Cyclic scheduling for an ethylene cracking furnace system using diversity learning teaching-learning-based optimization

Accepted Manuscript Title: Cyclic Scheduling for an Ethylene Cracking Furnace System using Diversity Learning Teaching-learning-based Optimization Author: Kunjie Yu Lyndon While Mark Reynolds Xin Wang Zhenlei Wang PII: DOI: Reference:

S0098-1354(17)30024-8 http://dx.doi.org/doi:10.1016/j.compchemeng.2017.01.024 CACE 5680

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

24-6-2016 16-12-2016 14-1-2017

Please cite this article as: Kunjie Yu, Lyndon While, Mark Reynolds, Xin Wang, Zhenlei Wang, Cyclic Scheduling for an Ethylene Cracking Furnace System using Diversity Learning Teaching-learning-based Optimization, (2017), http://dx.doi.org/10.1016/j.compchemeng.2017.01.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Cyclic Scheduling for an Ethylene Cracking Furnace System using Diversity Learning Teaching-learning-based Optimization Kunjie Yua,b , Lyndon Whileb , Mark Reynoldsb , Xin Wangc , Zhenlei Wanga,∗ a Key

cr

ip t

Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China b School of Computer Science & Software Engineering, The University of Western Australia, WA 6009, Australia c Center of Electrical & Electronic Technology, Shanghai Jiao Tong University, Shanghai 200240, China

us

Abstract

The ethylene cracking furnace system is central to an olefin plant. Multiple cracking furnaces are employed for processing different hydrocarbon feeds to produce various smaller hydrocarbon molecules, such as ethylene, propylene,

an

and butadiene. We develop a new cyclic scheduling model for a cracking furnace system, with consideration of different feeds, multiple cracking furnaces, differing product prices, decoking costs, and other more practical constraints. To obtain an efficient scheduling strategy and the optimal operational conditions for the best economic performance of

M

the cracking furnace system, a diversity learning teaching-learning-based optimization (DLTLBO) algorithm is used to simultaneously determine the optimal assignment of multiple feeds to different furnaces, the batch processing time and sequence, and the optimal operational conditions for each batch. The performance of the proposed scheduling

ed

model and the DLTLBO algorithm is illustrated through a case study from a real-world ethylene plant: experiments show that the new algorithm out-performs both previous studies of this set-up, and the basic TLBO algorithm.

Ac ce

1. Introduction

pt

Keywords: Ethylene cracking furnace; Cyclic scheduling; Teaching-learning-based optimization

Ethylene is the most widely-produced organic compound in the world; it is extremely important for the chemical industries and for daily life. Multiple cracking furnaces are employed in industrial ethylene production, to convert various hydrocarbon feeds to smaller hydrocarbon molecules through complex pyrolysis reactions, resulting mostly in ethylene and propylene. The cracked gas is sequentially sent to quenching, compression, chilling, and separating sections to recover the various products. The operating performance of the cracking furnace system plays a crucial role in ethylene plants, since the major product yields are mainly determined in this operation. A thermal cracking operation is a typical semi-continuous dynamic process, due to the fact that coke accumulates on the inner tube surface of the cracking coils. This increases the heat transfer resistance and the reactor pressure drop, ∗ Corresponding

author Email address: [email protected] (Zhenlei Wang)

Preprint submitted to Computers & Chemical Engineering

January 16, 2017

Page 1 of 23

leading to a reduction in both reaction selectivity and productivity. Thus for the sake of production efficiency and plant safety, a cracking furnace must be periodically shut down for decoking [1]; this means that multiple cracking furnaces are needed in an ethylene plant, so that when one furnace is decoking, other furnaces can continue processing. Due to limited resources for decoking and safety concerns which can arise if downstream processes are disturbed, practical

ip t

ethylene plants allow only one furnace to be decoked at a given time. In recent years, the rapid growth of the ethylene demand and volatile raw material and product markets have forced ethylene plants to enhance their manufacturing flexibility to process different types of feeds and effectively arrange

cr

their schedules for maximizing operation profitability. These requirements highlight the significance of cracking furnace system scheduling, to satisfy material balance constraints, feedstock and production requirements, and non-

us

simultaneous decoking. We need to determine the optimum allocation of multiple feeds to different furnaces, the optimum processing sequence and time of each furnace, and the corresponding decoking sequence. Because of the importance of the cracking furnace, this is an active area of research. Riverol and Pilipovik

an

[2] formulated a fuzzy system for studying operational optimization on the ethane pyrolysis process. Li et al. [3] constructed an artificial neural network model for the yields of ethylene and propylene and developed a new multiobjective particle swarm optimization method to optimize the operational condition of a naphtha cracking furnace.

M

The validity and reliability of the proposed algorithm were demonstrated through two test functions studied, and actual optimization of operation condition for cracking process. Moreover, the yields of ethylene and propylene were improved. Nabavi et al. [4] studied the multi-objective optimization of an industrial liquefied petroleum gas thermal

ed

cracker by employing an elitist non-dominated sorting genetic algorithm with the jumping gene strategy. Keyvanloo et al. [5] investigated the effect of temperature, steam-to-naphtha ratio, and residence time and their quadratic and

pt

cubic interactions on the yield of ethylene and propylene in naphtha steam cracking. Berreni and Wang [6] studied the dynamic modeling, simulation and optimization of thermal cracking of propane in a tubular reactor by employing gPROMS; they illustrated that the dynamic optimization can improve operating profit by 13.1%. Nian et al. [7]

Ac ce

developed a differential evolution group search optimization algorithm to obtain optimal operational conditions of a naphtha cracking furnace for maximizing the sum mass yield of ethylene and propylene. To handle the multi-objective operation optimization for the yields of ethylene and propylene, Wang and Tang [8] designed a multi-objective parallel differential evolution with competitive evolution strategies. The computational results on practical problems indicated that the operation of an ethylene plant can be enhanced by increasing the yields of ethylene and propylene. Xia et al. [9] integrated a fuzzy C-means multi-swarm competitive particle swarm optimization algorithm with a radial basis function neural network to study the intelligent optimization control of cracking depth of an ethylene cracking furnace. Yu et al. [10] presented a self-adaptive multi-objective teaching-learning-based optimization (SA-MTLBO) to determine the optimal control variables for three conflicting objectives: maximization of the yields of ethylene, propylene, and butadiene. The results on one naphtha pyrolysis process showed that SA-MTLBO can obtain a good spread non-dominated solutions and provide more options for decision maker to improve the benefit of cracking furnace. 2

Page 2 of 23

It is worth noting that the aforementioned work mainly concentrates on the process simulation, advanced control, and operational optimization of a single furnace. Few papers can be found on the production scheduling of a multifurnace cracking system as the thermal cracking process involves highly complex reactions. Jain and Grossman [11] first developed a MINLP (mixed-integer non-linear programming) model for the cyclic scheduling of multiple feeds

ip t

cracked by multiple furnaces with the exponential decaying functions for product yields. The mathematical property of the designed model was analyzed and a solving algorithm for global optimality was proposed and demonstrated. However, the MINLP model did not consider the non-simultaneous decoking constraint and assumed that the same

cr

feed cracked in the same furnace in different batches always has the identical processing time. Schulz et al. [12] proposed a MINLP model to study the optimal performance of cyclic furnace shutdowns and downstream separation

us

systems. But they assumed that the coke thickness linearly increases with operation time, which is not consistent with the coking mechanism in practical situations [13, 14]. The non-simultaneous decoking constraint was also ignored and only one type of feed was considered. To determine optimal decoking policy, Lim et al. [1] developed

an

a neural network-based scheduling model by employing online information of ethylene and propylene yields, coil skin temperature, and pressure drop to assist the scheduling decisions. They also proposed three alternative solution strategies to solve the developed large-scale MINLP model. However, in this study, the situation of multiple feeds is

