Evaluating the ε-domination based multi-objective evolutionary algorithm for a quick computation of pareto-optimal solutions
Abstract
Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the epsilon-dominance concept introduced earlier(Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the epsilon-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.
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NSGA-II significantly improves the convergence speed of the iteration, reduces the computational complexity, and ensures the diversity of the population.
“It significantly improves the convergence speed of the iteration, reduces the computational complexity, and ensures the diversity of the population [25,26].”
From Research on high efficiency and high dynamic optimal matching of the electro-hydraulic servo pump control system based on NSGA-II (2023) · cites this paper as [25]
NSGA-II introduces fast non-dominant sorting, elite retention, and congestion comparison methods.
“the non-dominant sorting genetic algorithm based on the elite strategy (NSGA-II) introduces fast non-dominant sorting, elite retention, and congestion comparison methods.”
From Research on high efficiency and high dynamic optimal matching of the electro-hydraulic servo pump control system based on NSGA-II (2023) · cites this paper as [25]
Cites
A fast and elitist multiobjective genetic algorithm: NSGA-II
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002) · IEEE Transactions on Evolutionary Computation · doi:10.1109/4235.996017 · Cited by 50,053 · see citing works
Self-citationMulti-Objective Optimization Using Evolutionary Algorithms
Deb, K., & Kalyanmoy, D. (2001) · Andalas University Repository (Andalas University) · Cited by 14,936 · see citing works
Self-citationMultiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach
Zitzler, E., & Thiele, L. (1999) · IEEE Transactions on Evolutionary Computation · doi:10.1109/4235.797969 · Cited by 8,857 · see citing works
Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
Srinivas, N., & Deb, K. (1994) · Evolutionary Computation · doi:10.1162/evco.1994.2.3.221 · Cited by 6,935 · see citing works
Self-citationComparison of Multiobjective Evolutionary Algorithms: Empirical Results
Zitzler, E., Deb, K., & Thiele, L. (2000) · Evolutionary Computation · doi:10.1162/106365600568202 · Cited by 5,728 · see citing works
Self-citationEvolutionary Algorithms for Solving Multi-Objective Problems
Coello, C. A. C., Veldhuizen, D. A. V., & Lamont, G. B. (2007) · Springer eBooks · doi:10.1007/978-0-387-36797-2 · Cited by 5,722 · see citing works
Performance assessment of multiobjective optimizers: an analysis and review
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., & da Fonseca, V. G. (2003) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2003.810758 · Cited by 4,360 · see citing works
Simulated Binary Crossover for Continuous Search Space.
Deb, K., & Agrawal, R. B. (1995) · Complex Systems · Cited by 2,977 · see citing works
Self-citationA Comparative Analysis of Selection Schemes Used in Genetic Algorithms
Goldberg, D. E., & Deb, K. (1991) · Foundations of genetic algorithms · doi:10.1016/b978-0-08-050684-5.50008-2 · Cited by 2,456 · see citing works
Self-citationApproximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Knowles, J. D., & Corne, D. (2000) · Evolutionary Computation · doi:10.1162/106365600568167 · Cited by 2,286 · see citing works
Scalable multi-objective optimization test problems
Deb, K., Thiele, L., Laumanns, M., et al. (2003) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2002.1007032 · Cited by 1,634 · see citing works
Self-citationCombining Convergence and Diversity in Evolutionary Multiobjective Optimization
Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002) · Evolutionary Computation · doi:10.1162/106365602760234108 · Cited by 1,493 · see citing works
Self-citationMulti-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems
Deb, K. (1999) · Evolutionary Computation · doi:10.1162/evco.1999.7.3.205 · Cited by 1,457 · see citing works
Self-citationA combined genetic adaptive search (GeneAS) for engineering design
Deb, K., & Goyal, M. K. (1996) · Cited by 1,221 · see citing works
Self-citationThe Pareto Envelope-Based Selection Algorithm for Multiobjective Optimization
Corne, D., Knowles, J. D., & Oates, M. J. (2000) · Lecture notes in computer science · doi:10.1007/3-540-45356-3_82 · Cited by 890 · see citing works
On metrics for comparing nondominated sets
Knowles, J. D., & Corne, D. (2003) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2002.1007013 · Cited by 562 · see citing works
Performance Scaling of Multi-objective Evolutionary Algorithms
Khare, V., Yao, X., & Deb, K. (2003) · Lecture notes in computer science · doi:10.1007/3-540-36970-8_27 · Cited by 455 · see citing works
Self-citationEvaluating the quality of approximations to the non-dominated set
Hansen, M. P., & Jaszkiewicz, A. (1998) · Cited by 301 · see citing works
Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions
Deb, K., Mohan, M., & Mishra, S. (2003) · Lecture notes in computer science · doi:10.1007/3-540-36970-8_16 · Cited by 252 · see citing works
Self-citationDiversity assessment of Pareto optimal solution sets: an entropy approach
Farhang-Mehr, A., & Azarm, S. (2003) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2002.1007015 · Cited by 76 · see citing works
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Yang, M., Yan, G., Zhang, Y., Zhang, T., & Ai, C. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e13805 · Cited by 19 · see citing works
“It significantly improves the convergence speed of the iteration, reduces the computational complexity, and ensures the diversity of the population [25,26].”
Background
- Authors
- Deb, K., Mohan, M., & Mishra, S.
- Affiliations
- Indian Institute of Technology Kanpur (IN)
- Manikanth Mohan, Palappallil House, Nalkalickal P.O., (via) Aranmula, Pathnamthitta (Dist), Kerala, PIN 689533, INDIA,
- University of Missouri–St. Louis (US)
- ORCID
- Deb, Kalyanmoy
- Venue
- Evolutionary Computation
- Publisher
- MIT Press
- Published
- 2005-12
- Volume
- 13
- Issue
- 4
- Pages
- 501-525
- ISSN
- 1063-6560 (ISSN-L)
- 1530-9304
- OpenAlex
- W2105511939
- Cited by
- 637
- References
- 20
- Citations by year
- 2026: 18 · 2025: 21 · 2024: 30 · 2023: 35 · 2022: 45 · 2021: 33 · 2020: 37 · 2019: 40 · 2018: 49 · 2017: 55 · 2016: 31 · 2015: 42 · 2014: 40 · 2013: 30 · 2012: 25
- FWCI
- 10.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Evolutionary Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Multi-Objective Optimization Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Evolutionary Algorithms and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Keywords
- epsilon-dominance, multi-objective evolutionary algorithms, Pareto optimal solutions, solution distribution, convergence, computational efficiency, SPEA, NSGA-II
- MeSH terms
- Algorithms, Computer Simulation, Biological Evolution, Models, Theoretical, Time Factors
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