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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.
Key
words: Cleaner
production; Multi-objective programming; Multi-objective evolutionary
algorithms; Steady-state non-dominated sorting genetic algorithm
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 ε–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
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
. The variable is coded using binary strings of size 30. The
population size
is 100, and the replacement size
is 60.
The probability of crossover is set to be 1.0, and the same is to
mutation. The initial value of
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
for
with
as the global minimum and
as the local minimum
solutions. Variables are coded in 20-bit binary strings each, in the
ranges
and
. The population size
is 100, and the replacement size
is 60.
The probability of crossover is set to be 1.0, and the same is to
mutation. The value of
is 0.0125.
Figure 5 shows the
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.
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.
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.
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].
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
is 100, and the replacement size
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.
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