18th European Symposium on Computer Aided Process Engineering – ESCAPE 18
Bertrand Braunschweig and Xavier Joulia (Editors)
© 2008 Elsevier B.V./Ltd. All rights reserved.
Teaching Mono and Multi-objective Genetic
Algorithms in Process Systems Engineering: an
illustration with the MULTIGEN environment
Adrien Gomeza,b, Catherine Azzaro-Pantela,b, Luc Pibouleaua,b, Serge
Domenecha,b
a
ENSIACET INPT, 118 Route de Narbonne, Toulouse 31077 Cedex 04, France
Laboratoire de Génie Chimique, LGC UMR CNRS 5503, 5 Rue Paulin Talabot BP
1301, Toulouse 31106 Cedex 1,France
b
Abstract
Engineering design problems are usually characterized by the presence of many
conflicting objectives that the design has to fulfill. Therefore, it is natural to look at
many engineering problems as multi-objective optimization problems, with continuous
and integer variables. The case is commonly encountered in several process systems
engineering problems and such courses modules begin to make part of the curriculum of
chemical engineering education.
The aim of the paper is to develop the teaching strategy used in the master-level
program “EcoEnergy” given in ENSIACET (Toulouse, France) which presents the main
concepts of mono and multi-objective genetic algorithms. The MULTIGEN algorithm is
then applied to a gas turbine using natural gas as a fuel with a thermo-economic
optimization taking into account both the maximization of an efficiency criterion and
minimization of natural gas consumption, in order to reduce CO 2 emissions. The
students learn how to obtain and interpret Pareto fronts in multi-objective
configurations.
Keywords: Optimization, Multi-objective, Genetic Algorithm, Thermo Economy.
1. Introduction
Optimization of linear, nonlinear, mixed integer linear and nonlinear problems is
commonly encountered in several process systems engineering problems. Typical
application examples include heat and mass exchange network synthesis, distillationsequencing, reactors, utility systems, scheduling, planning and design of batch
processes, supply chain optimization, … Several elegant deterministic mathematical
programming techniques are usually taught in Process Systems Engineering
Departments. Heuristics, meta-heuristics, and evolutionary techniques like adaptive
random search, Simulated Annealing, Genetic Algorithms (GA) and Ant Colony
techniques that mimic the process of natural selection (see the reference books of
Holland, 1975 and Goldberg, 1989) are much less widespread in chemical engineering
education. A Conventional GA basically involves five components: a chromosomal
representation of potential solutions, an evaluation function mimicking the role of the
environment, selection of solutions in terms of their current fitness, genetic operators
that alter the chromosomes of children during reproduction and values of the
algorithmic parameters (population size, probabilities of applying genetic operators,
etc…). The main advantage of GAs over other methods is that a GA manipulates a
population of individuals, and provides the possibility to develop a strategy in which the
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A. Gomez et al.
population captures the whole Pareto front in one single optimization run. This paper
presents the teaching strategy used in the master-level program “EcoEnergy” given in
ENSIACET (Toulouse, France) which overviews the main concepts of mono and multiobjective genetic algorithms. The course (12 h) is illustrated with a computer-aided
education tool called MULTIGEN, designed as a library of algorithms with an Excel
interface, which is presented in detail in section 2 of this paper. The main objective is to
enable students to “get the knack” of using correctly stochastic methods, during 4 hours,
learning them how to find the optima of some well-known mathematical bench
problems, either in mono or in multi-objective cases, by performing a sensitivity
analysis on GA specific parameters (mutation and crossover rates, generation number,
population size, …). According to the Energy orientation topic of the “EcoEnergy”
program, students work on a gas turbine optimal design problem using gas as a fuel (8
hours), with the didactic support of MULTIGEN. They use a thermoeconomic approach
for maximizing electricity production and minimizing natural gas consumption, in order
to reduce CO2 emissions. Pure economic concepts are also considered with the
minimization of electricity production costs. The students obtain and interpret Pareto
fronts in multi-objective configurations, and discover how industrial considerations can
be taken into account for result analysis.