M

still not considered and the scheduling is not formed in a cyclic way such that only limited time horizon needs to be designated in advance. Liu et al. [15] presented a new cyclic scheduling model by considering multiple feeds, multiple cracking furnaces, and non-simultaneous decoking constraints to obtain the best performance of cracking furnace

ed

system. However, the operational conditions, such as feed rate and coil outlet temperature, are kept constant during the total cyclic time in their model. Zhao et al. [16] proposed a new cyclic scheduling model by considering secondary

pt

ethane cracking to make the scheduling results more applicable in reality. Subsequently, Zhao et al. [17] extended the model in a rescheduling framework to dynamically generate reschedules based on the new feed deliveries, the leftover feeds, and current furnace operating conditions. Wang et al. [18] proposed a novel synchronized scheduling

Ac ce

framework to solve the integrated scheduling problem of upstream naphtha inventory management and the related downstream furnace cracking operation. The performance of the proposed integrated framework was demonstrated through a comprehensive case study from a real-world ethylene plant. Very recently, Jin et al. [19] developed an integrated framework to simultaneously optimize the operational conditions and cyclic scheduling for an ethylene cracking furnace system. The incorporation of dynamic models into their integrated scheduling resulted in a mixedinteger dynamic optimization (MIDO) problem. The MIDO problem was converted into a MINLP problem by a discrete method. Traditional methods with fixed operational conditions were compared with their model, which demonstrated better economic performance. However, this model has the following shortcomings: (i) simultaneous decoking process is allowed, leading to a scheduling solution which is inapplicable in actual ethylene plants; and (ii) identical batch processing time for the same feed cracked in the same furnace is assumed, which might restrict the scheduling flexibility. Most of the problems in engineering applications are highly constrained and nonlinear due to limitations im3

Page 3 of 23

posed by various constraints. These characteristics often lead to non-convexity and multi-modality, thus challenging gradient-based methods such as branch and bound and outer-approximation. Thus nature-inspired population-based algorithms are becoming increasingly popular to solve a wide range of these problems. Based on simulating various natural phenomena, they work remarkably efficiently and have many advantages over traditional, deterministic meth-

ip t

ods and thus have been applied to a variety of problems, ranging from scientific research to industry and commerce [20, 21, 22]. In particular, the teaching-learning-based optimization (TLBO) algorithm [23], which simulates the teaching-learning process in a classroom, is a recently proposed population-based algorithm and has emerged as one

cr

of the simplest and most efficient techniques. It has been refined and successfully applied in electric power problems [24, 25, 26, 27], artificial neural network [28, 29], production planning [30], job shop scheduling [31, 32], and many

us

other fields [33, 34, 35, 36, 37, 38]. However, although some studies have been done for the operational optimization of a single cracking furnace utilizing the population-based algorithm [3, 4, 7, 8, 10, 39], to the best of our knowledge no attempts to use population-based algorithms in solving the production scheduling of a cracking furnace system

an

have been reported in the literature.

Based on previous study [19], a new cyclic scheduling model is designed in this paper to obtain a scheduling strategy and the corresponding operational conditions for the best performance of cracking furnace system. It overcomes

M

shortcomings in the literature [19] by avoiding the simultaneous decoking for multiple furnaces and by allowing different batch processing times for the same feed cracked in the same furnace. Moreover, a diversity learning TLBO (DLTLBO) algorithm is proposed for solving the developed model, to simultaneously determine the optimal alloca-

ed

tion of multiple feeds to different furnaces, the processing sequence with the corresponding batch processing time in each furnace, and the optimal operational conditions for each batch. The performance of the system is demonstrated

pt

by an actual case study.

The main contributions of this work are as follows.

Ac ce

• A novel cyclic scheduling model for cracking furnace system is developed. It is more practical and flexible than previous models, since some previously-ignored practical constraints and assumptions have been considered and addressed.

• A DLTLBO algorithm is proposed to efficiently solve the designed scheduling model. This is the first attempt to utilize this population-based algorithm for solving the scheduling problem of a cracking furnace system. • The effectiveness of the developed cyclic scheduling model and the performance of the DLTLBO algorithm are evaluated through a case study from a real-world ethylene plant. Experiments show that the new algorithm out-performs both previous studies of this set-up, and the basic TLBO algorithm. The results demonstrate that the new algorithm is a significant contribution to the state-of-the-art. The paper is organized as follows. Section 2 briefly introduces the problem we study. Section 3 provides the formulation of the developed cyclic scheduling model in detail. Section 4 presents the DLTLBO-based solving ap4

Page 4 of 23

F1

Arriving rates

Charging tanks

…

FNF

…

…

i

NF

1

…

2

…

j

Key products

…

l

…

NP

M

1

NC

an

Downstream Processing units

NC-1

us

Cracking furnaces

cr

ip t

1

Fi

…

Figure 1: An illustration of a cracking furnace system.

Section 6 concludes the paper.

pt

2. Problem statement

ed

proach. Section 5 describes a case study of an actual ethylene plant, to demonstrate the performance of the approach.

Figure 1 shows an ethylene cracking furnace system with several furnaces ( j = 1, ..., NC) for cracking multi-

Ac ce

ple feeds (i = 1, ..., NF). The different feeds are deposited continuously into corresponding charging tanks, and are allocated to different batches in the parallel furnaces to undergo complex reactions to generate the cracked gas. The cracked gas is sent to downstream processing units including quenching, compression, chilling, and separating sections to recover various products (l = 1, ..., NP). Figure 2 presents some of the important concepts in the system. Batch processing time is the time from a particular furnace starting to crack a feed to the next shutdown for decoking. It depends on furnace design, feed properties, and operational conditions like feed rate and coil outlet temperature; it is restricted by the tube maximum temperature (TMT) for the sake of plant safety. Decoking time means the time required to decoke a furnace; it is usually fixed for a specific kind of furnace. Total cycle time is the duration of the scheduling problem. Note that the cyclic schedule is implemented repeatedly, and during a total cycle time, a furnace may have multiple batches (e.g. in Figure 2, Furnace 1 performs two 5

Page 5 of 23

Batch processing time S NC ,1

Furnace NC

B NC ,2

B NC ,3

B NC ,1

Decoking time

B j ,k

S1,1

Furnace 1

B1,2

B1,1

us

Total cycle time

cr

ip t

Non-simultaneous decoking Furnace j

an

B j , k  [ Feed j , k , t j ,k , Cot j , k , D j ,k ], j , k

Figure 2: Example Gantt chart for cyclic scheduling of a cracking furnace system.

batches with starting time point S 1,1 , and Furnace NC performs three batches with starting time point S NC,1 ).

