{ "id": "epgk6drxx5", "slug": "opposition-based-learning", "title": "Opposition-based learning", "updated": "2026-10-15", "topic_path": [ { "id": "technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/topics/technology" }, { "id": "technology.computing", "label": "Computing and digital systems", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing" }, { "id": "technology.computing.ai", "label": "Artificial intelligence and data", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai" }, { "id": "technology.computing.ai.algorithms", "label": "Algorithms and computational methods", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.algorithms" }, { "id": "technology.computing.ai.optimization_dp", "label": "Optimization and dynamic programming", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.optimization_dp" }, { "id": "technology.computing.ai.optimization_dp.local-search-and-metaheuristics", "label": "Local search and metaheuristics", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.computing.ai.optimization_dp.local-search-and-metaheuristics" } ], "geo": [ { "id": "geo.nongeo.t2001.technology.computing.ai.optimization_dp", "label": "Non-geographic · 2001 to 2020: Optimization and dynamic programming", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology.computing.ai.optimization_dp", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t2001", "label": "Non-geographic · 2001 to 2020", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001" }, { "id": "geo.nongeo.t2001.technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology" }, { "id": "geo.nongeo.t2001.technology.computing", "label": "Computing and digital systems", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology.computing" }, { "id": "geo.nongeo.t2001.technology.computing.ai", "label": "Artificial intelligence and data", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology.computing.ai" }, { "id": "geo.nongeo.t2001.technology.computing.ai.algorithms", "label": "Algorithms and computational methods", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology.computing.ai.algorithms" }, { "id": "geo.nongeo.t2001.technology.computing.ai.optimization_dp", "label": "Optimization and dynamic programming", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.technology.computing.ai.optimization_dp" } ] } ], "excerpt": "Opposition-based learning is a machine intelligence technique that pairs each candidate solution with its opposite point in the search space, keeping the fitter to speed convergence.", "snippet": "Opposition-based learning is a machine intelligence technique that pairs each candidate solution with its opposite point in the search space, keeping the fitter to speed convergence.", "node": "technology.computing.ai.optimization_dp.local-search-and-metaheuristics", "markdown": "# Opposition-based learning\n\nOpposition-based learning (OBL) is a machine intelligence and optimization technique that evaluates each candidate solution together with its opposite point in a bounded search space, keeping the fitter of the two to accelerate convergence in metaheuristic and evolutionary algorithms. The motivation is probabilistic: according to probability theory, 50% of the time a guess is farther from the solution than its opposite guess.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) The original framing treats learning as a comparison between estimates and counter-estimates, weights and opposite weights, and actions versus counter-actions, on the premise that a random starting guess may lie worst-case in the opposite location from the solution, making search considerably slower if only one direction is explored.[2](http://facweb.iitkgp.ac.in/~shamik/spring2008/sca/tutorials/download/pami.uwaterloo.ca/tizhoosh/opposition_based_learning.htm)\n\n| Key fact | Detail |\n|---|---|\n| Opposite-point definition | For \\( x \\in [a, b] \\), the opposite is \\( \\breve{x} = a + b - x \\); in \\( n \\) dimensions it is applied component-wise.[3](https://www.sciencedirect.com/science/article/pii/S0898122107001344) |\n| Probabilistic basis | A guess is farther from the solution than its opposite guess 50% of the time.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) |\n| Main embedding points | Opposition-based population initialization and opposition-based generation jumping, tested on 58 benchmark functions in differential evolution.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) |\n| Jump rate | Average optimal jumping rate 0.37 over 58 functions; large-scale work recommends a small value in \\( (0, 0.4] \\).[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) • [4](https://www.sfu.ca/~gwa5/pdf/2008_01.pdf) |\n| Initialization speedup | Opposition-based initialization made DE about 10% faster on average (14.7% for \\( D \\le 10 \\) versus 6.2% for \\( D > 10 \\)).[3](https://www.sciencedirect.com/science/article/pii/S0898122107001344) |\n| Contested speedup | ODE was reported as 44% faster than DE with jump rate 0.3, but a re-examination measured 5.26% with jump rate 0.05.