2. MULTIGEN environment description
2.1. MULTIGEN user-interface on Excel
Until now, genetic algorithms were not familiar tools for engineers, particularly in the
multiobjective case, which constitutes the major part of engineering problems.
MULTIGEN has a simple user interface, which is well-fitted to complex optimization
constrained problems, on Excel workbooks, using a specific toolbar and worksheet, as
shown in Fig. 1.
Keyword column Problem definition columns
Evolutionary Parameters
Algorithm Parameters
Additional Parameters
Excel Toolbar
Criteria Definition
Variables Definition
Additional Parameters
Size Extension
Zone (columns)
Constraint Definition
Data Calculation
Fig. 1 MULTIGEN user interface
The first column of the user interface (Fig. 1) contains keywords to locate the
information in the Excel sheet: for instance, NPOPULATION represents the number of
Teaching Mono and Multi-objective Genetic Algorithms in Process System
Engineering: an illustration with the MULTIGEN environment
3
individuals in a population. Comments are also added to the cells to avoid user
misunderstandings. An extensible zone makes it possible to define up to 255 criterions,
variables, constraints, and additional data (not involved in optimization) from models.
Mathematical problem formulation is performed very simply, just by establishing a link
between criteria and constraint cells and the MULTIGEN interface, or by a direct
formulation.
For stochastic methods such as GAs, the main objective is to ensure a safe
communication between the mathematical model and the algorithm core of
MULTIGEN. With a black box model, commonly used by engineers for design tasks,
there is an uncertainty related to the current solution feasibility for a given set of
decision variables, so it is possible that a black box model returns nothing! On Excel
worksheets, when a function does not give a result, generally returning an error
message, a numerical value is assigned to the non-computed criterion or constraint, to
avoid an irreversible stopping of the GA running. The selected method consists in
applying a high penalization value for the infeasible solutions. The automatic checking
procedure returns error messages, using window dialog boxes, to indicate the error type
and locus on the interface sheet with instructions to correct them.
2.2. Algorithm library content
Due to the mathematical problems diversity, it is well-known that a general algorithm
able to solve all the problems perfectly does not exist. The only solution is to implement
several algorithms, distinguishing them by their structure and by the variable category
types (continuous, integer or binary) and collect them into a library: following this
principle, five different algorithms are available in MULTIGEN (Table. 1).
Table 1. Algorithms available in the MULTIGEN library
Algorithm
NSGA-II
NSGA-IIb
NSGA-II MI
NSGA-II MIB
NSGA-II MIB structural
Continuous
variables
X
X
X
X
X
Integer variables
X
X
X
Binary variables
X
X
All the implemented algorithms are based on NSGA-II (Deb & al., 2002) structure, with
different genetic operators included in the MULTIGEN genetic operator library. NSGAII is an elitist multi-objective algorithm including population diversity management.
Mixed Integer (MI) and Mixed Integer and Binary (MIB) problems can be also treated.
MIB structural problems are based on particular rules, taking into account links between
binary or integer variables (existence or not of components in a flow sheet) and
continuous variables (temperature, pressure …).
3. Teaching Mono/Multiobjective Genetic Algorithm: from
mathematical problem to gas turbine performance optimization
pure
3.1. General description of training
The main objective of this training course is first to make students familiar with GA
specific use for the resolution of pure mono/multiobjective mathematical problem, by
studying the impact of parameters such as mutation and crossover rates and density
probabilities, generation numbers and population sizes, on Pareto front quality. Then,
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A. Gomez et al.
after gaining practical experience with these numerical experiments, students are ready
for tackling an engineering problem related to a technico-economic optimization of a
gas turbine, as a concrete application in connection with the other “EcoEnergy” training
courses.
3.2. GA parameters sensitivity analysis
Three mathematical problems are studied with the didactic support of MULTIGEN.