M

We denote the maximum number of batches in a schedule by NB.

Non-simultaneous decoking refers to the fact that decoking for different furnaces cannot be overlapped with respect

ed

to time. This is because of two practical reasons: (1) the decoking process of a practical ethylene cracking furnace needs large amounts of decoking air that are generated by the air compressor. The limited capacity of air compressor unable to offer sufficient decoking air for cleaning up more one cracking furnace at a time;

pt

and (2) simultaneously decoking two or more cracking furnaces will result in the substantial decrement on the amount of feedstock cracked, thus cause significant disturbances to downstream processing units, deteriorating

Ac ce

the productivity of plant even leading to safety issues[17]. The information needed for the kth batch of the jth furnace is presented by the matrix B j,k ; it includes the type of feed cracked (Feed j,k ), the batch processing time (t j,k ), the coil outlet temperature (Cot j,k ), and the feed rate (D j,k ).

3. Formulation of the cyclic scheduling model The components of the developed scheduling model are the objective function, the cracking furnace surrogate model, the material balance constraints, the timing constraints, the non-simultaneous decoking constraints, and the variable constraints.

6

Page 6 of 23

3.1. Objective function Eq. (1) formalizes the objective in this model: to maximize the average daily profit over a long cycle period T.

(1)

ip t

 NP R t j,k P  NC X NB   X   [ (Pl · 0 D j,k · Y(t)Feed j,k , j,l dt) − CsFeed j,k , j ]/T, if t j,k > 0 l=1 max Pro f it =     0, otherwise j=1 k=1 

Feed j,k is the type of feed allocated for the kth batch in Furnace j, and Y(t)Feed j,k , j,l is the corresponding yield function for key product l, which describes the dynamic change in l’s yield with respect to time. D j,k is the batch feed rate. Pl

cr

is the unit price of l. t j,k is the batch processing time for the kth batch in the furnace j. If t j,k is zero, this means the

us

related batch slot is not utilized for cracking and thus the profit is also zero. When the batch is used to crack one type R t j,k NP P of feed (t j,k > 0 ), it can be seen that (Pl · 0 D j,k · Y(t)Feed j,k , j,l dt) is the total sale income from all key products. l=1

CsFeed j,k , j is the decoking cost.

an

3.2. Cracking furnace surrogate model

Operational conditions affect the coking rate and have significant influence on the product yields, so we need to consider the performance dynamically. Jin et al. [19] have developed a surrogate model for the dynamic process using

M

a feed-forward neural network (FNN). The surrogate model is more computationally efficient than rigorous models built in commercial simulators like SPYRO and Coilsim1D, and validation has shown that the surrogate model can

pt

ed

successfully replace the rigorous models [19]. Thus, the surrogate model presented in Eq. (2) is adopted in this study.   ∗   xcoke,  j,k (t) = fFeed j,k , j (xcoke, j,k (t), Cot j,k (t), D j,k (t)) · CokeFeed j,k , j        Y(t)Feed j,k , j,l = gFeed j,k , j,l (xcoke, j,k (t), Cot j,k (t), D j,k (t))      (2) T MT j,k (t) = gFeed j,k , j,T MT (xcoke, j,k (t), Cot j,k (t), D j,k (t))        ∗  xcoke, j,k (t + 1) = xcoke, j,k (t) + xcoke,   j,k (t) · S T (t)       x (0) = 0

Ac ce

coke, j,k

f and g are nonlinear functions determined by the FNN. xcoke, j,k (t) is the coke thickness for the kth batch in Furnace j at time t. Cot j,k (t) and D j,k (t) are the input variables of Cot and D, respectively, for the dynamic process. CokeFeed j,k , j ∗ are the coke scaling factors to match the industrial run length for each feed in the corresponding furnace. xcoke, j,k (t)

is the coking rate. One of the output variables is the yield Y(t)Feed j,k , j,l for product l of feed Feed j,k in Furnace j; the other one is the tube maximum temperature T MT j,k (t) for the kth batch in Furnace j at time t. S T (t) is the sampling time interval and is set as one day in the present work. The initial coke thickness xcoke, j,k (0) is set to be zero, this means the tube is clean at the beginning of each batch. Considering that cyclic scheduling research for a real ethylene production plant tends to concern the scheduling level, rather than the detailed operation level, Cot j,k (t) and D j,k (t) are kept constant during one batch in our study.

7

Page 7 of 23

3.3. Material balance constraints For each feed, the total amount consumed by all cracking furnaces should be equal to the amount deposited into

j=1 k=1

Eq. (4) states that the deposit rate of feed i should be within its upper and lower bounds.

cr

Floi ≤ Fi ≤ Fupi , ∀i

(3)

ip t

the relevant charging tank during the scheduling horizon T, as described by Eq. (3).  NC X NB   X   (t j,k · D j,k ), if Feed j,k = i , ∀i Fi · T =     0, otherwise

us

3.4. Timing constraints

(4)

Eq. (5) states that when one batch is used to process one feed, its batch processing time t j,k should not be larger

an

than its upper limitation tup j,k , which is determined by the upper TMT as shown in Eq. (6).

(5)

T MT j,k (tup j,k ) ≤ T MT upFeed j,k , j , ∀ j, k

(6)

M

0 ≤ t j,k ≤ tup j,k , ∀ j, k

Eq. (7) states that the total cycle times for the furnaces are the same, and each is equal to the summation of its batch processing times and decoking times.

ed

 NB   X   (t j,k + τFeed j,k , j ), if t j,k > 0 T= , ∀j     0, otherwise k=1

(7)

pt

3.5. Non-simultaneous decoking constraints

Because the cyclic schedule is repeated, the first batch may start from the previous cycle or from the current cycle.

Ac ce

The end point E j,k for the kth batch in Furnace j is expressed by Eq. (8), in which Mod returns the remainder between its two arguments. The S j,1 of each furnace is the variable in the search process: once this is determined, the start and end points of the following batches can be calculated by Eqs. (8) and (9). Based on the start and end points of each batch, the non-simultaneous decoking constraint can be described by Eq. (10). Details are given in [15].

S j,k

  E j,k = Mod (S j,k + t j,k ), T , ∀ j, k

       Mod (E j,k−1 + τFeed j,k−1 , j ), T , if t j,k−1 > 0 = , ∀ j, ∀k ≥ 2    E j,k−1 , otherwise (E j,k − S j0 ,k0 +1 ) · (E j0 ,k0 − S j,k+1 ) ≤ 0, ∀ j < j0 , ∀k, k0

(8) (9) (10)

8

Page 8 of 23

3.6. Variable constraints All variables in the model have their own bounds. Eq. (11) shows the type of feed Feed j,k for the kth batch in Furnace j is one type from the set {1, 2, ..., NF}. Eqs. (12) and (13) represent the feed rate D j,k and the coil outlet temperature Cot j,k should within their corresponding bounds. For the first batch starting time point of each furnace, it

DloFeed j,k , j ≤ D j,k ≤ DupFeed j,k , j , ∀ j, k

0 ≤ S j,1 ≤ T, ∀ j

us

CotloFeed j,k , j ≤ Cot j,k ≤ CotupFeed j,k , j , ∀ j, k

cr

Feed j,k ∈ {1, 2, ..., NF} , ∀ j, k

ip t

has a lower bound of zero and is not over the total cycle time T, as shown in Eq. (14). (11) (12) (13) (14)

In summary, the cyclic scheduling model consists of the objective function of Eq. (1), the cracking furnace process

an

model of Eq. (2), and various constraints of Eqs. (3)–(14).

