Using evolutionary algorithms to determine the environmental projects effectiveness

Abstract

Environmental projects have a high degree of uncertainty and risk of their implementation. In the process of assessing their effectiveness, it is necessary to take into account the interests of all the participants in the environmental project. The environmental projects effectiveness evaluation is formalized in the form of a mathematical problem of nonlinear programming with Boolean variables with constraints such as equality and inequality. To solve it, the interactive genetic algorithm for the environmental projects implementation trajectory formation was developed.

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Using evolutionary algorithms to determine the environmental projects
effectiveness
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Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
1
Using evolutionary algorithms to determine the environmental
projects effectiveness
I B Mamai1, B I Savelyev1, S V Pronichkin1,2,3, and A V Kholstov4
1Federal Center of Theoretical and Applied Sociology of Russian Academy of
Sciences, 24/35, Krzhizhanovsky Street, Moscow, 117218, Russia
2Federal Research Center “Computer Science and Control” of Russian Academy of
Sciences, 40, Vavilov Street, Moscow, 119333, Russia
3National University of Science and Technology "MISiS", 4, Leninsky Prospect,
Moscow, 119049, Russia
4N.N. Semenov Federal Research Center for Chemical Physics Russian Academy of
Sciences, 4, Kosygina Street, Moscow, 119991, Russia
E-mail: ibmamay@yandex.ru
Abstract. Environmental projects have a high degree of uncertainty and risk of their
implementation. In the process of assessing their effectiveness, it is necessary to take into
account the interests of all the participants in the environmental project. The environmental
projects effectiveness evaluation is formalized in the form of a mathematical problem of
nonlinear programming with Boolean variables with constraints such as equality and
inequality. To solve it, the interactive genetic algorithm for the environmental projects
implementation trajectory formation was developed.
1. Introduction
The development and use of systems for assessing the sustainability of ecosystems is essential to
address the depletion of natural resources, as well as the increase in energy consumption and
associated greenhouse gas emissions in large cities and suburbs. Composite indicators are an effective
means of assessing, comparing and communicating indicators of ecosystem resilience, stimulating
active participation and involvement of a wide range of stakeholders in decision-making processes.
The efficiency in the use of natural resources and improvement in environmental performance are
usually given priority over other dimensions. The peculiarities of tools for ensuring the sustainability
of complex socio-economic systems are manifested in innovative projects, which are currently more
focused on the environment than on the social and economic dimensions of sustainability. Sustainable
development of ecosystems should take into account, first of all, the need to achieve a long-term
balance between social and economic characteristics of environmental projects.
Environmental projects have a high degree of uncertainty and the risk of their implementation; a
long period passes from idea to implementation. In addition, there are possible cases of revision,
which increase both the direct costs of additional research and the time indicators of their
implementation. These features directly affect the assessment of the projects economic efficiency, as
they increase costs and the payback period of investments.

Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
2
2. Investment design of environmental projects
Recently, decision support systems (DSS) for investment design of environmental projects are
becoming more widespread [1, 2]. Such systems combine data from internal and external sources and
generate analytical information on their basis, thanks to which the subjects of management carry out
the decision-making process. With the right approach to building a DSS, all the participants in the
environmental project should have a powerful and convenient tool to support decision-making at any
stage of an investment project. In this case, the system should be built in such a way as to ensure the
formation of retrospective, current and forecast reporting. Such a structure will allow solving the
following main tasks of investment design:
 evaluating the effectiveness of investment decisions in the environmental retrospective;
 formation of operational reporting on the current state of the environmental project;
 obtaining predictive information of high value and allowing to take preventive measures to
manage an environmental project;
 tracking and modeling the dynamics of the ecological project development, taking into
account the control actions.
In the process of investment design, many different factors must be considered, such as cash flows
in the form of net discounted income, payback period, return on investment and profitability index. At
the same time, the internal rate of return, payback period and profitability should not be used as an
environmental project effectiveness criterion, but only as a limitation in decision making. And the use
of the principle of "maximum net discounted income" seems to be the most correct and theoretically
justified.
In the process of effectiveness assessing, it is necessary to take into account the interests of all the
participants in the environmental project. The efficiency assessment should be made not in general,
but for some specific participant based on a comparison of cash inflows and cash outflows from the
project from this participant. Of course, at the first stage of calculations, when specific participants
have not yet decided, it is possible and necessary to assess the environmental project effectiveness for
one participant. But this participation efficiency in the environmental project is true if the participant
implements the entire project at his own expense. Such a calculation of the environmental project
effectiveness for one participant can be carried out at the final stages of investment project the
implementation in order to advertise it, in order to attract investors, turn them from potential into real
ones by providing information about the high efficiency of the project. And then, at the next stage,
calculate the efficiency for each participant, for his own capital.
The use of investment decision support systems allows developing special evolutionary strategies
for investing funds of participants in the environmental project [3, 4]. In such systems, the optimal
trajectories of management decisions for each project participant are used as the initial population.
In existing papers, the sum of the net discounted income (NDI) of the project participants or their
average value is used as an objective function characterizing the optimal trajectory of all the project
participants [5, 6]. The algorithms for finding the optimal trajectory are based on excluding
investments from the initial trajectory that have the lowest NDI until the condition of exceeding the
threshold value is met.
Such algorithms have a number of disadvantages, since they do not take into account the limitation
on the payback period for each participant and on the level of profitability; the solution may be a
trajectory in which the NDIs for each participant are very different.
3. Social effectiveness of environmental projects
The assessment of public effectiveness implies that the only participant in an environmental project is
the whole society, which implements the project entirely at its own expense, evaluates inflows and
outflows from the point of view of public interests, not at market prices, but at economic prices,
reflecting the usefulness of resources and products from a social point of view - the economic interests
of society as a whole, and not in the way the market estimates it. These prices differ significantly from
the market ones, and the society receives all the incomes from the project calculated on them
(including taxes) and bears all the necessary expenses. It is clear that for such a participant, no loans

Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
3
and other transfer payments (taxes, subsidies, loan repayment, etc.) should be taken into account in the
calculation, since from the point of view of the system as a whole society, they represent a zero
financial transaction: one element of the system loses a certain amount, and the other gets it, while the
system balance is zero.
When assessing the investment project effectiveness, it is also important to take into account the
organizational and technical problems that may arise during its implementation, including changes in
the nature of relations between managers and line personnel [7, 8]. These tasks include both the
organization and management of personnel, and the determination of new environmental products
production volume, taking into account the needs and opportunities of the market, the search and
attraction of material and technical resources, ensuring the sale of products, conducting timely
settlements with suppliers and consumers, determining the competitiveness of new products, etc. In
order to effectively implement R&D, the manager must have clearly defined goals. After all, not every
enterprise is able to implement science-intensive environmental technology. At the same time, the
range of tasks that need to be solved and for which one need to answer is significantly expanding. It is
necessary to implement a system of measures to ensure a consistent and predictable for the long term
process of mastering the results of scientific and technical activities, taking into account the
requirements for the efficiency of the natural resources use by enterprises, the safety of products
(services) for the environment and public health and the reduction of energy and material
consumption, as well as the determination a system of appropriate rewards and sanctions. The
specified system should include such measures as improving the qualifications of management
personnel, promoting cooperation between manufacturers, stimulating the formation of manufacturers'
associations, encouraging those who buy and apply new environmental technologies, reducing or
abolishing customs duties on the import of modern equipment, personnel training, policy public
procurement and the provision of preferences to companies and products that use certain technological
solutions [9].
4. Genetic algorithms for the environmental projects implementation the trajectory formation
The following formulation of the problem of forming a trajectory for the environmental projects
implementation is proposed - it is required to select one of the many options for management decisions
that has the maximum NDI so that NDIs in the group of participants in the investment project do not
differ much, and the internal rate of return, payback period and profitability index do not exceed a
given value.
The mathematical formulation of the problem is the objective function (1) as a parametric
convolution of the mean and standard deviation of NDI
d
K
for each participant in the environmental
project
d
ps
. Internal rate of return
d
IRR
, payback period
d
PP
and profitability
d
PI
form constraints
(2).
**
*
2
()
g( ) (1 ) min
1
d d d d
d D d D
ps PS
K ps K K ps
ps mm



  
   


, (1)
where
*
()
ddD
ps ps 

is the group of participants in the environmental project;
*
*{}
ddD
PS PS 

is a set of potential participants in the environmental project;
1,if the d-th potential participant participates in the project
0, otherwise
d
ps 


;
*dd
dD
K ps
Km



is the
average NDI;

is a model parameter,
]1,0[

.

Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
4
*
*
;
,
d
dD
dv d v
dD
ps m
C ps b






(2)
where
dv
С
is the interest of the participation
d
-th potential participant in the environmental
project
{ , , }v IRR PP PI
;
The formulated equation is a nonlinear programming equation with Boolean variables with
constraints such as equality and inequality. The upper bound for the complexity of the exact algorithm
for solving the equation is exponential, i.e. the task is np-full.
To solve the problem, the algorithm was developed, which is based on the approach of
evolutionary computations - genetic algorithms. Genetic algorithms make it possible to obtain a
“good” solution relatively quickly (in a finite number of steps) [10]. The proposed algorithm consists
of the following basic operations: generation of the initial population; selection of parental couples;
the use of crossover operators; calculation of the fitness function; selection; checking the condition of
population degeneration, if it is satisfied, apply the inversion operator; check the break condition, if it
is not met go to the selection of parent pairs.
1. Set
T
– number of iterations,
m
,
b
,

,
E
– population size,
0

.
2.
0t
. Generate (uniform distribution) the initial population
},,{ 1t
E
tt ppP 
, where
*
*
1
( ) ( )
D
t t t
e ed d ed dD
p p ps


–
e
-th chromosome of the population,
Ee ,1
, is satisfying (2).
Calculate








 t
e
tC
e
t
e
tC
e
t
e
t
e
t
es
s
s
s
pvpvpv 21 ,))(),(()( 21
,
21 tC
e
tC
e
t
esss 
,
21 ,tC
e
tC
ess
– the number of
applications of the crossing over operators for
e
-th chromosome at the iteration
t
, for
0t
,






2
1
,
2
1
)( t
e
pv
,
0, 21 
tC
e
tC
ess
.
3. Calculate
},,{ 1t
E
tt ffF 
,
)( t
e
t
epgf 
,
Ee ,1
by (1).
4. Sort
t
F
,
}1,1,:{ 1
' EefffF t
e
t
e
t
e
t
. Find quartiles
4
1
)(: 4
1
4
1 tt
e
tffpf
and
4
3
)(: 4
3
4
3 tt
e
tffpf
,
Ee ,1
. Select randomly (uniform distribution)
])([: 4
1
4
1
4
11tt
e
tt
efpgfp 
,
])([: 4
3
2
1
4
1
2
1
tt
e
tt
efpgfp 
,
])([: 4
3
4
3
4
3
t
E
t
e
tt
efpgfp 
,
Ee ,1
from
t
P
. Find
)),(minarg( 4
1
*
4
1
t
e
t
eH
e
t
eppDp 
,
)),(minarg( 2
1
*
2
1
t
e
t
eH
e
t
eppDp 
,
)),(maxarg( 2
1
**
2
1
t
e
t
eH
e
t
eppDp 
,
)),(maxarg( 4
3
*
4
3
t
e
t
eH
e
t
eppDp 
, where
H
D
is Hamming distance.
5. For
t
e
p*
4
1
,
t
e
p*
2
1
,
t
e
p**
2
1
,
t
e
p*
4
3
choose randomly with probability
)( 1
1t
x
pv
,
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
operator
1
C
, or
2
C
with probability
)( 1
2t
x
pv
,
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
. In the case of choosing a one-

Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
5
point crossing-over operator
),( 21
1t
x
t
xppC
, where
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
,
 
4
3
2
1
4
1,,
2eeex 
, generate
r
(uniform distribution
),1( *
D
), calculate
*
11 1
'' )( D
d
tdx
t
xpp 

, where
1
1
2
',
,
t
xd
t
xd t
xd
p if d r
pp if d r





,
1
1
1
1
1 tC
x
tC
xss
, and
*
22 1
'' )( D
d
tdx
t
xpp 

, where
2
2
1
',
,
t
xd
t
xd t
xd
p if d r
pp if d r





,
1
1
2
1
2 tC
x
tC
xss
. In the case of
choosing a two-point crossing-over operator
),( 21
2t
x
t
xppC
, where
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
,
 