Only one of these simple problems is presented here as an illustrative example (Eqn. 1.).


Min f1x   x1
g1( x )  x2  9 x1  6

1 x2  g ( x )   x  9 x  1
Min f 2 ( x ) 
2
2
1
x1

x  x1, x2 , x1  [0,1 ; 1], x2  [0 ; 5]
(Eqn. 1. )
Students have to perform several runs with a given range of variation for some
parameters, i.e. crossover probability from 0 to 90%, mutation rate from 0 to 50%, with
a population of 100 individual along 300 generations. A sensitivity study of these
parameters is a quite difficult task for an inexperienced user, and only the general trends
were studied. An increase in crossover probability improves the search mechanism but
decelerates the convergence speed, whereas the mutation rate growth favours the
capacity to extract the search from a local optimum. These tendencies are quite difficult
to check by a simple observation. Without implementing quite sophisticated statistical
indicators, only the impact of the generation number on the Pareto front can be easily
detected (see Fig. 2).
10
9
8
Generation 0
Generation 10
Generation 300
7
f2
6
5
4
3
2
1
0
0,3
0,4
0,5
0,6
0,7
f1
0,8
0,9
1
1,1
Fig. 2. Generation number impact on Pareto Front Evolution
3.3. Thermoeconomic optimization of a gas turbine
The thermoeconomic optimization of electricity production by a gas turbine (Fig. 3) is
finally proposed, with thermodynamic and cost models of gas turbine taken from
Silviera and Tuna (2003, Part I & II) with the following assumptions: steady state
operational conditions, ideal gas model for air and combustion products, complete
combustion reaction; adiabatic components except combustion chamber. Pressure losses
for combustion chamber and air pre-heater are fixed, as well as isentropic efficiencies
for compressor and turbine. The first task for the students was to build the
thermodynamic model of the gas turbine using enthalpy balance for each component,
and considering a polytropic transformation for both the compressor and turbine: the
objective is to assess temperature, pressure and flow for each point in the gas turbine.
The second step was to check the operational rates of the gas turbine.
Teaching Mono and Multi-objective Genetic Algorithms in Process System
Engineering: an illustration with the MULTIGEN environment
5
Whatever the optimization criterion, the optimization variables are turbine pressure
ratio, combustion gas flow rate, turbine outlet temperature and air-preheater efficiency.
Air Pre-Heater
mGas
mFuel
Electric
Production
COMBUSTION
CHAMBER
mAir
Air
Compressor
Gas Turbine
Fig. 3. Gas Turbine system flowsheet
3.3.1. Gas Turbine operational regime study
It is then interesting to study the optimal relation between fuel gas consumption and
electricity production. Logically, the decrease in fuel consumption, in order to reduce
CO2 and to minimize operating cost, implies a decrease in electrical production. An
optimal operative condition set yet exists for a maximal electrical output. The objective
was to find this set of solutions maximizing electrical output and minimizing the fuel
flow rate. At first sight, the Pareto Front (Fig. 4) presents three distinct operative zones
with the associated operating conditions presented in Table 2.
1300
1200
28500
Zone I
24500
P élec (kW)
P élec (kW)
20500
Zone II
1000
900
800
16500
Zone I
12500
700
8500
600
4500
500
0,06
Zone III
Zone II
1100
500
0,065
0,07
0,075
0,08
0,085
0,09
0,095
0,1
0
mFuel (kg/s)
0,5
1
1,5
2
2,5
mFuel (kg/s)
Fig. 4. Optimal relation between fuel consumption and electric output.
Table 2. Operating conditions for optimal zones I, II & III
Zone
I
II
III
Pr
(Turbine)
8  8.05
8.05  15
15
Tout (°C)
(Turbine)
450  597
600
600
Preheater
efficiency (%)
95
95
88.7  0
Electrical
Output (kW)
498  947
960  26380
26460  26640
Fuel (kg/s)
0.06 0.07
0.07  1.96
1.98  2.16
3.3.2. Thermoeconomic optimization of the Gas Turbine
The final part consists in finding the optimal conditions, from the thermodynamics point
of view, while considering jointly the economical aspect. The economic criterion is the
annualized production cost of electricity (Eqn. 2).