Note that although the cracking furnace surrogate model from [19] is employed in our developed scheduling model, some practical constraints ignored and assumptions made in [19] are handled in our model to make the schedul-

M

ing result more applicable to real-world ethylene plants. They are the non-simultaneous decoking constraint, and the assumption of identical batch processing time for the same feed cracked in the same furnace.

ed

4. Diversity learning Teaching-learning-based Optimization 4.1. Basic TLBO

pt

Based on the teaching-learning process in a typical classroom, Rao et al. [23] first developed the concept of teaching-learning-based optimization (TLBO). Similar to other nature-inspired algorithms, TLBO is a population-

Ac ce

based method that uses a collection of solutions to search for the global solution. The population in TLBO is composed of a class of learners. Different subjects offered to the learners are analogous to the design variables, while a learner’s outcomes correspond to its fitness value. The algorithm proceeds through a sequence of generations: in each generation, the best solution obtained thus far is designated as the teacher. Each generation in TLBO consists of two phases: the teacher phase, where learners learn from the teacher; and the learner phase, where learners learn through their interaction with other learners. 4.1.1. Teacher phase In the teacher phase, the teacher xteacher provides knowledge to the learners to improve the mean result of the class. For a problem with n-dimensional variables, let xr = (xr,1 , xr,2 , ..., xr,n ) represent the rth learner, and let Mean = PPS PPS PPS ( r=1 xr,1 , r=1 xr,2 , ..., r=1 xr,n )/PS denote the mean of a class with PS learners. Each learner is updated using Eq. (15). xr,new = xr,old + rand · (xteacher − T F · Mean)

(15)

9

Page 9 of 23

x r1    ( x r 2  x r 3 ) rand1  0.5

x r , new

ip t

otherwise

Figure 3: An illustration of diversity learning.

cr

x r ,old

us

T F = round[1 + rand(0, 1)] is the teaching factor and is randomly assigned a value of either 1 or 2, and rand is a uniformly distributed random number in [0, 1]. xr,new is the update to the current learner xr,old : xr,new is accepted if it

an

gives a better objective value. 4.1.2. Learner phase

In the learner phase, a learner randomly interacts with other learners to enhance its knowledge. Each learner

M

xr randomly selects another learner xr0 (r0 , r) and for a maximization objective function f (x) the learning process proceeds as in Eq. (16).

(16)

ed

     xr,new = xr,old + rand · (xr − xr0 ), if f (xr ) > f (xr0 )     xr,new = xr,old + rand · (xr0 − xr ), if f (xr0 ) > f (xr ) Again, the update xr,new is accepted if it gives a better objective value.

pt

4.2. Diversity learning TLBO

In any search-based optimization process, there is always tension between exploration, which means searching for

Ac ce

novel solutions; and exploitation, which means fine-tuning known good solutions. In TLBO, the teacher phase focuses on exploitation, encouraging other learners to approach a promising region of the search space. By contrast, the learner phase focuses on exploration, generating new solutions by randomly pairing up learners and exchanging knowledge between them. However, the greedy technique of accepting an updated solution whenever it is an improvement on its parent can lead to a premature loss of diversity in the population; solutions may tend to quickly group around local optima. Thus we propose Eq. (17), which maintains diversity by occasionally mixing up the genes from various learners in the class to generate new updates.   d d d d    xr1 + φ · (xr2 − xr3 ) if rand1 ≤ 0.5 xdr,new =     xd otherwise r,old

(17)

r1, r2, and r3 (r1 , r2 , r3 , r) are integers randomly selected from {1, 2, ..., PS }, d ∈ {1, 2, ..., n}, and φd is a uniformly distributed random number in [−1, 1]. This is reminiscent of uniform crossover [40] as used in genetic algorithms, and illustrated in Figure 3. Again, xr,new is accepted if it provides a better objective value. 10

Page 10 of 23

t j , k , Cot j ,k , D j ,k

Feed j ,k

Continuous variables

B j , k  [ Feed j , k , t j ,k , Cot j , k , D j ,k ]

cr

Figure 4: The representation of a solution.

ip t

Integral variables

4.3. Constraint handling method

us

The scheduling model discussed in Section 3 incorporates several (equality and inequality) constraints, related to material balance, TMT, non-simultaneous decoking, and cycle times. Any search process will always generate solutions that break one or more constraints (so-called infeasible solutions), so we use a penalty function and a repair

an

mechanism to help generate good feasible solutions.

The first three types of constraints are handled via a penalty function, which transforms a constrained problem into an unconstrained one by subtracting a penalty value from the objective value of each infeasible solution. Because the

M

constraint violation values of different constraints are orders of magnitude different, in order to treat each constraint equally we set the penalty term to be the number of constraint violations, which means the transformed objective function Pro f it∗ is expressed by Eq. (18).

ed

max Pro f it∗ = Pro f it − δ · (Numin,c,v )

(18)

Pro f it is the original objective function as described in Eq. (1), δ is the penalty coefficient, set as 2 × 107 according

non-simultaneous decoking.

pt

to [19], and Numin,c,v is the number of inequality constraint violations with respect to the material balance, TMT, and

Ac ce

The requirement for total cycle times to be equal is dealt with by a repair mechanism. The maximum cycle time among all furnaces is identified as the current total cycle time C, and the last batch processing time of each furnace can be calculated by subtracting from C the summation of previous batch processing times and decoking times. This method simply and effectively assures all the equality constraints are satisfied. Furthermore, we repair each variable that violates boundary constraints by the corresponding upper or lower limits of the allowed range.

4.4. Representation of solutions According to the variables’ characteristics and the problem statement in Section 2, the representation of a solution is divided into two parts as shown in Figure 4. The first part holds the integral variables for the type of feed assigned to different batches in each furnace, while the second part holds the continuous variables for the other parameters. These two parts constitute the matrix B j,k as presented in Figure 2. Moreover, the first batch starting time point S j,1 for each furnace is also a variable in the search process. 11

Page 11 of 23

Table 1: Parameter values for the cracking furnace system.

Dloi, j (ton/day) Dupi, j (ton/day) Cotloi, j (◦ C) Cotupi, j (◦ C) T MT upi, j (◦ C) Cokei, j

2

3

4

5

2

2

2

2

2

NAP

2

2

2

2

2

LNAP

255150

243000

145800

243000

486000

NAP

278441

253128

151877

253128

530364

LNAP

504

480

480

480

960

NAP

528

480

480

480

960

LNAP

624

552

552

552

1200

NAP

672

552

552

552

1200

LNAP

830

830

830

830

NAP

820

820

820

820

LNAP

845

845

845

845

NAP

840

840

840

LNAP

1090

1090

1090

NAP

1090

1090

1090

LNAP

0.890

0.888

0.839

NAP

0.959

0.969

0.947

830 820 845

840

840

1090

1090

1090

1090

0.958

0.854

1.071

0.914

M

5. Case study

cr

Csi, j (RMB)

1

LNAP

us

τi, j (day)

Furnace j

ip t

Feed i

an

Parameter

To demonstrate the performance of the developed scheduling model and the proposed DLTLBO algorithm, we analyse a case study taken from [19]. The plant has five furnaces (NC=5) processing two types of feeds (NF=2): light

ed

naphtha (LNAP) and naphtha (NAP). Five key products are considered: hydrogen (H2 ), ethylene (C2 H4 ), propylene (C3 H6 ), butadiene (C4 H6 ), and benzene (C6 H6 ). The parameters used are presented in Tables 1 and 2. In addition, although the upper limitation for the batch processing time of each furnace is determined by the TMT constraints, one

pt

upper bound is needed to generate the initial population and reduce the search space. Thus, the upper bound for each batch processing time is set at eighty days, consistent with industrial experience.

