Multi-energy systems (MES) play a key role in solving many significant problems related to economic efficiency, reliability, and impacts on the environment. The multiplicity of goals pursued in the creation of MES gives rise to the problem of multi-criteria choice. The long-life cycle of MES and different development scenarios cause uncertainty in the preferences of decision makers. Focusing on these problems, the article proposes a framework for MES sizing based on multi-criteria optimization and decision-making techniques. Multi-criteria optimization is carried out to find Pareto-optimal MES configurations using the metaheuristic non-dominated sorting genetic algorithm III (NSGA-III). Multi-criteria evaluation of Pareto front alternatives under uncertainty of preferences is performed with fuzzy technique for order of preferences by similarity to ideal solution (TOPSIS). To develop MES that is the most suitable for various scenarios, a new indicator is proposed within the multi-scenario approach, calculated as the geometric mean of fuzzy TOPSIS assessments. The effectiveness of the proposed framework is demonstrated for a remote settlement located on the coast of the Sea of Japan under three scenarios. The geometric mean indicator through the multi-scenario approach identified the MES configuration most suitable for all considered scenarios (levelized cost of energy 0.21 $/kW h (within the interval 0.178–0.275), investment costs 294 289 $(43 573–535 439), CO2 emission 43 008 kg/year (3069–118 542), and unmet load 3262 kW h/year (0–24 044). Furthermore, for the problem being solved, the modified Inverted Generational Distance indicator was used to compare NSGA-III and NSGA-II algorithms. The superiority of NSGA-III over NSGA-II was confirmed (intervals of the indicator estimates are 1874–4040 and 3445–21 521, respectively).

1.
Abid
,
M.
,
Apon
,
H. J.
,
Nafi
,
I. M.
,
Ahmed
,
A.
, and
Ahshan
,
R.
, “
Multi-objective architecture for strategic integration of distributed energy resources and battery storage system in microgrids
,”
J. Energy Storage
72
,
108276
(
2023
).
2.
Aoun
,
N.
, “
Methodology for predicting the PV module temperature based on actual and estimated weather data
,”
Energy Convers. Manage.
14
,
100182
(
2022
).
3.
See https://atb.nrel.gov/electricity/2024/data for
Annual Technology Baseline NREL
(
2023
).
4.
Aydoğdu
,
E.
,
Güner
,
E.
,
Aldemir
,
B.
, and
Aygün
,
H.
, “
Complex spherical fuzzy TOPSIS based on entropy
,”
Expert Syst. Appl.
215
,
119331
(
2023
).
5.
Bertsiou
,
M.
,
Feloni
,
E.
,
Karpouzos
,
D.
, and
Baltas
,
E.
, “
Water management and electricity output of a Hybrid Renewable Energy System (HRES) in Fournoi Island in Aegean Sea
,”
Renewable Energy
118
,
790
798
(
2018
).
6.
Bonamini
,
G.
,
Colombo
,
E.
,
Llorca
,
N.
, and
Sanchez-Soriano
,
J.
, “
Cost allocation for rural electrification using game theory: A case of distributed generation in rural India
,”
Energy Sustainable Dev.
50
,
139
152
(
2019
).
7.
Cao
,
Y.
,
Wang
,
L.
,
Jiang
,
S.
,
Yang
,
W.
,
Zeng
,
M.
, and
Guo
,
X.
, “
Optimal operation of cold–heat–electricity multi-energy collaborative system based on price demand response
,”
Global Energy Interconnect.
3
(
5
),
430
441
(
2020
).
8.
Chen
,
C.-T.
, “
Extensions of the TOPSIS for group decision-making under fuzzy environment
,”
Fuzzy Sets Syst.
114
(
1
),
1
9
(
2000
).
9.
Chen
,
C.-T.
and
Chiu
,
Y.-T.
, “
A study of dynamic fuzzy cognitive map model with group consensus based on linguistic variables
,”
Technol. Forecasting Soc. Change
171
,
120948
(
2021
).
10.
Das
,
B. K.
,
Hassan
,
R.
,
Tushar
,
M. S. H. K.
,
Zaman
,
F.
,
Hasan
,
M.
, and
Das
,
P.
, “
Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh
,”
Energy Convers. Manage.
230
,
113823
(
2021
).
11.
Das
,
I.
and
Dennis
,
J. E.
, “
Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems
,”
SIAM J. Optim.
8
(
3
),
631
657
(
1998
).
12.
Deb
,
K.
and
Jain
,
H.
, “
An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: Solving problems with box constraints
,”
IEEE Trans. Evol. Comput.
18
(
4
),
577
601
(
2014
).