[5](https://doi.org/10.1109/access.2018.2890402) |\n| Technique families | A recent classification counts nine OBL techniques, from basic opposition to quasi-reflection and stochastic variants.[6](https://doi.org/10.7717/peerj-cs.2935) |\n\n## How it works\n\nOBL pairs every candidate \\( P \\) with an opposite \\( \\breve{P} \\) and evaluates both simultaneously, continuing with the fitter one; formally, if \\( f(\\breve{P}) \\ge f(P) \\) the candidate is replaced by its opposite, otherwise the original is kept.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) In a one-dimensional interval \\( [a, b] \\) the opposite of a real number \\( x \\) is \\( \\breve{x} = a + b - x \\); for \\( a = 0, b = 1 \\) this reduces to \\( \\breve{x} = 1 - x \\), and for \\( a = -b \\) to \\( \\breve{x} = -x \\).[3](https://www.sciencedirect.com/science/article/pii/S0898122107001344) In \\( n \\) dimensions the map is component-wise, \\( \\breve{x}_{i} = a_{i} + b_{i} - x_{i} \\) for \\( x_{i} \\in [a_{i}, b_{i}] \\).[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf)\n\nTwo notions of oppositeness coexist. Most implementations use the linear definition above, called type-I opposition. Type-II (true) opposition is a stricter notion whose use requires knowing evaluation values in the target space in advance, which is difficult in black-box problems, so published research deals almost entirely with type-I opposition.[7](https://ar5iv.labs.arxiv.org/html/1504.05619) • [8](https://link.springer.com/article/10.1007/s40747-023-01069-5)\n\n## How it is done\n\nOBL enters an evolutionary algorithm at two points. **Initialization.** Each randomly drawn individual \\( P_{k} \\) gets an opposite \\( \\mathrm{OP}_{k,j} = a_{j} + b_{j} - P_{k,j} \\) per variable, all \\( 2n \\) points are evaluated, and the fittest individuals from the union \\( \\{P \\cup \\mathrm{OP}\\} \\) form the initial population.[3](https://www.sciencedirect.com/science/article/pii/S0898122107001344) **Generation jumping.** After mutation, crossover, and selection, and controlled by a jumping rate \\( J_{r} \\) (a jumping probability), the opposite of the current population is computed and the fittest individuals are selected from the union of the current and opposite populations.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) During jumping, opposites are computed dynamically from the current population's own range rather than the static boundaries, \\( \\mathrm{OP}_{i,j} = \\mathrm{MIN}^{p}_{j} + \\mathrm{MAX}^{p}_{j} - P_{i,j} \\), which keeps the opposite points inside the region the population actually occupies.[4](https://www.sfu.ca/~gwa5/pdf/2008_01.pdf)\n\nThe jump rate is the main parameter. Across 58 test functions the average optimal value was 0.37, with 0.3 and 0.6 occurring most often; higher rates suited low-dimensional functions and lower rates high-dimensional ones.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) A large-scale study recommends \\( J_{r} \\) be a small number in \\( (0, 0.4] \\).[4](https://www.sfu.ca/~gwa5/pdf/2008_01.pdf) Quasi-oppositional DE used a much smaller rate, \\( J_{r\\mathrm{QODE}} = \\frac{1}{6} J_{r\\mathrm{ODE}} \\), because higher rates reduced population diversity and caused premature convergence.[9](http://rahnamayan.ca/assets/documents/Quasi-Oppositional%20Differential%20Evolution.pdf)\n\n## Origin\n\nOpposition-based learning is a scheme for machine intelligence.[2](http://facweb.iitkgp.ac.in/~shamik/spring2008/sca/tutorials/download/pami.uwaterloo.ca/tizhoosh/opposition_based_learning.htm) The earliest related records are Tizhoosh's opposition-based reinforcement learning paper in the Journal of Advanced Computational Intelligence and Intelligent Informatics (2006)[10](https://doi.org/10.20965/jaciii.2006.p0578) and the population-initialization method for accelerating evolutionary algorithms by Shahryar Rahnamayan, Hamid R. Tizhoosh, and Magdy M.A. Salama in Computers & [Mathematics](https://www.edgepedia.org/mathematics) with Applications (2007).[3](https://www.sciencedirect.com/science/article/pii/S0898122107001344) Opposition-based differential evolution was reported by Shahryar Rahnamayan, Hamid R. Tizhoosh, and Magdy M. A. Salama in Studies in Computational Intelligence (2008).[11](https://doi.org/10.1007/978-3-540-68830-3_6) OBL builds on differential evolution, reported by Rainer Storn and Kenneth Price in the Journal of Global Optimization (1997).[12](https://doi.org/10.1023/a:1008202821328) Later development includes generalized opposition-based learning in particle swarm optimization by Hui Wang and colleagues in Information Sciences (2011)[13](https://doi.org/10.1016/j.ins.2011.03.016) and the mathematical and experimental analysis of oppositional algorithms, including quasi-reflection, by Mehmet Ergezer and Dan Simon in [IEEE Transactions on Cybernetics](https://www.edgepedia.org/ieee-transactions-on-cybernetics) (2014).