I   CMaintenance  CFuel  / 1  i  p
10
APC 
p 1
H  PElec
(Eqn. 2. )
This objective function takes into account investment (I), maintenance and fuel costs,
with an actualization rate of 8 % per year during 10 years, and an operational period of
8000 hours per year. Maintenance costs represent 6 % per year of capital cost. Two
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A. Gomez et al.
cases are studied: fixing air pre-heater efficiency at 95 % (case 1), and considering this
efficiency as a variable (case 2) (see Pareto Fronts of both cases in Fig. 5).
0,195
0,0125
2,2
CASE 1: Eff Pre-Heater = 95%
0,012
2,15
CASE 2: Eff Pre-Heater = 0%
0,0115
2,1
0,011
2,05
0,193
Case 1 Scale
CASE 2: Eff Pre-Heater = 0%
0,0105
0,192
0,01
0,191
0,0095
0,009
0,19
Case 2 Scale
0,189
20 20,5 21 21,5 22 22,5 23 23,5 24 24,5 25 25,5 26 26,5 27
Pelec (MW)
0.192 kg/s
m Fuel (kg/s)
APC ($US 2003/kWhelec)
CASE 1: Eff Pre-Heater = 95%
0,194
2
0.314 kg/s
1,95
1,9
1,85
0,0085
1,8
0,008
1,75
20
21
22
23
24
25
26
27
Pelec (MW)
Fig. 5. Influence of Pre-Heater efficiency on production cost & fuel consumption
The optimization of case 2 provides solutions without air pre-heater, with fuel rate up to
2.03 kg/s (Fig. 5., right side), whereas the pre-heater efficiency is a variable. For an
efficiency set at 95% (case 1), it can be pointed that production costs are multiplied by
ten, with a fuel consumption lower than 1.98 kg/s. The important difference between
these two cases implies that there is no interest in a pre-heater investment because the
fuel purchase cost (0.01092 $/kWh) is too low: if a CO2 tax is imposed, the use of the
pre-heater may be economically profitable.
4. Conclusions
The teaching objectives of the master-level program “EcoEnergy” are twice. First,
students learn how to use multiobjective GAs with the MULTIGEN environment, and
to perform a parameter sensitivity analysis, only based on a simple observation of the
Pareto front quality. The second step of the teaching course consists in applying the
acquired knowledge on GAs to tackle a thermoeconomic problem related to a gas
turbine. Two points of view are emphasized: an “industrial” one with a unique objective
for production cost minimization (even if there is an increase in fuel consumption), and
an “energy efficiency” one with the computation of the efficient relation between
electrical output and fuel consumption, without any economic consideration. It is
emphasized that metaheuristic methods as GAs, can handle complex engineering
problems, particularly within a multiobjective perspective. The simplicity of
MULTIGEN using enables students to focus on the interpretation of results analysis of
the physical model of gas turbine.
References
K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, 2002, A Fast and Elitist Multiobjective Genetic
Algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, Volume 2, issue 6,
182-197
D.E. Goldberg, 1989, Genetic Algorithms in Search, Optimization, and Machine Learning.
Addison-Wesley Publishing company.
H.J. Holland, 1975, Adaptation in natural and artificial system, Ann Harbor, The University of
Michigan Press, 1975
J. L. Silveira, C. E. Tuna, 2003, Thermoeconomic analysis method for optimization of combined
heat and power systems. Part I, Progress in Energy and Combustion Science, 29, 479-485
J. L. Silveira, C. E. Tuna, 2003, Thermoeconomic analysis method for optimization of combined
heat and power systems. Part II, Progress in Energy and Combustion Science, 30, 673-678