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In Computer Science, '''Optimal Computing Budget Allocation (OCBA)''' is a simulation optimization method designed to maximize the Probability of Correct Selection (PCS) while minimizing computational costs. First introduced by Dr. Chun-Hung Chen in the mid-1990s, OCBA determines how many simulation runs (or how much computational time) or the number of replications each design alternative needs to identify the best option while using as few resources as possible.<ref name="Chen1995">{{cite conference | last=Chen | first=Chun-Hung | title=An Effective Approach to Smartly Allocate Computing Budget for Discrete Event Simulation | book-title=Proceedings of the 34th IEEE Conference on Decision and Control | year=1995 | pages=2598–2605 | url=https://ieeexplore.ieee.org/document/
Simply put, OCBA ensures that computational resources are distributed efficiently by allocating more simulation effort to design alternatives that are harder to evaluate or more likely to be the best. This allows researchers and decision-makers to achieve accurate results faster and with fewer resources.
OCBA has also been shown to enhance partition-based random search algorithms for solving deterministic global optimization problems.<ref name="Chen2014">{{cite journal | last1=Chen | first1=Wei | last2=Gao | first2=
== Intuitive Explanation ==
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<math>N_i</math>: The number of simulation replications allocated to alternative <math>i</math>.
This formula ensures that alternatives with smaller performance gaps (<math>\delta_{1,i}</math>) or higher variances (<math>\sigma_i</math>) receive more simulation replications. This maximizes computational efficiency while maintaining a high Probability of Correct Selection (PCS), ensuring computational efficiency by reducing replications for non-critical alternatives and increasing them for critical ones.<ref>Chen, C. H., J. Lin, E. Yücesan, and S. E. Chick, "Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization," Journal of Discrete Event Dynamic Systems, 2000.</ref> Numerical results show that OCBA can achieve the same simulation quality with only one-tenth of the computational effort compared to traditional methods.<ref name="Chen2011">{{cite book | last1=Chen
== Some extensions of OCBA ==
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According to Szechtman and Yücesan (2008),<ref>Szechtman R, Yücesan E (2008) [https://calhoun.nps.edu/bitstream/handle/10945/38580/031.pdf?sequence=3 A new perspective on feasibility determination]. Proc of the 2008 Winter Simul Conf 273–280</ref> OCBA is also helpful in feasibility determination problems. This is where the decisions makers are only interested in differentiating [[Logical possibility|feasible]] alternatives from the infeasible ones. Further, choosing an alternative that is simpler, yet similar in performance is crucial for other decision makers. In this case, the best choice is among top-r simplest alternatives, whose [[performance]] rank above desired levels.<ref>Jia QS, Zhou E, Chen CH (2012). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3653338/ efficient computing budget allocation for finding simplest good designs]. IIE Trans, To Appear.</ref>
In addition, Trailovic<ref>Trailovic Tekin E, Sabuncuoglu I (2004) Simulation optimization: A comprehensive review on theory and applications. IIE Trans 36:1067–1081</ref> and Pao<ref>Trailovic L, Pao LY (2004) [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.15.1213&rep=rep1&type=pdf Computing budget allocation for efficient ranking and selection of variances with application to target tracking algorithms], IEEE Trans Autom Control 49:58–67.</ref> (2004) demonstrate an OCBA approach, where we find alternatives with minimum [[variance]], instead of with best mean. Here, we assume unknown variances, voiding the OCBA rule (assuming that the variances are known). During 2010 research was done on an OCBA algorithm that is based on a t distribution. The results show no significant differences between those from t-distribution and [[normal distribution]]. The above presented extensions of OCBA is not a complete list and is yet to be fully explored and compiled.<ref name="
== Multi-Objective OCBA ==
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* <math>\delta_{i,j}=\mu_i-\mu_j</math>.
The budget allocation problem with the EOC objective measure is given by Gao et al. (2017)<ref>
: <math>
\begin{align}
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* '''Simulation-Based Ranking and Selection:'''
** A 2023 study introduced a budget-adaptive allocation rule for OCBA, dynamically adjusting simulation budgets to maximize the probability of correct selection. This approach was validated through synthetic examples and case studies, showcasing its efficiency in identifying optimal system designs.<ref>{{cite conference | last=Chen
* '''Data-Driven Decision Making:'''
** In 2022, researchers developed a data-driven OCBA method that addresses input uncertainty by updating distribution estimates with streaming data. This method ensures consistent and asymptotically optimal selection of the best design, enhancing decision-making in dynamic environments.<ref name="Chen2011">{{cite book | last1=Chen
* '''Monte Carlo Tree Search (MCTS):'''
** A 2020 study proposed an OCBA-based tree policy for MCTS, optimizing computational resource allocation to maximize the probability of correct action selection. This
* '''Online Serving Systems:'''
** The
*'''Digital Twinning and Decision Support Systems for Maintaining A Resilient Port:'''
**As real-world physical systems become increasingly more elaborate and subject to wide-ranging external factors and disruptions, it becomes necessary to develop mechanisms to both monitor changes and coordinate the successful operation of all the aspects of the system. A 2021 paper proposes OCBA as a means of ensuring the successful allocation of resources to reduce the impact of hazards and environmental factors that may block the timely transfer of cargo across ports. By implementing OCBA within a digital twin-based framework, decision makers will be able to use real-time data to optimize the number of simulation runs for each recovery alternative.<ref>{{cite journal | doi=10.1016/j.dss.2021.113496 | title=Analytics with digital-twinning: A decision support system for maintaining a resilient port | date=2021 | last1=Zhou | first1=Chenhao | last2=Xu | first2=Jie | last3=Miller-Hooks | first3=Elise | last4=Zhou | first4=Weiwen | last5=Chen | first5=Chun-Hung | last6=Lee | first6=Loo Hay | last7=Chew | first7=Ek Peng | last8=Li | first8=Haobin | journal=Decision Support Systems | volume=143 | article-number=113496 }}</ref>
These recent innovations demonstrate OCBA's growing versatility and effectiveness in optimizing resource allocation for diverse applications.
