Dynamic performance evaluation of evolutionary multi-objective optimization algorithms for gait cycle optimization of a 25-DOFs NAO humanoid robot

Researchers are increasingly using optimization methods to achieve optimal dynamic performance of humanoid robots, often involving multiple conflicting objectives. Multi-objective optimization algorithms (MOAs) aim to find a Pareto front of optimal solutions, but selecting the best algorithm based o...

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Published in:Swarm and evolutionary computation Vol. 99; p. 102144
Main Authors: Gupta, Pushpendra, Pratihar, Dilip Kumar, Deb, Kalyanmoy
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2025
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ISSN:2210-6502
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Abstract Researchers are increasingly using optimization methods to achieve optimal dynamic performance of humanoid robots, often involving multiple conflicting objectives. Multi-objective optimization algorithms (MOAs) aim to find a Pareto front of optimal solutions, but selecting the best algorithm based on solution quality and computational efficiency remains challenging. This study comprehensively evaluates MOAs from different paradigms: swarm intelligence (CMOPSO), genetic algorithms (NSGA-II, DCNSGA-III), and decomposition-based approaches (CMOEA/D) for optimizing the gait cycle of a 25 DOF NAO humanoid robot during single support phase (SSP) and double support phase (DSP) scenarios. The algorithms’ convergence, diversity, and constraint-handling capabilities are systematically analyzed in solving the gait generation problem. The bi-objective optimization simultaneously minimizes power consumption and maximizes dynamic stability subject to eight functional constraints with 12-13 decision parameters. Through performance evaluation using running inverted generational distance (IGD) and hypervolume (HV) metrics across eleven independent runs of each algorithm, NSGA-II emerges as the most suitable algorithm, demonstrating superior convergence and solution quality, while CMOPSO shows competitive performance with faster initial convergence. DCNSGA-III exhibits moderate performance with constraint-handling difficulties, and CMOEA/D demonstrates poor convergence characteristics requiring significantly more computational resources. Two distinct knee regions emerge during both SSP and DSP, representing optimal trade-off solutions, with a systematic framework provided for practitioners to select appropriate gait parameters based on operational priorities. The running IGD metric combined with HV validation demonstrates effectiveness in providing robust algorithmic insights, enabling practitioners to select suitable algorithms for similar complex real-world optimization problems.
AbstractList Researchers are increasingly using optimization methods to achieve optimal dynamic performance of humanoid robots, often involving multiple conflicting objectives. Multi-objective optimization algorithms (MOAs) aim to find a Pareto front of optimal solutions, but selecting the best algorithm based on solution quality and computational efficiency remains challenging. This study comprehensively evaluates MOAs from different paradigms: swarm intelligence (CMOPSO), genetic algorithms (NSGA-II, DCNSGA-III), and decomposition-based approaches (CMOEA/D) for optimizing the gait cycle of a 25 DOF NAO humanoid robot during single support phase (SSP) and double support phase (DSP) scenarios. The algorithms’ convergence, diversity, and constraint-handling capabilities are systematically analyzed in solving the gait generation problem. The bi-objective optimization simultaneously minimizes power consumption and maximizes dynamic stability subject to eight functional constraints with 12-13 decision parameters. Through performance evaluation using running inverted generational distance (IGD) and hypervolume (HV) metrics across eleven independent runs of each algorithm, NSGA-II emerges as the most suitable algorithm, demonstrating superior convergence and solution quality, while CMOPSO shows competitive performance with faster initial convergence. DCNSGA-III exhibits moderate performance with constraint-handling difficulties, and CMOEA/D demonstrates poor convergence characteristics requiring significantly more computational resources. Two distinct knee regions emerge during both SSP and DSP, representing optimal trade-off solutions, with a systematic framework provided for practitioners to select appropriate gait parameters based on operational priorities. The running IGD metric combined with HV validation demonstrates effectiveness in providing robust algorithmic insights, enabling practitioners to select suitable algorithms for similar complex real-world optimization problems.
ArticleNumber 102144
Author Gupta, Pushpendra
Pratihar, Dilip Kumar
Deb, Kalyanmoy
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  givenname: Dilip Kumar
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  surname: Deb
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  email: kdeb@egr.msu.edu
  organization: Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
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Keywords Performance metrics
Multi-objective optimization
Swarm intelligence
Evolutionary algorithms
NAO humanoid robot
Language English
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Snippet Researchers are increasingly using optimization methods to achieve optimal dynamic performance of humanoid robots, often involving multiple conflicting...
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StartPage 102144
SubjectTerms Evolutionary algorithms
Multi-objective optimization
NAO humanoid robot
Performance metrics
Swarm intelligence
Title Dynamic performance evaluation of evolutionary multi-objective optimization algorithms for gait cycle optimization of a 25-DOFs NAO humanoid robot
URI https://dx.doi.org/10.1016/j.swevo.2025.102144
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