13.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
, “
A fast and elitist multiobjective genetic algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
6
(
2
),
182
197
(
2002
).
14.
Ghilardi
,
L. M. P.
,
Castelli
,
A. F.
,
Moretti
,
L.
,
Morini
,
M.
, and
Martelli
,
E.
, “
Co-optimization of multi-energy system operation, district heating/cooling network and thermal comfort management for buildings
,”
Appl. Energy
302
,
117480
(
2021
).
15.
Glücker
,
P.
,
Pesch
,
T.
, and
Benigni
,
A.
, “
Optimal sizing of battery energy storage system for local multi-energy systems: The impact of the thermal vector
,”
Appl. Energy
372
,
123732
(
2024
).
16.
Guo
,
F.
,
Li
,
Y.
,
Xu
,
Z.
,
Qin
,
J.
, and
Long
,
L.
, “
Multi-objective optimization of multi-energy heating systems based on solar, natural gas, and air- energy
,”
Sustainable Energy Technol. Assess.
47
,
101394
(
2021
).
17.
Han
,
H.
,
Ge
,
Y.
,
Wang
,
Q.
,
Yang
,
Q.
,
Xing
,
L.
,
Ba
,
S.
,
Chen
,
G.
,
Tian
,
T.
,
Chen
,
X.
, and
Jian
,
P.
, “
Life cycle techno-economic-environmental optimization for capacity design and operation strategy of grid-connected building distributed multi-energy system
,”
Renewable Energy
230
,
120766
(
2024
).
18.
Hwang
,
C. L.
and
Yoon
,
K.
, “
Methods for multiple attribute decision making
,” in
Multiple Attribute Decision Making: Methods and Applications. A State-of-the-Art Survey
, edited by
Hwang
,
C.-L.
and
Yoon
,
K.
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
1981
), pp.
58
191
.
19.
Ishibuchi
,
H.
,
Masuda
,
H.
,
Tanigaki
,
Y.
, and
Nojima
,
Y.
, “
Modified distance calculation in generational distance and inverted generational distance
,” in
Evolutionary Multi-Criterion Optimization
, edited by
Gaspar-Cunha
,
A.
,
Henggeler Antunes
,
C.
, and
Coello
,
C. C.
(
Springer International Publishing
,
Cham
,
2015
), pp.
110
125
.
20.
See https://www.irena.org/Publications/2023/Aug/Renewable-Power-Generation-Costs-in-2022 for “
IRENA, Renewable Power Generation Costs in 2022
(
2022
).”
21.
Ivanova
,
I. Y.
,
Shakirov
,
V. A.
,
Ermakov
,
M. V.
, and
Bukher
,
F. S.
, “
Feasibility study of using geothermal heat-pump units for substituting small-capacity coal-fired boiler houses (taking the Baikal natural area as an example)
,”
Therm. Eng.
67
,
741
750
(
2020
).
22.
Jiang
,
W.
,
Wang
,
X.
,
Huang
,
H.
,
Zhang
,
D.
, and
Ghadimi
,
N.
, “
Optimal economic scheduling of microgrids considering renewable energy sources based on energy hub model using demand response and improved water wave optimization algorithm
,”
J. Energy Storage
55
,
105311
(
2022
).
23.
Klemm
,
C.
and
Vennemann
,
P.
, “
Modeling and optimization of multi-energy systems in mixed-use districts: A review of existing methods and approaches
,”
Renewable Sustainable Energy Rev.
135
,
110206
(
2021
).
24.
Kumar
,
R.
and
Channi
,
H. K.
, “
A PV-Biomass off-grid hybrid renewable energy system (HRES) for rural electrification: Design, optimization and techno-economic-environmental analysis
,”
J. Cleaner Prod.
349
,
131347
(
2022
).
25.
Lin
,
Y.
,
Yang
,
Q.
,
Zhou
,
J.
,
Chen
,
X.
, and
Wen
,
J.
, “
A time-coupling consideration for evaluation of load carrying capacity in district multi-energy systems
,”
Appl. Energy
351
,
121842
(
2023
).
26.
Liu
,
L.
,
Zhai
,
R.
, and
Hu
,
Y.
, “
Multi-objective optimization with advanced exergy analysis of a wind-solar‐hydrogen multi-energy supply system
,”
Appl. Energy
348
,
121512
(
2023
).
27.
Luo
,
X.
,
Liu
,
J.
,
Liu
,
Y.
, and
Liu
,
X.
, “
Bi-level optimization of design, operation, and subsidies for standalone solar/diesel multi-generation energy systems
,”
Sustainable Cities Soc.
48
,
101592
(
2019
).
28.
Ma
,
X.