Ac ce

We report three results from this case study.

• The best-performing schedule derived by our system. This schedule satisfies all constraints described in Section 3.

• A comparison with the best-performing schedule from [19]. This schedule allows simultaneous decoking, so we also report the best-performing schedule derived by our system when it is allowed to ignore this constraint. • A comparison with the best-performing schedule derived by basic TLBO. All the results are obtained on a PC Intel Core 5 Duo 2.50 GHz with a 4GB RAM that runs on Windows 7 with Matlab R2014a implementation.

12

Page 12 of 23

Table 2: Parameter values for products and feeds. Pl (RMB/ton)

Feed i

Floi (ton/day)

H2

14620

LNAP

1000

Fupi (ton/day) 2000

C2H4

8480

NAP

1300

2600

C3H6

8210

-

-

-

C4H6

10799

-

-

-

C6H6

10500

-

-

-

Table 3: Detailed solution results based on the optimal result from DLTLBO.

4

5

Total

Coil outlet

rate

temperature

time (day)

(ton/day)

(◦ C)

TMT (◦ C)

Products

Decoking

revenue

cost

(×108 RMB)

Batch

profit

(×105 RMB)

(×108 RMB)

(×106 RMB/day) 3.239

1

NAP

48

672

829.9

1079

1.622

2.784

1.619

2

NAP

48

672

829.9

1079

1.622

2.784

1.619

1.152

3

NAP

56

552

829.5

1090

1.543

2.531

1.540

1

LNAP

49

552

845

1083

1.270

1.458

1.268

2

LNAP

48

552

845

1080

1.244

1.458

1.242

3

NAP

49

672

829.9

1081

1.656

1

LNAP

44

552

845

1079

1.154

2

LNAP

45

552

845

1082

1.180

2.784

1.653

2.430

2.430

1.178

3

LNAP

48

552

845

1080

1.244

1.458

1.242

1

NAP

53

552

831.7

1090

1.456

2.531

1.453

2

LNAP

40

552

845

1067

1.035

2.430

1.033

3

NAP

52

552

832.3

1090

1.430

2.531

1.428

1

NAP

48

1200

833.6

1090

2.852

5.304

2.846

2

NAP

48

1200

833.6

1090

2.852

5.304

2.846

3

NAP

49

1200

832.8

1090

2.906

5.304

2.901

-

-

151

-

-

-

25.07

43.52

25.02

2.562

2.485

2.592

5.691

16.570

pt

5.1. The optimal result from DLTLBO

Daily

profit

cr

type

Feed

us

3

number

Batch processing

an

2

Feed

M

1

Batch

ed

Furnace

ip t

Product l

When the maximum number of batches NB for each furnace is set to four, the developed scheduling model for this

Ac ce

problem has 85 variables, comprising 20 integral variables and 65 continuous variables. The model is solved by the proposed DLTLBO-based method with population size 20 and maximum number of generations 300. One solution simultaneously determines the allocations of two feeds to different batches in five furnaces, the number of actual batches employed in each furnace, the starting point of each furnace, the batch processing time, and the operational conditions in each batch. In accordance with normal practice, we run the algorithm thirty times independently and report the best performance values. The optimal schedule gives a total cycle time of 151 days and an average profit of 1.657016 × 107 RMB/day.

The detailed optimum scheduling result obtained by DLTLBO is presented in Table 3, and the corresponding Gantt chart is shown in Figure 5. Table 3 shows that the final TMT for each batch is close to the TMT upper bounds; this is reasonable because decoking is an expensive operation that should be avoided until it is necessary. Figure 6 gives the key products yield curves for each furnace to further analyze the optimal scheduling result. It is clear that NAP has a higher yield rate than LNAP, which can be seen most obviously from the curves of different batches in Furnaces 2 and 13

Page 13 of 23

NAP

NAP

NAP

Furnace 5

LNAP

NAP

NAP

Furnace 4

LNAP

LNAP

ip t

LNAP Furnace 3

LNAP

LNAP

NAP

NAP

cr

Furnace 2

NAP

NAP

20

40

60

80 Time (day)

100

120

140

an

0

us

Furnace 1

Figure 5: Gantt chart for the optimal result from DLTLBO.

M

4. Thus more batches are allocated to process NAP than LNAP. Although the yield rate of LNAP is lower, adequate batches are needed to crack LNAP due to the material balance constraints. Taking into account the different product prices and feed rates, the curves of revenue from five key products are shown in Figure 7. The profit of each batch can

ed

be calculated by the batch revenue minus the corresponding decoking cost, then the sum of all batches’ profit in one furnace is divided by the total cycle time to get the daily profit of each furnace as shown in the last column of Table 3.

pt

5.2. Comparison with the previous study

[19] formulated the problem with GAMS and derived solutions with SBB as the MINLP solver and CONOPT as

Ac ce

the nonlinear sub-solver. The Gantt chart for their best result is given in Figure 8. It provides 139.8 days of total cycle time with 1.652970 × 107 RMB/day of average profit, 40,460 RMB less per day than our solution (a difference of 0.25%), about 1.47679 × 107 RMB less per year. However, [19] derived a schedule ignoring the decoking constraints, which obviously makes the problem somewhat easier. Applying our DLTLBO system to this relaxed problem gives the result shown in Figure 9. This schedule has 149 days of total cycle time and 1.657565 × 107 RMB/day of average profit. This is an extra 45,954 RMB per day (a difference of 0.28%) compared with the previous study result. The profit increment is slightly larger than that of the optimal result for the integrated developed model obtained by DLTLBO due to the removing of decoking constraints. This comparison highlights that our DLTLBO system can derive superior schedules while also dealing with morecomplex constraints, such as imposing non-simultaneous decoking and allowing variable batch-lengths. Thus the scheduling results obtained are more practical in real-world situations.