[14](https://doi.org/10.1109/tcyb.2014.2303117)\n\n## Variants\n\n**Quasi-oppositional learning** replaces opposite points with quasi-opposite points; a mathematical proof shows quasi-opposite points have a higher chance of being closer to the solution than opposite points in black-box problems. On 30 test problems (15 functions, two dimensions), this variant outperformed DE and ODE on 22 functions, ODE on 6, and DE on just one.[9](http://rahnamayan.ca/assets/documents/Quasi-Oppositional%20Differential%20Evolution.pdf) **Generalized opposition-based learning (GOBL)** transforms solutions from the current search space to a new one, with \\( k \\) a real number and out-of-box candidates assigned random values; the resulting GOPSO algorithm combines GOBL with Cauchy mutation and performed better than other PSO variants on the majority of 18 benchmarks, including 6 shifted and large-scale problems.[13](https://doi.org/10.1016/j.ins.2011.03.016) **Opposite-center learning (OCL)** redefines the opposite as the center point that minimizes the expected distance of the candidate/opposite pair to a uniformly distributed optimum, approximated by [Monte Carlo sampling](https://www.edgepedia.org/monte-carlo-sampling); applied to DE it improved convergence by about 8% over DE on five common benchmarks and beat OBL in sampling experiments up to dimension 20.[15](https://dare.uva.nl/document/2/162770)\n\nOther named directions include SQOBL, a diversity-driven fusion of quasi-opposite and extended opposite learning,[8](https://link.springer.com/article/10.1007/s40747-023-01069-5) and dynamic-opposite learning, in which a random opposite number is the opposite multiplied by a random value in \\( [0, 1] \\), introducing asymmetry into the search space.[16](https://www.nature.com/articles/s41598-026-46614-7)\n\n## Applications\n\nBeyond benchmark functions, early OBL work targeted reinforcement learning and backpropagation learning in neural networks.[1](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf) A survey records applications across differential evolution, particle swarm optimization, reinforcement learning, [biogeography-based optimization](https://www.edgepedia.org/biogeography-based-optimization), artificial neural networks, harmony search, ant colony system, and artificial bee colony.[17](https://www.sciencedirect.com/science/article/abs/pii/S0952197613002388) Recent applied studies include wrapper-based feature selection, where a leveraged OBL method inside fitness-landscape PSO won on classification accuracy on over half of 24 benchmark datasets against 13 advanced metaheuristics while selecting fewer features,[18](https://www.sciopen.com/article/10.32604/cmc.2025.072593) and flexible job-shop scheduling, where DOLDEMFO (dynamic-opposite learning plus differential evolution inside moth-flame optimization) was tested on 20 CEC2014 benchmarks and 20 scheduling problems.[16](https://www.nature.com/articles/s41598-026-46614-7)\n\n## Limitations and alternatives\n\n**Failure modes.** When a benchmark function is symmetric about the center of its definition interval, paired solutions have equal fitness and the opposite point cannot be superior to the original, giving a utilization rate of 0%.[5](https://doi.org/10.1109/access.2018.2890402) The extra fitness evaluations for opposite points degrade performance when the improvement is insufficient compared with the population's own evolution; one re-examination interprets OBL as a form of mutation operation.[5](https://doi.org/10.1109/access.2018.2890402) Because each candidate and its opposite are both evaluated, the OBL variant of an algorithm shares the parent's asymptotic complexity, \\( O(T \\cdot D \\cdot N) \\), but incurs approximately double the evaluation cost per iteration; applying OBL too frequently can become redundant or disrupt convergence, and its static application lacks adaptive control.[19](https://www.mdpi.com/2227-7390/13/16/2556) The stochastic OBL variant is susceptible to rotations in the coordinate system, motivating rotationally invariant versions.[6](https://doi.org/10.7717/peerj-cs.2935) Quasi-opposite and quasi-reflection learning converge better toward the global optimum than original OBL but are less effective when a local optimum exists.[16](https://www.nature.com/articles/s41598-026-46614-7)\n\n**Contested speedup.** The original ODE study reported ODE on average 44% faster than DE with jump rate 0.3, but a re-examination measured a 5.26% speedup with jump rate 0.05, attributing the discrepancy to jumping-rate settings; its population-based embedding gave a total average acceleration of 8.00%.[5](https://doi.org/10.1109/access.2018.2890402)\n\n**Alternatives.** In the CEC2022 comparison of five OBL variants across five metaheuristics, quasi-reflection OBL consistently outperformed the others in convergence speed and solution quality across most benchmark functions.