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=== Applications ===
'''Predictive Multi-Fidelity Models:''' Gaussian Mixture Models (GMMs) predict relationships between low- and high-fidelity simulations, enabling OCBA to focus on the most promising alternatives. Multi-fidelity models combine insights from low-fidelity simulations, which are computationally inexpensive but less accurate, and high-fidelity simulations, which are more accurate but computationally intensive. The integration of GMMs into this process allows OCBA to strategically allocate computational resources across fidelity levels, significantly reducing simulation costs while maintaining decision accuracy.<ref>{{cite journal |last1=Peng |first1=Y. |last2=Xu |first2=J. |last3=Lee |first3=L. H. |last4=Hu |first4=J. |last5=Chen |first5=C. H. |title=Efficient Simulation Sampling Allocation Using Multifidelity Models |journal=IEEE Transactions on Automatic Control |year=2019 |volume=64 |issue=8 |pages=3156–3169 |doi=10.1109/TAC.2018.2886165 |bibcode=2019ITAC...64.3156P }}</ref>
'''Dynamic Resource Allocation in Healthcare:''' A Bayesian OCBA framework has been applied to allocate resources in hospital emergency departments, balancing service quality with operational efficiency. By minimizing expected opportunity costs, this approach supports real-time decision-making in high-stakes environments.<ref>{{cite journal | title=Optimizing Resource Allocation in Service Systems via Simulation: A Bayesian Formulation | journal=Production and Operations Management | year=2023 | doi=10.1111/poms.13825 | last1=Chen | first1=Weiwei | last2=Gao | first2=Siyang | last3=Chen | first3=Wenjie | last4=Du | first4=Jianzhong | volume=32 | pages=65–81 | doi-access=free }}</ref> Additionally, the integration of OCBA with real-time digital twin-based optimization has further advanced its application in predictive simulation learning, enabling dynamic adjustments to resource allocation in healthcare settings.<ref>{{cite journal | last1=Goodwin | first1=Timothy | last2=Xu | first2=Jie | last3=Celik | first3=Niyazi | last4=Chen | first4=Chun-Hung | title=Real-Time Digital Twin-Based Optimization with Predictive Simulation Learning | journal=Journal of Simulation | year=2024 | volume=18 | issue=1 | pages=47–64 | doi=10.1080/17477778.2022.2046520 | url=https://www.tandfonline.com/doi/full/10.1080/17477778.2022.2046520 | url-access=subscription }}</ref> Furthermore, a contextual ranking and selection method for personalized medicine leverages OCBA to optimize resource allocation in treatments tailored to individual patient profiles, demonstrating its potential in personalized healthcare.<ref>{{cite journal | last1=Gao | first1=Siyang | last2=Du | first2=Jianzhong | last3=Chen | first3=Chun-Hung | title=A Contextual Ranking and Selection Method for Personalized Medicine | journal=Manufacturing and Service Operations Management | year=2024 | volume=26 | issue=1 | pages=167–181 | doi=10.1287/msom.2022.0232 | arxiv=2206.12640 | url=https://pubsonline.informs.org/doi/10.1287/msom.2022.0232 }}</ref>
'''Sequential Allocation using Machine-learning Predictions as Light-weight Estimates (SAMPLE):''' SAMPLE is an extension of OCBA that presents a new opportunity for the integration of machine learning with digital twins for real-time simulation optimization and decision-making. Current methods for applying machine learning on simulation data may not produce the optimal solution due to errors encountered during the predictive learning phase since training data can be limited. SAMPLE overcomes this issue by leveraging lightweight machine learning models, which are easy to train and interpret, then running additional simulations once the real-world context is captured through the digital twin.<ref>{{cite journal | doi=10.1080/17477778.2022.2046520 | title=Real-time digital twin-based optimization with predictive simulation learning | date=2024 | last1=Goodwin | first1=Travis | last2=Xu | first2=Jie | last3=Celik | first3=Nurcin | last4=Chen | first4=Chun-Hung | journal=Journal of Simulation | volume=18 | pages=47–64 }}</ref>
== References ==
{{Reflist}}
<!--- See [[Wikipedia:Footnotes]] on how to create references using<ref></ref> tags which will then appear here automatically -->
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