14

Page 14 of 23

6

Furnace 5 0.53 20

Yield of key products

0.56

40

60

80

LNAP

100 NAP

120

140 NAP

Key products revenue (1.0E+6 RMB)

0

Furnace 4

0.52 0 0.54

20 40 LNAP

60

80

100

120

LNAP

140 LNAP Furnace 3

0.52 0 0.56

20

40

60

80

LNAP

LNAP

100 120 NAP

140 Furnace 2

0.53 0 0.56

20 NAP

40

60

80 NAP

100

120 140 NAP

0

20

0

20 40 LNAP

40

60

80

100

120

60

80

100 NAP

60

80 LNAP

LNAP

2.6

Furnace 5

120

140 NAP

Furnace 4

100

120

140 LNAP

Furnace 3

2.5 0 2.8

20

40

60

2.4 3.4

20 NAP

140

0

Time (day)

20

80

100

120

40

60

40

140

NAP

LNAP

LNAP

3.3 20

40

2.5

Furnace 1 0

NAP

2.8

0

0.54

NAP

NAP

5.8

ip t

NAP

cr

NAP

NAP

80 NAP

100

us

0.56

60

80

Furnace 2

120 140 NAP Furnace 1

100

120

140

an

Time (day)

Figure 7: Key products revenue for the optimal result from DLTLBO.

NAP

Furnace 5 LNAP

NAP

LNAP

Furnace 3

LNAP

Furnace 2

0

20

NAP

NAP

NAP

LNAP

LNAP

LNAP

LNAP

LNAP

LNAP

NAP

NAP

NAP

Furnace 3

NAP

Furnace 2

NAP

40

NAP

60

80

Furnace 4

NAP

NAP

LNAP

Furnace 1

NAP

Furnace 5

NAP

Ac ce

Furnace 4

NAP

NAP

pt

LNAP

ed

M

Figure 6: Key products yield for the optimal result from DLTLBO.

NAP

Furnace 1

100

120

0

140

20

Time (day)

Figure 8: Gantt chart for the result from [19].

40

60

80 Time (day)

100

120

140

Figure 9: Gantt chart for the optimal result from DLTLBO, disregarding decoking constraints.

15

Page 15 of 23

LNAP

NAP

NAP

Furnace 5 NAP

NAP

NAP

Furnace 4 LNAP

LNAP

ip t

LNAP Furnace 3 LNAP

NAP

NAP

NAP

cr

Furnace 2 NAP

NAP

15

30

45

60

75 90 Time (day)

105

120

135

150

an

0

us

Furnace 1

Figure 10: Gantt chart for the optimal result from TLBO.

M

5.3. Comparison with basic TLBO

In order to demonstrate the effectiveness of the proposed DLTLBO algorithm, the original problem is also solved using the basic TLBO algorithm. The problem is solved thirty times independently using basic TLBO; the optimal

ed

scheduling result gives a total cycle time of 155 days and an average profit of 1.655127 × 107 RMB/day. While this is 21,570 RMB per day (a difference of 0.13%) more than the result in [19], it is still 18,891 RMB less per day than the optimal result of DLTLBO, about 6.89522 × 106 RMB less per year. The results indicate that the introduced diversity

pt

learning strategy enhances the performance of the algorithm. The Gantt chart for the optimal result of TLBO is shown in Figure 10, and the curves of the key products yield

Ac ce

and revenue are shown in Figures 11 and 12. We also present the convergence graphs of DLTLBO and TLBO in Figure 13; we can see that while TLBO exhibits relatively rapid convergence in the very early stages of searching, DLTLBO quickly overtakes and it approaches its optimal result much earlier in the process. This comparison highlights that the proposed DLTLBO algorithm has improved exploration and exploitation capabilities than the original TLBO system, delivering both increased convergence rates and superior ultimate solutions. 5.4. Summary of results

Table 4 gives a summary of the best results presented here. Table 5 presents the statistical results of DLTLBO and basic TLBO for non-simultaneous decoking situation over thirty times independently run. We can see that the proposed DLTLBO has the superior robustness, since it can consistently obtain the advantage on daily profit compared with the previous study and TLBO. For the mean computational time, DLTLBO consumes a shorter time (277.6s) than TLBO (381.7s), this shows that DLTLBO has a higher efficient. Compared with the reported computation time 16

Page 16 of 23

0.56

NAP

LNAP

NAP

LNAP

Furnace 5

Furnace 5

5.3 45

60

75

90

105

120

135

150

NAP

NAP

Furnace 4

0.54 0

15

30

0.54

45 60 LNAP

75

90

105

120

LNAP

135

150

LNAP Furnace 3

0.52 0 0.56

15

30

45

60

75 90 NAP

105

120

135 NAP

150

LNAP

Furnace 2

0.53 0 0.56

15 30 NAP

45

15

45

60

75 NAP

90

75

90

105

120 NAP

135

120

135

0

15

2.8

60

105

75

0

15

30

45 LNAP

60

75

0

15

30

45

60

75 NAP

2.6

90 NAP

105

120

90 105 LNAP

120

90

120

135 NAP

150

135 150 LNAP

Furnace 3

2.5 2.8

LNAP

2.4 0

15 30 NAP

0

15

3.4 3.3

30

60

Furnace 4

Furnace 1 0

45

2.5

150

0.54

30 NAP

ip t

30 NAP

150

45

60

30

45

105

135 NAP

cr

15

75 NAP

90

us

0 0.57

Key products revenue (1.0E+6 RMB)

0.51

60

75

90

150

Furnace 2

105

120 135 NAP

150

105

120

150

Furnace 1 135

Time (day)

an

Time (day)

Figure 12: Key products revenue for the optimal result from TLBO.

7

1.66

x 10

pt

1.65

ed

M

Figure 11: Key products yield for the optimal result from TLBO.

1.64

TLBO DLTLBO

Daily profit (RMB)

1.63 1.62

Ac ce

Yield of key products

NAP

6

NAP

1.61 1.6

1.59 1.58 1.57 1.56 1.55

0

50

100

150

200

250

300

Generation

Figure 13: Convergence graphs of TLBO and DLTLBO.

17

Page 17 of 23

Table 4: Average profit for the four results compared in this paper. 1.657565 × 107

DLTLBO (no simultaneous decoking)

1.657016 × 107

TLBO (no simultaneous decoking)

1.655127 × 107

[19] (allowing simultaneous decoking)

1.652970 × 107

ip t

RMB/day DLTLBO (allowing simultaneous decoking)

Table 5: Statistical results of DLTLBO and TLBO (Boldface values are the best results). Daily Profit (RMB/day)

Method

Worst

CPU (s)

Std

1.6570161× 107

1.6570084× 107

1.6569480× 107

213.669

277.6

7

7

1.6550102× 107

374.070

381.7

1.6551269× 10

1.6550870× 10

us

TLBO

Mean

cr

DLTLBO

Best

125.644s in previous study, although little more time is needed both in DLTLBO and TLBO, it is very worth using more time for an improvement on daily profit. In fact, there is no significant difference between the different computa-

an

tional times, since they are both acceptable for real cyclic scheduling of an ethylene cracking furnace system[17, 19]. Table 6 gives a detailed breakdown of the comparison between the best results obtained from DLTLBO and basic

M

TLBO.

6. Conclusions

ed

We have described a new cyclic scheduling model for multiple feeds cracked in parallel ethylene cracking furnaces to obtain the maximum profitability with consideration of various product prices, decoking costs, and a series of rigorous process constraints. The developed model is more practical and flexible than previous studies since it avoids

pt

unpractical simultaneous decoking and handles the assumption of identical batch processing time for the same feed cracked in the same furnace. We have used a diversity leaning TLBO (DLTLBO) algorithm to derived optimized

Ac ce

schedules for this set-up, which enhances the learner phase of the algorithm to improve exploration. Experiments on a case study from an actual ethylene plant show that the DLTLBO algorithm can derive schedules that outperform both previous studies of this set-up that used GAMS to formulate the problem, and the basic TLBO algorithm, which sometimes leads to solutions that converge on local optima. The new algorithm is a significant contribution to the state-of-the-art.

