Papers Delivered at International Conference on Cleaner Production
Beijing, China -- September 2001 -- Paper 29 of 30

A new cleaner production framework based on multi-objective evolutionary algorithms

Shi Lei*, Shi Hanchang, Qian Yi 
State Key Joint Laboratory of Environment Simulation and Pollution Control,
Tsinghua University, Beijing, 100084, P.R. China

Abstract

A new framework for the solution to cleaner production problems is built by introducing the multi-objective evolutionary algorithms. The framework provides a friendly, interactive environment for decision-makers where economic and environmental objectives can be coped with simultaneously. The well-documented problem of a Hydrodealkylation (HDA) plant synthesis is studied on the decision level of recycling to primarily prove the feasibility and effectiveness of this framework.

Keywords: Cleaner production; Multi-objective programming; Multi-objective evolutionary algorithms; Steady-state non-dominated sorting genetic algorithm

*corresponding author, Fax: 86+010-62771472; E-mail: slone@mail.tsinghua.edu.cn 

1. Introduction

Cleaner production, a preventative integrated continuous strategy for modifying products, processes or services, has been considered as the best technological strategy and means of Sustainable Development. Many successes show that cleaner production can give often both environmental and economic benefits, because it promotes facility efficiency, reduces the need for expensive end-of-pipe treatment and disposal technologies, and reduces the long-term liabilities associated with releases into the environment [1]. However, cleaner production is not easy to implement. The development of cleaner technologies for a specific production process is a complex task with a large number of options, such as avoiding leaks and spills, better materials handling, closing internal material loops for auxiliary materials, and designing and redesigning processes for improved material and energy efficiency. Process integration provides a systematic methodology to cope with such engineering problems that result from cleaner production. Many approaches under the banner of process integration, such as pinch analysis, knowledge-based approaches, and numerical optimization have been widely used to solve these problems [2-3]. The complexity of optimization problems involving environmental impacts necessitates the development of combined or hybrid approaches where frameworks usually include available tools and technologies [4]. Generally speaking, mathematical programming is included in these frameworks because of its advantages of simultaneous synthesis by incorporating many cleaner production options into a MINLP model. Some pioneer work has been done on this aspect [5-8]. By integrating the environmental issues into one or more objectives instead of constraints, multi-objective programming is desirable because it can provide a more natural way to solve cleaner production problems which require economic and environmental merits to be balanced simultaneously. Several reviews have been cast on the applications in chemical engineering since the middle of 1970s [9-11]. Among the various multi-objective programming techniques, the techniques of generating Pareto sets are highlighted because they can present a whole collection of Pareto optimal points. Recently, Bhaskar et al [11] well reviewed techniques of generating Pareto sets in chemical engineering, such as utility functions, indifference functions, the lexicographic approach, parametric approach, the e–constraint approach, goal programming, evolutionary algorithms, and other techniques.

Among the approaches mentioned above, evolutionary search algorithms have been shown to be efficient since they use a population of solutions and are less susceptible to the shape or continuity of the Pareto front [12]. Since the Vector Evaluated Genetic Algorithm (VEGA), the first implementation of multi-objective evolutionary algorithms (MOEAs), was developed by Schaffer in 1984, many MOEAs have been implemented, such as the Niched Pareto Genetic Algorithm, the Multi-objective Genetic Algorithm, the Non-dominated Sorting Genetic Algorithm (NSGA), etc.[13]. It appears that the evolutionary algorithms used in recent years are quite robust for generation non-inferior solutions for large-scale complex problems. For example, the non-dominated sorting genetic algorithm (NSGA), has been used to solve a variety of multi-objective optimization problems in chemical engineering, such as polymer reaction engineering, catalytic reactors, membrane modules, cyclone separators and venturi scrubbers [11]. More recently, MOEAs have also been reported in the process synthesis problems[14,15].

