排序最佳化（ordinal optimization）也称为序最佳化，是最优化中的一种，是针对在偏序集（poset）上取值函数的最佳化[1][2][3][4]。排序最佳化可以应用在等候网络的理论中。
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偏序是指在集合P内的二元关系 "≤"，是自反关系、反对称关系及传递关系。针对集合P内的所有a, b及c，会有以下的关系：
- a ≤ a（自反关系）;
- 若 a ≤ b 且 b ≤ a ，则 a = b（反对称关系）;
- if a ≤ b and b ≤ c，则 a ≤ c（传递关系）.
偏序关系也可以说是预序关系。具有偏序关系的集合称为偏序集（poset）。
针对偏序集P内的两个相异元素a, b，若a ≤ b或b ≤ a，则a和b 是可比较的，否则是不可比较的。若偏序集中任两个元素都是可比较的，此偏序集称为全序关系或“chain”（也就是依顺序排列的自然数）。若任两个元素都是不可比较的，则称为反链。
以下是一些数学中偏序集的例子：
- 实数的偏序关系是标准的小于等于关系 ≤ ，也是全序集。
- 特定集合子集形成的集合（幂集），偏序关系是包含。
- 向量空间子空间的集合，偏序关系也是包含。
在许多领域都有排序最佳化的问题。计算机科学中会研究选择算法，这种算法比排序算法要简单[5][6]
决策论会研究选择算法，会要识别出“最佳”的子群体，或是识别出“近乎最佳”的子群体[7][8][9][10][11]。
自1960年代起，排序最佳化在其理论及应用上都有许多的扩展。其中的antimatroid及max-plus代数已应用在网络分析及等候理论中，特别是在等候网路中。排序最佳化也应用在离散事件仿真上[12][13][14]。
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Santner, Thomas J., and Tamhane, A. C., Design of Experiments: Ranking and Selection, M. Dekker, (1984).
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Friedrich Liese, Klaus-J. Miescke. 2008. Statistical Decision Theory: Estimation, Testing, and Selection. Springer Verlag.
Heidergott, Bernd; Oldser, Geert Jan; van der Woude, Jacob. Max plus at work: Modeling and analysis of synchronized systems, a course on max-plus algebra and its applications. Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press. 2006: xii+213. ISBN 978-0-691-11763-8. MR 2188299.
- Fujishige, Satoru Submodular functions and optimization. Second edition. Annals of Discrete Mathematics, 58. Elsevier B. V., Amsterdam, 2005. xiv+395 pp. ISBN 0-444-52086-4
- Gondran, Michel; Minoux, Michel Graphs, dioids and semirings. New models and algorithms. Operations Research/Computer Science Interfaces Series, 41. Springer, New York, 2008. xx+383 pp. ISBN 978-0-387-75449-9
- Dietrich, B. L.; Hoffman, A. J. On greedy algorithms, partially ordered sets, and submodular functions. IBM J. Res. Dev. 47 (2003), no. 1, 25–30.
- Murota, Kazuo Discrete convex analysis. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003. xxii+389 pp. ISBN 0-89871-540-7
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- Björner, Anders; Ziegler, Günter M. Introduction to greedoids. Matroid applications, 284–357, Encyclopedia Math. Appl., 40, Cambridge Univ. Press, Cambridge, 1992,
- Zimmermann, U. Linear and combinatorial optimization in ordered algebraic structures. Ann. Discrete Math. 10 (1981), viii+380 pp.
- Cuninghame-Green, Raymond Minimax algebra. Lecture Notes in Economics and Mathematical Systems, 166. Springer-Verlag, Berlin-New York, 1979. xi+258 pp. ISBN 3-540-09113-0
- Baccelli, François Louis; Cohen, Guy; Olsder, Geert Jan; Quadrat, Jean-Pierre. Synchronization and linearity: An algebra for discrete event systems. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Chichester: John Wiley & Sons, Ltd. 1992: xx+489. ISBN 0-471-93609-X. MR 1204266.
- Glasserman, Paul; Yao, David D. Monotone structure in discrete-event systems. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: John Wiley & Sons, Inc. 1994: xiv+297. ISBN 0-471-58041-4. MR 1266839.
- Heidergott, Bernd; Oldser, Geert Jan; van der Woude, Jacob. Max plus at work: Modeling and analysis of synchronized systems, a course on max-plus algebra and its applications. Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press. 2006: xii+213. ISBN 978-0-691-11763-8. MR 2188299.
- Ho, Y.C., Sreenivas, R., Vakili, P.,"Ordinal Optimization of Discrete Event Dynamic Systems", J. of DEDS 2(2), 61-88, (1992).
- Allen, Eric, and Marija D. Ilic. Price-Based Commitment Decisions in the Electricity Market. Advances in industrial control. London: Springer, 1999. ISBN 978-1-85233-069-9