,
Deveci
,
M.
,
Yan
,
J.
, and
Liu
,
Y.
, “
Optimal capacity configuration of wind-photovoltaic-storage hybrid system: A study based on multi-objective optimization and sparrow search algorithm
,”
J. Energy Storage
85
,
110983
(
2024
).
29.
Madi
,
E. N.
,
Garibaldi
,
J. M.
, and
Wagner
,
C.
, “
A comparison between two types of fuzzy TOPSIS method
,” in
2015 IEEE International Conference on Systems, Man, and Cybernetics
(
IEEE
,
2015
), pp.
291
297
.
30.
Maleki Tehrani
,
M.
,
Akhtari
,
M.
,
Kasaeian
,
A.
,
Vaziri Rad
,
M. A.
,
Toopshekan
,
A.
, and
Sadeghi Motlagh
,
M.
, “
Techno-economic investigation of a hybrid biomass renewable energy system to achieve the goals of SDG-17 in deprived areas of Iran
,”
Energy Convers. Manage.
291
,
117319
(
2023
).
31.
Mancò
,
G.
,
Tesio
,
U.
,
Guelpa
,
E.
, and
Verda
,
V.
, “
A review on multi energy systems modelling and optimization
,”
Appl. Therm. Eng.
236
,
121871
(
2024
).
32.
Mejía-Giraldo
,
D.
,
Velásquez-Gomez
,
G.
,
Muñoz-Galeano
,
N.
,
Cano-Quintero
,
J. B.
, and
Lemos-Cano
,
S.
, “
A BESS sizing strategy for primary frequency regulation support of solar photovoltaic plants
,”
Energies
12
(
2
),
317
(
2019
).
33.
Mitterrutzner
,
B.
,
Callegher
,
C. Z.
,
Fraboni
,
R.
,
Wilczynski
,
E.
, and
Pezzutto
,
S.
, “
Review of heating and cooling technologies for buildings: A techno-economic case study of eleven European countries
,”
Energy
284
,
129252
(
2023
).
34.
Modu
,
B.
,
Abdullah
,
M. P.
,
Bukar
,
A. L.
,
Hamza
,
M. F.
, and
Adewolu
,
M. S.
, “
Energy management and capacity planning of photovoltaic-wind-biomass energy system considering hydrogen-battery storage
,”
J. Energy Storage
73
,
109294
(
2023
).
35.
Mousavipour
,
S. H.
,
Farughi
,
H.
, and
Ahmadizar
,
F.
, “
A novel bi-objective model for a job shop scheduling problem with consideration of fuzzy parameters, modified learning effects and multiple preventive maintenance activities
,”
Sci. Iran.
29
(
6
),
3418
3433
(
2022
).
36.
Neri
,
M.
,
Guelpa
,
E.
, and
Verda
,
V.
, “
Design and connection optimization of a district cooling network: Mixed integer programming and heuristic approach
,”
Appl. Energy
306
,
117994
(
2022
).
37.
Nguyen
,
H. T.
,
Safder
,
U.
,
Nhu Nguyen
,
X. Q.
, and
Yoo
,
C.
, “
Multi-objective decision-making and optimal sizing of a hybrid renewable energy system to meet the dynamic energy demands of a wastewater treatment plant
,”
Energy
191
,
116570
(
2020
).
38.
See https://www.oecd-nea.org/jcms/pl_51110/projected-costs-of-generating-electricity-2020-edition for OECD Nuclear Energy Agency and International Energy Agency, “
Projected Costs of Generating Electricity 2020 Edition
” (
2020
).
39.
Oyewole
,
O.
,
Nwulu
,
N.
, and
Okampo
,
E. J.
, “
Multi-objective optimal sizing and design of renewable and diesel-based autonomous microgrids with hydrogen storage considering economic, environmental, and social uncertainties
,”
Renewable Energy
231
,
120987
(
2024
).
40.
Palczewski
,
K.
and
Sałabun
,
W.
, “
The fuzzy TOPSIS applications in the last decade
,”
Procedia Comput. Sci.
159
,
2294
2303
(
2019
).
41.
Rasool
,
M. H.
,
Taylan
,
O.
,
Perwez
,
U.
, and
Batunlu
,
C.
, “
Comparative assessment of multi-objective optimization of hybrid energy storage system considering grid balancing
,”
Renewable Energy
216
,
119107
(
2023
).
42.
Raveendhra
,
D.
,
Poojitha
,
R.
,
Narasimharaju
,
B. L.
,
Dreglea
,
A.
,
Liu
,
F.
,
Panasetsky
,
D.
,
Pathak
,
M.
, and
Sidorov
,
D.