Future work will include deriving a multi-objective version of this system, capable of deriving multiple schedules that facilitate optimal profitability under varying price regimes.

Acknowledgments This research was supported by Major State Basic Research Development Program of China (2012CB720500), National Natural Science Foundation of China (61174118), Shanghai Natural Science Foundation (14ZR1421800),

18

Page 18 of 23

ip t

Table 6: Comparison on the optimal schedule results of DLTLBO and TLBO (Boldface values are the result of TLBO) Feed

number

type

1

2

2

3

1

3

2

3

1

2

3

(◦ C)

Decoking

revenue

cost

(×108 RMB)

Batch

Daily

profit

profit

(×105 RMB)

(×108 RMB)

(×106 RMB/day)

NAP

48

672

829.9

1079

1.622

2.784

1.619

3.239

NAP

49

672

829.4

1079

1.656

2.784

1.653

3.242

NAP

48

672

829.9

1079

1.622

2.784

1.619

NAP

50

671.8

829.8

1084

1.689

NAP

48

672

829.9

1079

1.622

NAP

50

672

829.6

1083

1.689

2.784

1.687

LNAP

44

552

845

1079

1.154

2.430

1.152

2.562

LNAP

45

552

845

1082

1.180

2.430

1.178

2.612

LNAP

45

552

845

1082

1.180

2.430

1.178

2.784

1.686

2.784

1.619

NAP

52

552

832.1

1090

1.438

2.531

1.436

NAP

56

552

829.5

1090

1.543

2.531

1.540

NAP

52

484

838.8

1090

1.438

2.531

1.436

LNAP

49

552

845

1083

1.270

1.458

1.268

2.485

LNAP

49

552

845

1083

1.270

1.458

1.268

2.488

LNAP

48

552

845

1080

1.244

1.458

1.242

LNAP

50

1.294

LNAP

48

LNAP

50

1.295

NAP

53

831.7

1090

1.456

2.531

1.453

2.592

NAP

49

552

834.3

1090

1.354

2.531

1.351

2.648

LNAP

40

552

845

1067

1.035

2.430

1.033

552

845

1086

1.458

552

845

1080

1.244

1.458

1.242

552

845

1086

1.295

1.458

1.294

552

NAP

50

552

833.6

1090

1.379

2.531

1.377

NAP

52

552

832.3

1090

1.430

2.531

1.428

50

552

833.7

1090

1.379

2.531

1.377

NAP

48

1200

833.6

1090

2.852

5.304

2.846

5.691

NAP

52

1200

830.6

1090

3.070

5.304

3.065

5.561

NAP

48

1200

833.6

1090

2.852

5.304

2.846

LNAP

45

1200

844.9

1085

2.496

4.860

2.491

NAP

49

1200

832.8

1090

2.906

5.304

2.901

NAP

52

1200

830.6

1090

3.070

5.304

3.064

-

-

151

-

-

-

-

-

-

16.570

-

-

155

-

-

-

-

-

-

16.551

2

3

Total

(◦ C)

Products

NAP

1

5

(ton/day)

Ac ce

4

time (day)

TMT

us

3

temperature

an

2

Coil outlet

rate

M

1

Feed

ed

1

Batch processing

cr

Batch

pt

Furnace

19

Page 19 of 23

and the State Key Laboratory of Synthetical Automation for Process Industries. The authors would like to acknowledge the financial support of China Scholarship Council (CSC) and the Dr. Y. Jin for providing the cracking furnace surrogate model.

ip t

Nomenclature Subscripts i = 1, ..., NF index of different feeds for cracking

cr

j = 1, ..., NC index of cracking furnaces k = 1, ..., NB index of batches for each furnace

us

l = 1, ..., NP index of considered key products Parameters

an

Pl The price parameter for the product l Csi, j decoking cost for the feed i cracked in the furnace j

τi, j decoking time used after the feed i cracked in the furnace j

M

Cokei, j coking scaling factors for the feed i cracked in the furnace j Floi lower bound of the rate of arrival of the feed i

Fupi upper bound of the rate of arrival of the feed i

ed

Dloi, j lower bound of the flow rate for the feed i cracked in the furnace j Dupi, j upper bound of the flow rate for the feed i cracked in the furnace j Cotloi, j lower bound of the coil outlet temperature for the feed i cracked in the furnace j

pt

Cotupi, j upper bound of the coil outlet temperature for the feed i cracked in the furnace j tupi, j upper bound of the processing time for the feed i cracked in the furnace j

Ac ce

T MT upi, j upper bound of the tube temperature for the feed i cracked in the furnace j T MT i, j (t) the tube temperature function for the feed i cracked in the furnace j Y(t)i, j,l the yield function of product l for the feed i cracked in the furnace j Variables

Feed j,k the type of feed assigned to kth batch of the furnace j t j,k processing time for kth batch of the furnace j D j,k flow rate for kth batch of the furnace j Cot j,k coil outlet temperature for kth batch of the furnace j S j,1 starting time point of the first batch in the furnace j T total cycle time of the scheduling problem Fi rate of arrival of the feed i

20

Page 20 of 23

References [1] H. Lim, J. Choi, M. Realff, J. H. Lee, S. Park, Development of optimal decoking scheduling strategies for an industrial naphtha cracking furnace system, Industrial & engineering chemistry research 45 (16) (2006) 5738–5747. [2] C. Riverol, M. Pilipovik, Optimization of the pyrolysis of ethane using fuzzy programming, Chemical Engineering Journal 133 (1) (2007) 133–137.

ip t

[3] C. Li, Q. Zhu, Z. Geng, Multi-objective particle swarm optimization hybrid algorithm: An application on industrial cracking furnace, Industrial & engineering chemistry research 46 (11) (2007) 3602–3609.

[4] S. Nabavi, G. Rangaiah, A. Niaei, D. Salari, Multiobjective optimization of an industrial lpg thermal cracker using a first principles model,

cr

Industrial & Engineering Chemistry Research 48 (21) (2009) 9523–9533.

[5] K. Keyvanloo, J. Towfighi, S. Sadrameli, A. Mohamadalizadeh, Investigating the effect of key factors, their interactions and optimization of naphtha steam cracking by statistical design of experiments, Journal of Analytical and Applied Pyrolysis 87 (2) (2010) 224–230.

us

[6] M. Berreni, M. Wang, Modelling and dynamic optimization of thermal cracking of propane for ethylene manufacturing, Computers & Chemical Engineering 35 (12) (2011) 2876–2885.

[7] N. Xiaoyu, W. Zhenlei, Q. Feng, A hybrid algorithm based on differential evolution and group search optimization and its application on ethylene cracking furnace, Chinese Journal of Chemical Engineering 21 (5) (2013) 537–543.

an

[8] X. Wang, L. Tang, Multiobjective operation optimization of naphtha pyrolysis process using parallel differential evolution, Industrial & Engineering Chemistry Research 52 (40) (2013) 14415–14428.