By introducing MOEAs, a new framework for the solution to cleaner production problems is built. A simple description about the Steady-state Non-dominated Sorting Genetic Algorithm (SNSGA), one of MOEAs, is given first, then the framework to solve cleaner production problems is presented in detail. Finally, the well documented problem of the Hydrodealkylation (HDA) plant synthesis is studied on the decision level of recycling to prove the feasibility and effectiveness of this framework primarily.

2. Multiobjective evolutionary algorithms

Figure 1. The flowchart of SNSGA

The Steady-state Non-dominated Sorting Genetic Algorithm (SNSGA), a new form of multi-objective evolutionary algorithm, is adopted in the construction of a new framework for cleaner production problems. The illustrative flowchart of SNSGA is shown in Figure 1. This algorithm has been proved to be more efficient both computationally and in terms of quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one[15]. Here are two small examples presented to illustrate the general applicability of SNSGA. The first example, taken from Schaffer[16], is a classical test problem having two objective functions and one variable.

(1)

The Pareto-optimal solutions lie in  s_share. The variable is coded using binary strings of size 30. The population size s_share is 100, and the replacement size s_share is 60. The probability of crossover is set to be 1.0, and the same is to mutation. The initial value of s_share is 0.002, and finally reaches 0.000125 after about 45 generations. Figure 2 shows the population distribution in the initial generation. This figure shows that the population is widely distributed. Figure 3 shows the population of 100 members after 9 generations and shows the rate at which the SNSGA has managed to get the Pareto fronts.

The second example, a multi-modal problem designed by Srinivas & Deb [17], brings great challenge to evolutionary algorithms (such these problems are called to be genetic algorithm difficult problems).

(2)

Figure 4 shows the dominator function of the second objective s_share for s_share with s_share as the global minimum and as the local minimum solutions. Variables are coded in 20-bit binary strings each, in the ranges s_share and s_share. The population size s_share is 100, and the replacement size s_share is 60. The probability of crossover is set to be 1.0, and the same is to mutation. The value s_share of is 0.0125. Figure 5 shows the f₁-f₂ plot with local and global Pareto-optimal solutions corresponding to the two-objective optimization problem. No individual in the initial population lies in the global Pareto-optimal front, however, all individuals at 100th generation lie in the global Pareto-optimal front. Other runs of SNSGA show the same results. This example shows that SNSGA has the ability of avoiding being trapped at the local Pareto-optimal solutions.

Figure 6. A framework based on MOEA for cleaner production

3. Methodology

The new framework for cleaner production problems is shown in Figure 6. At the beginning of this methodology, a base case model representing an existing process or a newly-created one is built first through a conceptual hierarchical design procedure. This base case is used as a starting point to identify possible alternatives and to generate the Mixed Integer Non-Linear Programming (MINLP) superstructure. At the initialization stage of SNSGA, individuals are created to form the initial population, each individual representing one of process alternatives. At the evaluation stage, each individual is assigned a dummy fitness value according to its economic and environmental objectives. The better the economic and environmental objectives a individual has, the bigger the fitness value is. The population is then reproduced according to these dummy fitness values. A stochastic remainder proportionate selection is used in SNSGA. Individuals having the bigger fitness value usually get more copies than the rest of population, which is intended to search for nondominated regions, and results in quick convergence of the population towards Pareto-optimal fronts. When the convergence condition is satisfied, in general, all individuals in the final population will lie in the Pareto-optimal front. Thus, one or more better process alternatives emerge in the final population. Decision-maker can compare these alternatives offline. If he has chosen one or more satisfactory process alternatives, he can stop the decision process; otherwise, he can make modifications to existing alternatives or create new ones, then allows another MINLP superstructure model to form and another SNSGA to run.

The basic idea behind this framework is that the economic and environmental objectives can be dealt with simultaneously in a more natural way. Several non-inferior points instead of only one usually emerge at the end of the optimization stage, which provides a friendly interactive environment for decision-makers. Thus, hierarchical design approaches, numerical optimization methods and other methods are combined in a more productive way. The effectiveness of this framework depends on the implementation of MOEA, the construction of superstructure model, and the selection of an appropriate environmental impact index.