[6](https://doi.org/10.7717/peerj-cs.2935) Diversification-based learning, proposed by [Fred Glover](https://www.edgepedia.org/fred-w-glover) and Jin-Kao Hao in the Journal of Heuristics (2018), offers a broader framework for population diversification in computing and optimization.[20](https://doi.org/10.1007/s10732-018-9384-y)\n\n## References\n\n1. [Opposition-Based Differential Evolution (IEEE Transactions on Evolutionary Computation, 2008)](https://sci2s.ugr.es/keel/pdf/algorithm/articulo/2008-IEEE_TEC-Rahnamayan.pdf)\n2. [Opposition-Based Learning (Tizhoosh's own research page)](http://facweb.iitkgp.ac.in/~shamik/spring2008/sca/tutorials/download/pami.uwaterloo.ca/tizhoosh/opposition_based_learning.htm)\n3. [A novel population initialization method for accelerating evolutionary algorithms (Computers and Mathematics with Applications, 2007)](https://www.sciencedirect.com/science/article/pii/S0898122107001344)\n4. [Solving Large Scale Optimization Problems by Opposition-Based Differential Evolution (ODE)](https://www.sfu.ca/~gwa5/pdf/2008_01.pdf)\n5. [Exploring the Reasons Behind the Good Performance of Opposition-Based Learning](https://doi.org/10.1109/access.2018.2890402)\n6. [Opposition-based learning techniques in metaheuristics: classification, comparison, and convergence analysis](https://doi.org/10.7717/peerj-cs.2935)\n7. [Learning Opposites with Evolving Rules (arXiv:1504.05619)](https://ar5iv.labs.arxiv.org/html/1504.05619)\n8. [A particle swarm optimization algorithm based on diversity-driven fusion of opposing phase selection strategies (Complex & Intelligent Systems, Springer)](https://link.springer.com/article/10.1007/s40747-023-01069-5)\n9. [Quasi-Oppositional Differential Evolution (QODE)](http://rahnamayan.ca/assets/documents/Quasi-Oppositional%20Differential%20Evolution.pdf)\n10. [Hamid R. Tizhoosh (2006). Opposition-Based Reinforcement Learning. Journal of Advanced Computational Intelligence and Intelligent Informatics.](https://doi.org/10.20965/jaciii.2006.p0578)\n11. [Shahryar Rahnamayan, Hamid R. Tizhoosh, Magdy M. A. Salama (2008). Opposition-Based Differential Evolution. Studies in computational intelligence.](https://doi.org/10.1007/978-3-540-68830-3_6)\n12. [Rainer Storn, Kenneth Price (1997). Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. Journal of Global Optimization.](https://doi.org/10.1023/a:1008202821328)\n13. [Hui Wang and colleagues (2011). Enhancing particle swarm optimization using generalized opposition-based learning. Information Sciences.](https://doi.org/10.1016/j.ins.2011.03.016)\n14. [Mehmet Ergezer, Dan Simon (2014). Mathematical and Experimental Analyses of Oppositional Algorithms. IEEE Transactions on Cybernetics.](https://doi.org/10.1109/tcyb.2014.2303117)\n15. [How to Speed up Optimization? Opposite-Center Learning (Xu, Erdbrink, Krzhizhanovskaya)](https://dare.uva.nl/document/2/162770)\n16. [Dynamic-opposite learning enhanced meta-heuristic approach for solving multiple industrial optimization problems (Scientific Reports, 2026)](https://www.nature.com/articles/s41598-026-46614-7)\n17. [A review of opposition-based learning from 2005 to 2012 (Xu, Wang, Wang, Hei, Zhao; Engineering Applications of Artificial Intelligence, 2014)](https://www.sciencedirect.com/science/article/abs/pii/S0952197613002388)\n18. [Leveraging Opposition-Based Learning in Particle Swarm Optimization for Effective Feature Selection (Computers, Materials & Continua, 2026)](https://www.sciopen.com/article/10.32604/cmc.2025.072593)\n19. [Fick's Law Algorithm Enhanced with Opposition-Based Learning (Mathematics, MDPI, 2025)](https://www.mdpi.com/2227-7390/13/16/2556)\n20. [Fred Glover, Jin-Kao Hao (2018). Diversification-based learning in computing and optimization. Journal of Heuristics.](https://doi.org/10.1007/s10732-018-9384-y)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Computing and digital systems › Artificial intelligence and data › Algorithms and computational methods › Optimization and dynamic programming › Local search and metaheuristics*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/opposition-based-learning", "markdown_url": "https://www.edgepedia.org/opposition-based-learning.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Opposition-based learning\", Edgepedia (EdgeChat), https://www.edgepedia.org/opposition-based-learning. Edgepedia Community License 1.0.", "credit_md": "\"[Opposition-based learning](https://www.edgepedia.org/opposition-based-learning)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/opposition-based-learning](https://www.edgepedia.org/opposition-based-learning). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Opposition-based learning\", Edgepedia (EdgeChat), https://www.edgepedia.org/opposition-based-learning. Edgepedia Community License 1.0.", "speakable": "Opposition-based learning is a machine intelligence technique that pairs each candidate solution with its opposite point in the search space, keeping the fitter to speed convergence." }