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Single-, two-, three-, and four-objective optimizations for an irreversible vacuum thermionic generator via finite-time thermodynamics, NSGA-II and three decision-making techniques

  • Cheng Hu , Lingen Chen EMAIL logo , Yanlin Ge EMAIL logo and Huijun Feng
Published/Copyright: August 8, 2025

Abstract

Based on an irreversible vacuum thermionic generator model, this paper performs single-, two-, three-, and four-objective optimizations for it by utilizing NSGA-II algorithm, finite-time thermodynamics and three decision-making techniques. Output-power, thermal-efficiency, ecological-function and efficient-power are taken as optimization-objectives, and collector work-function and output-voltage are taken as optimization-variables. Total number of optimizations completed consists of one four-objective optimization, four three-objective optimizations, six two-objective optimizations, and four single-objective optimizations. Deviation indexes under various combinations of optimization objectives are compared by using three decision-making techniques: Shannon Entropy, LINMAP, and TOPSIS. Based on these comparisons, optimal design scheme is determined. Findings indicate that multi-objective optimization can take into account multiple performance indicators at the same time and have a better coordination ability. The deviation index is 0.1761 when selecting LINMAP decision mode to optimize the combination of output-power, efficient-power, thermal-efficiency and ecological-function which is the best scheme for four-objective optimization, and optimal ranges of collector work function and output voltage are 1.295–1.355 and 0.22–0.44, respectively. The important contribution herein is introducing NSGA-II algorithm and three decision-making techniques for performance optimization of vacuum thermionic generator and performing totally 15 optimization tasks for in the first time in open literature.


Corresponding authors: Lingen Chen and Yanlin Ge, Hubei Provincial Key Laboratory of Chemical Equipment Intensification and Intrinsic Safety, Wuhan Institute of Technology, Wuhan, 430205, P.R. China; Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan Institute of Technology, Wuhan, 430205, P.R. China; Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan, 430205, P.R. China; and School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan, 430205, P.R. China, E-mail: (L. Chen), (Y. Ge)

Acknowledgements

The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: This paper is supported by The Natural Science Foundation of China (Project Nos. 52171317 and 51779262).

  7. Data availability: Not applicable.

Nomenclature

A 0

Richardson’s constant A / m 2 K 2

D

Deviation index

E P

Efficient power W

F

Surface area of heat-transfer m 2

F 0

Emitter or collector’s active area m 2

k B

Boltzmann-constant J / K

P

Power W

q

An electron’s charge C

T

Temperature K

V

Output voltage V

Greek symbols

η

Efficiency

ε

Thermal emissivity

σ

Stefan-Boltzmann constant

ϕ 2

Collector work function V

Subscripts

C

Heat-sink

H

Heat-source

1,2

Emitter and collector

Abbreviations

CR

Cold-reservoir

ECO

Ecological-function

FTT

Finite-time thermodynamics

HR

Hot-reservoir

HT

Heat-transfer

MOO

Multi-objective optimization

OO

Optimization-objective

OV

Output voltage

TMG

Thermionic generator

WF

Work function

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Received: 2025-04-05
Accepted: 2025-07-11
Published Online: 2025-08-08
Published in Print: 2025-10-27

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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