4. Illustrative example

The performance of the new framework is demonstrated by the well-documented problem of a Hydrodealkylation (HDA) plant synthesis at the decision level of recycling. The problem data is taken from Douglas [18], and the superstructure on the level of recycling is shown in Figure 7. The selection of this superstructure was motivated by a design and suggested alternatives from Douglas. A hydrogen raw material stream is available at a purity of 95% (the remaining 5% is methane). A membrane separator can be used to yield a higher purity feed stream by removing methane. The exothermic reaction can be carried out in a plug flow reactor operating either adiabatically or isothermally. The effluent of reactor enters into separator system where benzene is separated from unreacted toluene, hydrogen and other by-products. The unreacted toluene is recycled to the reactor. The hydrogen can be recycled with or without purification or be purged.

Figure 7. The superstructure of HDA on the decision level of recycling

At the decision level of recycling, there are three main alternatives to be considered, these being whether or not 1) to purify the feed hydrogen, 2) adopt the adiabatical or isothermal reactor, and 3) to purify the recycled gas. Without considering the separation subsystem, the superstructure for this HAD process was modeled as an MINLP using simplified models. Although it is recognized that these models may be inaccurate, they are likely adequate for use for the preliminary synthesis stage on the recycling stage.

Only two decision variables, the conversion rate of toluene (x) and the content of hydrogen in the purge stream ( y_PH), are considered on the recycling stage. The economic objective function is the net profit of this process, meaning that the value of product and by-product subtracts the operating costs and capital costs.

There exist five main compounds in this process: hydrogen, methane, toluene, benzene and diphenyl. Their environmental impact indexes are given in order as follows[19].

Figure 8.  The distribution of the initial population	Figure 9.  The distribution of the final population

 U = (0.031   0.008   0.301   0.175  0.957)

The diphenyl by-product is considered here to be waste, therefore two waste streams, the purge flow and the diphenyl by-product flow, exist in this process. The impact output indexes per kilogram of product given by Cabezas [20] is adopted. Thus, the environmental impact objective function is as follows:

f₂ = 0.957P_D + [0.031g_PH + 0.008(1-g_PH)]P_G

(3)

Two continuous variables and four Boolean variables exist in the resulted MINLP model. In this simulation, binary code is adopted. String length is set to be 15 for each continuous variable and 1 for each Boolean variable. The population size m is 100, and the replacement size l is 60. For each individual chosen, the probability of both crossover and mutation is set to be 1.0. The value of finally reaches 0.05. We handle constraints by first normalizing them and then using the bracket-operator penalty function with a penalty parameter 1000. Figure 8 shows the population distribution in the initial generation and shows wide distribution. The economic and environmental objectives of individuals having different Boolean variables combinations differ greatly allowing obvious cluster behavior to be observed in the initial population. However, only the individuals having the combination of  “0101” survive in the final population, as shown in Figure 9. Thus, in the final optimum alternatives, adiabatical reactor and the membrane separator for the purge gas are adopted, while the isothermal reactor and membrane separator for the feed hydrogen are not. The schematic flowsheet of the resultant option is shown in Figure 10. The result obtained corresponds to the result of Kocis[21] that considers only the economic objective. Note that the economic objective is much higher than the one given by Kocis because the costs of separation subsystem are not involved on the level of recycling.

5. Concluding remarks

The framework for cleaner production problems presented here, to focus on three areas: MOEA, superstructure model and environmental merits. As the core of this framework, MOEA not only makes the economic and environmental objectives to be coped with simultaneously, but also provides a powerful solution to large scale engineering problems that result from cleaner production. As the base of the framework, superstructure model can be generated from cleaner production options. The model can be varied according to the generation of cleaner production options, for example, a life-cycle model may be generated if the upstream and downstream processes are considered. Compared to economic merits, environmental merits are difficult to measure, the selection of an appropriate environmental objective is also a multi-criteria problem with compromise between comprehensiveness/objectivity and simplicity.

