 (X) = 420(x0.5 + x3 + x0.125 ) − 1.2x0.3 1 + x2 4 9 s.t. g1 = |0.806x5 − x1 | − 1 ≤ 0 g2 = |0.801x6 − x2 | − 1 ≤ 0 g3 = |0.6671x7 − x3 | − 1 ≤ 0 g4 = |0.6718x8 − x4 | − 1 ≤ 0 180 ≤ x1 , x2 ≤ 250 70 ≤ x3 ≤ 90, 60 ≤ x4 ≤ 90 180 ≤ x5 , x6 ≤ 210 50 ≤ x7 ≤ 70, 30 ≤ x8 ≤ 50 0 ≤ x9 ≤ 105 y1 ∈ {0, 1} (13) 186

In the experiment, the crossover probability is set as 0.6, the probability of mutation is set as 0.1, and the population size is set as 2000. The experimental results of 20 times running are shown in Tab. 2, and the optimized Pareto curve is given in Fig.2. 10 4

4.398

4.3975

4.397

4.3965

f2

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4.396

4.3955

4.395

4.3945

0

0.5

1

1.5

2

f1

2.5 10 5

Fig. 2. The Pareto curve of the test function. Table 2. The comparisons of the test function. Method Penalty function Proposed method

Number of generations for the obtained feasible solutions No feasible solution in 2000 generation [200 300]

It can be seen that the improved constraint processing mechanism is better than the penalty function method. 3.3 GPU-based multi-objective evolutionary algorithm The non-dominated sorting mechanism and crowding distance calculation in EMOO result in the large complexity of the algorithm. The long solution time can not meet the real-time requirements of online optimization. The GPU acceleration mechanism is introduced to realize the parallel solution of EMOO, Fabris and Krohling (2012); Zhao et al. (2017).The GPU consists of a number of transistors, which are used primarily for data computation, Zhao et al. (2017). Compared with the traditional data processing flow of the central processing unit (CPU), its multi-thread structure makes the calculation speed improve greatly. The efficiency of the algorithm has been greatly improved to solve different problems, which makes the optimization algorithms more practical. Compute Unified Device Architecture (CUDA) uses a single-instruction-multiple-thread model. The GPU-CUDA parallel programming model is shown in Fig.3. For the test function in Equ. 13, the calculation platform configuration is given as follows: Intel (R) Core (TM) i33110M CPU @ 2.40GH, NVIDIA GeForce 610M GPU, 6 Gb memory. The CPU-based and GPU-based algorithms are running for 10 times. The average running time of CPU-based and GPU-based algorithms are 4218.8 and 210.6 seconds. The CPU-based EMOO algorithm is accelerated obviously.

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187

The parameters in Equations 14 and 15 are given in Sec. 2.2 . In the proposed steam system of an ethylene plant, the optimization variables include extraction steam flow rates of 4 steam turbines and 8 binary variables for running or standby of steam turbines or motors. For a special condition, the parameters of the extraction steam turbine are shown in Tab. 3. The steam flow rates of pump turbines and powers of the motors are listed in Tab. 4. Table 3. Model parameters of the turbines. GT1 GT2 GT3 GT4

a 0.80627 0.80097 0.66716 0.67182

b 3.8021 3.5078 3.7236 3.5018

Powers(kw) 23338.3 24400.7 14327.2 15319.2

Table 4. The rated power of motors and the steam flow rates of pump turbines.

Fig. 3. Parallel programming model of CUDA. 4. CASE STUDY In this paper, the steam system from an ethylene plant is investigated. The operational cost and environmental impact models of steam system are given as follows: minf1 = Pcoal mcoal + Pgas mgas + Pe E + Pnh3 mnh3(14) minf2 = mCO2 + 1.048 × mSO2 + 40.728 × mN Ox .(15) According to the conservation of mass, the flow rate of the production of SS is equal to the flow rate of the consumption of SS. The consumption of SS can be obtained by Equ. 16. fss =

n ∑

mss i .

No. 1 2 3 4 5 6 7 8

Level HS → MS HS → LS HS → LS HS → LS HS → LS HS → LS MS → LS MS → LS

Power(kw) 670 650 1100 1600 370 376 62 61

Steam flow rates (t/h) 8 20 13.4 17.5 8.3 9 3.2 3.2

The computation platform is same as Sec. 3.3. In NSGA-II algorithm, the population size is set as 2048, the iterations number is set as 2000, the crossover probability is set as 0.6, and the mutation probability is set as 0.1. The optimization result is presented in Fig.4. The variables and optimization results before and after optimization are listed in Tab. 5 and Tab. 6 respectively.

(16)

i=1

where, n is the number of extraction steam turbines. The model of extraction steam turbine is given in Equ. 17, Li et al. (2014). mss = a · mext + b · W.

(17)

where, a and b are the model parameters depending on the design and operation condition. mext is the extraction steam flow rate and W is the desired shaft power of the compressor. In the steam system, the consumption of electricity is related to the use of motor, and is given in Equ. 18. E=

M ∑ i=1

δi · ei ,

(18)

where δi is the binary variable and ei is the power of the ith motor. If δi equals to 0, it means the ith motor is not used; if δi equals to 1, it means the ith motor is used. 187

Fig. 4. Pareto curve of steam system optimization. In Tab. 5, x1 -x4 are the inlet steam flow rates (t/h) of the four compressor turbines. x5 -x8 are the extraction steam flow rates. x9 -x16 are the running or standby for the 8 turbine pumps and electric pump. x17 is the natural gas consumption (m3 ) and x18 is the coal consumption (t/h). In this case, the operating cost is reduced by 24 Yuan/h, which is 0.21% lower than the original condition. The environmental impact decreases 1659/h, which is 0.6% less than the original condition. Meanwhile, the solution time of GPU-based and CPU-based algorithms are 197 seconds and 4254 seconds respectively. The Speedup is 21.5. Thus,

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Table 5. The changes of optimization variables. Variables x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18

Before optimization 234.84 241.88 89.89 81.95 181.21 195.12 54.77 42.13 1 0 0 0 0 0 0 0 0 98.56

After optimization 239.35 235.30 87.36 82.56 188.03 187.88 51.79 44.15 1 0 0 0 0 0 0 0 11.91 97.86

Table 6. The optimization results. Before optimization After optimization Variation

Operating cost 11540 11516 -24

Envir. impact 267659 266000 -1659

the solution time of the GPU-based method can satisfy the requirements of real-time optimization. 5. CONCLUSIONS A dual-objective model including operation cost and environmental impact of the steam system are developed in this paper. A constraint processing mechanism of multiobjective evolutionary algorithm is proposed. The GPU and CUDA platform are introduced to accelerate the optimization process. The running time of CPU-based and GPU-based algorithms are compared, and the Speedup is more than 20. The feasibility and effectiveness of the multi-objective optimization model are compared. The optimization results can be used to guide the energy saving, consumption reduction and emission reduction for the industrial plants. REFERENCES Aguilar, O., Perry, S.J., Kim, J.K., and Smith, R. (2007). Design and optimization of flexible utility systems subject to variable conditions. Chemical Engineering Research and Design, 85, 1136–1148. Chen, C.L. and Lin, C.Y. (2011). A flexible structural and operational design of steam systems. Applied Thermal Engineering, 31, 2084–2093. Coello, C.C. (2006). Evolutionary multi-objective optimization: a historical view of the field. IEEE computational intelligence magazine, 1, 28–36. Coello, C.A.C. (2002). Theoretical and numerical constraint handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer methods in applied mechanics and engineering, 191, 1245–1287. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE transactions on evolutionary computation, 6, 182–197. 188

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