, “
Part-I: State-of-the-art technologies of solar powered DC Microgrid with Hybrid energy storage systems-architecture topologies
,”
Energies
16
,
923
(
2023a
).
43.
Raveendhra
,
D.
,
Poojitha
,
R.
,
Narasimharaju
,
B. L.
,
Domyshev
,
A.
,
Dreglea
,
A.
,
Dao
,
M. H.
,
Pathak
,
M.
,
Liu
,
F.
, and
Sidorov
,
D.
, “
Part II: State-of-the-art technologies of solar-powered DC microgrid with hybrid energy storage systems: Converter topologies
,”
Energies
16
,
6194
(
2023b
).
44.
Ridha
,
H. M.
,
Hizam
,
H.
,
Mirjalili
,
H.
,
Lutfi Othman
,
S.
,
Effendy Ya'acob
,
M.
,
Ahmadipour
,
M.
, and
Ismaeel
,
N. Q.
, “
Multi-objective optimization and multi-criteria decision making aided by numerical method: Framework and a case study of Malaysia and South Africa
,”
Energy Convers. Manage.
274
,
116468
(
2022
).
45.
Ridha
,
H. M.
,
Hizam
,
H.
,
Basil
,
N.
,
Mirjalili
,
S.
,
Othman
,
M. L.
,
Ya'acob
,
M. E.
, and
Ahmadipour
,
M.
, “
Multi-objective and multi-criteria decision making for technoeconomic optimum design of hybrid standalone renewable energy system
,”
Renewable Energy
223
,
120041
(
2024
).
46.
Ruiming
,
F.
, “
Multi-objective optimized operation of integrated energy system with hydrogen storage
,”
Int. J. Hydrogen Energy
44
(
56
),
29409
29417
(
2019
).
47.
Sun
,
P.
,
Teng
,
Y.
, and
Chen
,
Z.
, “
Robust coordinated optimization for multi-energy systems based on multiple thermal inertia numerical simulation and uncertainty analysis
,”
Appl. Energy
296
,
116982
(
2021
).
48.
Vahdani
,
B.
,
Mousavi
,
S. M.
, and
Tavakkoli-Moghaddam
,
R.
, “
Group decision making based on novel fuzzy modified TOPSIS method
,”
Appl. Math. Modell.
35
,
4257
4269
(
2011
).
49.
Vavrek
,
R.
, “
Evaluation of the impact of selected weighting methods on the results of the TOPSIS Technique
,”
Int. J. Inf. Technol. Decis. making
18
,
1821
1843
(
2019
).
50.
Wang
,
J.
,
Kang
,
L.
, and
Liu
,
Y.
, “
A multi-objective approach to determine time series aggregation strategies for optimal design of multi-energy systems
,”
Energy
258
,
124783
(
2022
).
51.
Wei
,
F.
,
Wu
,
Q. H.
,
Jing
,
Z. X.
,
Chen
,
J. J.
, and
Zhou
,
X. X.
, “
Optimal unit sizing for small-scale integrated energy systems using multi-objective interval optimization and evidential reasoning approach
,”
Energy
111
,
933
946
(
2016
).
52.
Yang
,
W.
,
Guo
,
J.
, and
Vartosh
,
A.
, “
Optimal economic-emission planning of multi-energy systems integrated electric vehicles with modified group search optimization
,”
Appl. Energy
311
,
118634
(
2022
).
53.
Yazdani
,
H.
,
Baneshi
,
M.
, and
Yaghoubi
,
M.
, “
Techno-economic and environmental design of hybrid energy systems using multi-objective optimization and multi-criteria decision making methods
,”
Energy Convers. Manage.
282
,
116873
(
2023
).
54.
Yue
,
X.
,
Pye
,
S.
,
DeCarolis
,
J.
,
Li
,
F. G. N.
,
Rogan
,
F.
, and
Gallachóir
,
B. Ó.
, “
A review of approaches to uncertainty assessment in energy system optimization models
,”
Energy Strategy Rev.
21
,
204
217
(
2018
).
55.
Zhou
,
X.
,
Tan
,
W.
,
Sun
,
Y.
,
Huang
,
T.
, and
Yang
,
C.
, “
Multi-objective optimization and decision making for integrated energy system using STA and fuzzy TOPSIS
,”
Expert Syst. Appl.
240
,
122539
(
2024
).
56.
Zhou
,
Y.
,
Ma
,
Z.
,
Zhang
,
J.
, and
Zou
,
S.
, “
Data-driven stochastic energy management of multi energy system using deep reinforcement learning
,”
Energy
261
,
125187
(
2022
).
You do not currently have access to this content.