Though the application on the problem of HDA plant synthesis on the decision level of recycling has proven the feasibility and effectiveness of this framework primarily, research on the three aspects mentioned above will continue.

Reference

[1] Allen DT, Rosselot KS. Pollution prevention for chemical processes. New York: John Wiley & Sons Inc, 1997.

[2] Buehner FW, Rossiter AP. Minimize waste by managing process design. CHEMTECH 1996; 13: 64-72.

[3] Cano-Ruiz JA, McRae GJ. Environmentally conscious chemical process design. Annu. Rev. of Energy and Environment 1998; 23: 499-536.

[4] Yang YQ, Shi L. Integrating environmental impact minimization into conceptual chemical process design - a process systems engineering review. Computers & Chemical Engineering 2000; 24(2-7): 1409-21.

[5] Rossiter AP, Spriggs HD, Howard KJ. Apply process integration to waste minimization. Chem. Eng. Progress 1993; 89(1): 30-36.

[6] Dantus MM, High KA. Economic evaluation for the retrofit of chemical processes through waste minimization and process integration. Ind. Eng. Chem. Res. 1996; 35: 4566-4578.

[7] Singh H, Smith R, Zhu XX. Economic achievement of environmental regulation in chemical process industries. Computers and Chemical Engineering 1998; 22: S917-S920.

[8] Dantus MM, High KA. Evaluation of waste minimization alternatives under uncertainty: a multiobjective optimization approach. Computers and Chemical Engineering 1999; 23: 1493-1508.

[9] Clark PA, Westerberg AW. Optimization for design problems having more than one objective. Computers and Chemical Engineering 1983; 7: 646-661.

[10] Grauer M, Lewandowski A, Wierzbicki A. Multiple-objective decision analysis applied to chemical engineering. Computers and Chemical Engineering 1984; 8: 285-293.

[11] Bhaskar V, Gupta SK, Ray AK. Applications of multiobjective optimization in chemical engineering. Reviews in Chem Eng 2000; 16(1): 1-54.

[12] Deb K. Evolutionary Algorithms for Multi-Criterion Optimization in Engineering Design. In Miettinen K, Mäkelä MM, Neittaanmäki P, Periaux J, editors, Evolutionary Algorithms in Engineering and Computer Science. Chichester (UK): John Wiley & Sons, 1999: 135-161.

[13] Carlos ACC. A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques. Knowledge and Information Systems, An International Journal 1999; 1(3):269-308.

[14] Efthimeros GA, Photeinos DI, Katsipou IG, Diamantis IG, Tsahalis DT. Optimisation of an industrial cogeneration system by means of a multiobjective genetic algorithms. In: Pierucci S, editor. Proceedings of the 10th European Symposium on Computer Aided Process Engineering. Florence (Italy), 2000: 25-29

[15] Shi L, Yao PJ. Multi-objective Evolutionary Algorithms for Solution of MILPs and MINLPs in Process Synthesis, Accepted by Chinese Journal of Chemical Engineering.

[16] Schaffer JD. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbaum, 1985: 93-100.

[17] Srinivas N, Deb K. Multi-objective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 1994; 2(3):221-248.

[18] Douglas JM. Conceptual Design of Chemical Processes. New York : McGraw-Hill, 1988.

[19] Shi L. Study on Process Integration Involving Environmental Impact. PHD Thesis (in Chinese), Dalian: Dalian Univ. of Technology, 1999.

[20] Cabezas H, Bare JC, Mallick SK. Pollution prevention with chemical process simulators: the generalized waste reduction(WAR) algorithm. Computers & Chem. Engng 1997; 21: S305-S310.

[21] Kocis GR, Grossmann IE. A modelling and decomposition strategy for the MINLP optimization of process flowsheets. Computers & Chem. Engng. 1989; 13(7): 797-819.