4
3
2
1
4
1,,
2eeex 
, generate
1
r
and
2
r
(uniform distribution
),1( *
D
), let
21 rr 
, calculate
*
11 1
'' )( D
d
tdx
t
xpp 

, where
1
12
1
1
'12
2
,
,
,
t
xd
tt
x d x d
t
xd
p if d r
p p if r d r
p if r d



  




,
1
2
1
2
1 tC
x
tC
xss
, and
*
22 1
'' )( D
d
tdx
t
xpp 

, where
2
21
2
1
'12
2
,
,
,
t
xd
tt
x d x d
t
xd
p if d r
p p if r d r
p if r d



  




,
1
2
2
2
2 tC
x
tC
xss
.
6. Check for
t
x
p'
1
and
t
x
p'
2
where
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
,
 
4
3
2
1
4
1,,
2eeex 
the fulfillment of (2).
Add in
},,{ 1t
E
tt ppP 
,
q
new chromosomes
t
x
p'
1
and
t
x
p'
2
where
 
*****
14
3
2
1
2
1
4
1,,, eeeex 
,
 
4
3
2
1
4
1,,
2eeex 
, are satisfying (2). Calculate
},,{ 1tqE
tt ffF 

.
7. Conduct sorting
t
F
,
}1,1,:{ 1
' qEefffF t
e
t
e
t
e
t
. Conduct an "elite selection" to
take the first
E
individuals.
8. Check the fulfillment of the inequations

 1
11 tt ff
and
T1t
. If the inequations are not
met, then go to step 10.
9. Set
L
. Choose randomly (uniform distribution)
t
e
p1
,
t
e
p2
,…,
t
eL
p
from
}{\ *
t
e
tpP
, where
)( *
1t
e
tpgf 
. For
t
x
p3
,
),,,( 213 L
eeex 
apply the "inversion" operator
)( 3
t
x
pR
, generate
1
r
and
2
r
(uniform distribution
),1( *
D
), calculate
*
33 1
'' )( D
d
tdx
t
xpp 

, where
3
3 3 2
31
12
'1
2
,,
,
,
t
xd
tt
x d x r
t
xr
p if d r r
p p if d r
p if d r








,
replace
t
x
p3
for
t
x
p'
3
,
),,,( 213 L
eeex 
in
}{\ *
t
e
tpP
, if
t
x
p'
3
,
),,,( 213 L
eeex 
satisfy (2).
10.
1 tt
.

Artificial Intelligence and Digital Technologies in Technical Systems II-2021
Journal of Physics: Conference Series 2060 (2021) 012009
IOP Publishing
doi:10.1088/1742-6596/2060/1/012009
6
11. Check the inequation
Tt
, if the inequation is satisfied go to step 3.
12. Remember

and
t
e
p*
, such that
tt
efpg 1
)( *
,
1.0

.
13. Check the inequation
1

, if the inequation is satisfied go to step 2.
14. If the solution is not found go to step 1.
The main difference between the proposed genetic algorithm and the existing genetic algorithms
[11-13] is the step - “choosing a parental pair”. It is proposed to use outbreeding and inbreeding when
choosing "parental pairs", and the use of quartiles makes the choice of "parental pairs" robust to the
distribution of chromosomes, which is confirmed by computational experiments. In the proposed
algorithm, new individuals obtained as a result of the implementation of the crossing-over operator do
not replace their parents, but form an intermediate population with them, to which the “elite” selection
operator is subsequently applied. Also the inversion operator is used instead of the mutation operator
based on the specifics of the problem.
5. Conclusion
The proposed algorithm makes it possible to search more efficiently in local optima, which actually
leads to the division of the population into separate local groups around trajectories suspicious for an
extremum with a shift towards the global optimum, which is confirmed by testing on experimental
data.
At the same time, the proposed approach, together with the parameterization of the "inversion"
operation, is aimed at preventing the convergence of the algorithm to the already found local solutions
and allows the decision-maker to view new, unexplored combinations in an interactive mode. As the
result, the decision maker of the DSS receives the optimal trajectory for the participants of the
environmental project, which has the maximum NDI. Moreover, the NDIs of the project participants
are not very different, and the internal rate of return, payback period and profitability index do not
exceed the specified values.
6. Acknowledgments
The article is prepared with the financial support of the Russian Science Foundation, project № 19-78-
10035.
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