[9] L. Xia, J. Chu, Z. Geng, A multiswarm competitive particle swarm algorithm for optimization control of an ethylene cracking furnace,

M

Applied Artificial Intelligence 28 (1) (2014) 30–46.

[10] K. Yu, X. Wang, Z. Wang, Self-adaptive multi-objective teaching-learning-based optimization and its application in ethylene cracking furnace operation optimization, Chemometrics and Intelligent Laboratory Systems 146 (2015) 198–210.

1623–1636.

ed

[11] V. Jain, I. E. Grossmann, Cyclic scheduling of continuous parallel-process units with decaying performance, AIChE Journal 44 (7) (1998)

[12] E. P. Schulz, J. A. Bandoni, M. S. Diaz, Optimal shutdown policy for maintenance of cracking furnaces in ethylene plants, Industrial & engineering chemistry research 45 (8) (2006) 2748–2757.

2379–2391.

pt

[13] S. Wauters, G. Marin, Kinetic modeling of coke formation during steam cracking, Industrial & engineering chemistry research 41 (10) (2002)

[14] S. Jazayeri, R. Karimzadeh, A surface kinetic model for coke deposition over stainless steel, chromium, and iron during ethane pyrolysis,

Ac ce

Petroleum Science and Technology 32 (7) (2014) 821–829. [15] C. Liu, J. Zhang, Q. Xu, K. Li, Cyclic scheduling for best profitability of industrial cracking furnace system, Computers & chemical engineering 34 (4) (2010) 544–554.

[16] C. Zhao, C. Liu, Q. Xu, Cyclic scheduling for ethylene cracking furnace system with consideration of secondary ethane cracking, Industrial & engineering chemistry research 49 (12) (2010) 5765–5774. [17] C. Zhao, C. Liu, Q. Xu, Dynamic scheduling for ethylene cracking furnace system, Industrial & engineering chemistry research 50 (21) (2011) 12026–12040.

[18] Z. Wang, Y. Feng, G. Rong, Synchronized scheduling approach of ethylene plant production and naphtha oil inventory management, Industrial & Engineering Chemistry Research 53 (15) (2014) 6477–6499. [19] Y. Jin, J. Li, W. Du, F. Qian, Integrated operation and cyclic scheduling optimization for an ethylene cracking furnaces system, Industrial & Engineering Chemistry Research 54 (15) (2015) 3844–3854. [20] S.-E. K. Fateen, A. Bonilla-Petriciolet, Unconstrained gibbs free energy minimization for phase equilibrium calculations in nonreactive systems, using an improved cuckoo search algorithm, Industrial & Engineering Chemistry Research 53 (26) (2014) 10826–10834. [21] L. Chen, X. Wang, L. Tang, Operation optimization in the hot-rolling production process, Industrial & Engineering Chemistry Research 53 (28) (2014) 11393–11410.

21

Page 21 of 23

[22] A. O. Elnabawy, S.-E. K. Fateen, A. Bonilla-Petriciolet, Phase stability analysis and phase equilibrium calculations in reactive and nonreactive systems using charged system search algorithms, Industrial & Engineering Chemistry Research 53 (6) (2014) 2382–2395. [23] R. V. Rao, V. J. Savsani, D. Vakharia, Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems, Information Sciences 183 (1) (2012) 1–15. [24] X. He, Y. Rao, J. Huang, A novel algorithm for economic load dispatch of power systems, Neurocomputing 171 (2016) 1454–1461.

using teaching learning based optimization algorithm, Applied Soft Computing 21 (2014) 72–83.

ip t

[25] M. Abirami, S. Ganesan, S. Subramanian, R. Anandhakumar, Source and transmission line maintenance outage scheduling in a power system

[26] P. K. Roy, C. Paul, S. Sultana, Oppositional teaching learning based optimization approach for combined heat and power dispatch, International Journal of Electrical Power & Energy Systems 57 (2014) 392–403.

generation control of multi-area power system, Applied Soft Computing 27 (2015) 240–249.

cr

[27] B. K. Sahu, S. Pati, P. K. Mohanty, S. Panda, Teaching–learning based optimization algorithm based fuzzy-pid controller for automatic

[28] L. Wang, F. Zou, X. Hei, D. Yang, D. Chen, Q. Jiang, An improved teaching–learning-based optimization with neighborhood search for

us

applications of ann, Neurocomputing 143 (2014) 231–247.

[29] D. Chen, R. Lu, F. Zou, S. Li, Teaching-learning-based optimization with variable-population scheme and its application for ann and global optimization, Neurocomputing 173 (2016) 1096–1111.

an

[30] R. Kadambur, P. Kotecha, Multi-level production planning in a petrochemical industry using elitist teaching–learning-based-optimization, Expert Systems with Applications 42 (1) (2015) 628–641.

[31] A. Baykaso˘glu, A. Hamzadayi, S. Y. K¨ose, Testing the performance of teaching–learning based optimization (tlbo) algorithm on combinatorial problems: Flow shop and job shop scheduling cases, Information Sciences 276 (2014) 204–218.

M

[32] Y. Xu, L. Wang, S.-y. Wang, M. Liu, An effective teaching–learning-based optimization algorithm for the flexible job-shop scheduling problem with fuzzy processing time, Neurocomputing 148 (2015) 260–268.

[33] R. V. Rao, Review of applications of tlbo algorithm and a tutorial for beginners to solve the unconstrained and constrained optimization

ed

problems, Decision Science Letters 5 (1) (2016) 1–30. [34] F. Zou, L. Wang, X. Hei, D. Chen, Teaching–learning-based optimization with learning experience of other learners and its application, Applied Soft Computing 37 (2015) 725–736.

[35] R. V. Rao, K. More, Optimal design of the heat pipe using tlbo (teaching–learning-based optimization) algorithm, Energy 80 (2015) 535–544.

(2015) 250–258.

pt

[36] T. Dede, Y. Ayvaz, Combined size and shape optimization of structures with a new meta-heuristic algorithm, Applied Soft Computing 28

[37] T. Dokeroglu, Hybrid teaching–learning-based optimization algorithms for the quadratic assignment problem, Computers & Industrial Engi-

Ac ce

neering 85 (2015) 86–101.

[38] R. V. Rao, V. Patel, Multi-objective optimization of two stage thermoelectric cooler using a modified teaching–learning-based optimization algorithm, Engineering Applications of Artificial Intelligence 26 (1) (2013) 430–445. [39] K. Yu, X. Wang, Z. Wang, Multiple learning particle swarm optimization with space transformation perturbation and its application in ethylene cracking furnace optimization, Knowledge-Based Systems 96 (2016) 156–170. [40] G. Syswerda, Uniform crossover in genetic algorithms. in: Proceedings of the third international conference on genetic algorithms (1989) 2–9.

22

Page 22 of 23

Highlights



A novel cyclic scheduling model for ethylene cracking furnace system is developed.



The developed model more practical and flexible than previous models.



A diversity learning TLBO (DLTLBO) algorithm is proposed to solve the scheduling model.



This is the first attempt to use population-based algorithm for solving the scheduling problem of

An actual case study demonstrates the effectiveness of the developed scheduling model and the

ce pt

ed

M

an

us

cr

proposed DLTLBO algorithm.

Ac



ip t

cracking furnace system.

Page 23 of 23