設計高品質的醫療人員排班表是一個重要的問題，在醫療行業中至關重要，因為精心設計的排班表直接影響醫療機構的運營效率、患者的治療效果以及醫護人員的服務滿意度。
找到一個快速且準確的排班問題解決方案至關重要。針對我們要解決的問題，我們提出了一個整數規劃模型，並使用了一種稱為螞蟻群體系統優化的局部搜索算法來解決該問題。我們還為此問題設計了一個啟發式訊息，並探討了參數變化如何影響問題解決方案的搜索過程。

Designing high quality medical staff schedule is a critical issue. This problem is crucial in the healthcare industry because well-designed scheduling directly impacts the operational efficiency of medical institutions, the treatment outcomes for patients, and the service satisfaction of healthcare professionals.
Finding a fast and accurate solution to the scheduling problem is crucial. For our problem, we propose an integer programming model and utilize one type of local search algorithm called the ant colony optimization to address the issue. We also come up with a design of heuristic for the problem and explore how variations in parameters affect the search process for solutions in this problem.

[1] Nadia Abd-Alsabour, Hesham Hefny, and Atef Moneim. Heuristic information for ant colony optimization for the feature selection problem. pages 1–5, 2013.
[2] Said Achmad, Antoni Wibowo, and Diana Diana. Ant colony optimization with semi random initialization for nurse rostering problem. International Journal for Simulation and Multidisciplinary Design Optimization, 12:31, 2021.
[3] Wallace Agyei, William Obeng-Denteh, and Emmanuel A Andaam. Modeling nurse scheduling problem using 0-1 goal programming: A case study of tafo government hospital, kumasi-ghana. International Journal of Scientific & Technology Research, 4(3):5–10, 2015.
[4] Uwe Aickelin and Jingpeng Li. An estimation of distribution algorithm for nurse scheduling. Annals of Operations Research, 155:289–309, 2007.
[5] Edmund Burke, Patrick De Causmaecker, and Greet Vanden Berghe. A hybrid tabu search algorithm for the nurse rostering problem. pages 187–194, 1999.
[6] Brenda Cheang, Haibing Li, Andrew Lim, and Brian Rodrigues. Nurse rostering problems–a bibliographic survey. European journal of operational research, 151 (3):447–460, 2003.
[7] Marco Dorigo and Luca Maria Gambardella. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on evolutionary computation, 1(1):53–66, 1997.
[8] Marco Dorigo, Vittorio Maniezzo, and Alberto Colorni. Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(1):29–41, 1996.
[9] Neng Fan, Syed Mujahid, Jicong Zhang, Pando Georgiev, Petraq Papajorgji, Ingrida Steponavice, Britta Neugaard, and Panos M Pardalos. Nurse scheduling problem: An integer programming model with a practical application. Systems analysis tools for better health care delivery, pages 65–98, 2013.
[10] Merrill M Flood. The traveling-salesman problem. Operations research, 4(1):61–75, 1956.
[11] Walter J Gutjahr and Marion S Rauner. An ACO algorithm for a dynamic regional nurse-scheduling problem in austria. Computers & Operations Research, 34(3):642–666, 2007.
[12] Hamed Jafari and Nasser Salmasi. Maximizing the nurses’preferences in nurse scheduling problem: mathematical modeling and a meta-heuristic algorithm. Journal of industrial engineering international, 11:439–458, 2015.
[13] Richard Karp. Reducibility among combinatorial problems. In R. E. Miller, J. W. Thatcher, and J. D. Bohlinger, editors, Complexity of Computer Computations, pages 85–103. Springer US, 1972. doi: 10.1007/978-1-4684-2001-2_9.
[14] Jingpeng Li and Uwe Aickelin. A bayesian optimization algorithm for the nurse scheduling problem. 3:2149–2156, 2003.
[15] Zhenyuan Liu, Zaisheng Liu, Zhipeng Zhu, Yindong Shen, and Junwu Dong. Simulated annealing for a multi-level nurse rostering problem in hemodialysis service. Applied Soft Computing, 64:148–160, 2018.
[16] Margarida Moz and Margarida Vaz Pato. A genetic algorithm approach to a nurse rerostering problem. Computers & Operations Research, 34(3):667–691, 2007.
[17] Ahmed Oughalime, Wan Rosmanira Ismail, and Liong Choong Yeun. A tabu search approach to the nurse scheduling problem. 1:1–7, 2008.
[18] Javier Puente, Alberto Gomez, Isabel Fernández, and Paolo Priore. Medical doctor rostering problem in a hospital emergency department by means of genetic algorithms. Computers & Industrial Engineering, 56(4):1232–1242, 2009.
[19] Kush Shrivastava and Shishir Kumar. The effectiveness of parameter tuning on ant colony optimization for solving the travelling salesman problem. pages 78–83, 2018.
[20] Angus R Simpson, HR Maier, WK Foong, KY Phang, HY Seah, and CL Tan. Selection of parameters for ant colony optimization applied to the optimal design of water distribution systems. pages 1931–1936, 2001.
[21] Rafał Skinderowicz. Improving ant colony optimization efficiency for solving large tsp instances. Applied Soft Computing, 120:108653, 2022.
[22] Thomas Stützle, Marco Dorigo, et al. Aco algorithms for the traveling salesman problem. Evolutionary algorithms in engineering and computer science, 4:163–183, 1999.
[23] John Thornton and Abdul Sattar. Nurse rostering and integer programming revisited. pages 49–58, 1997.
[24] Lorraine Trilling, Alain Guinet, and Dominiue Le Magny. Nurse scheduling using integer linear programming and constraint programming. IFAC Proceedings Volumes, 39(3):671–676, 2006.
[25] Aykut Melih Turhan and Bilge Bilgen. A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem. Computers & Industrial Engineering, 145:106531, 2020.
[26] Kuan Yew Wong et al. Parameter tuning for ant colony optimization: a review. In 2008 international conference on computer and communication engineering, pages 542–545. IEEE, 2008.
[27] Jie-jun Wu, Ying Lin, Zhi-hui Zhan, Wei-neng Chen, Ying-biao Lin, and Jianyong Chen. An ant colony optimization approach for nurse rostering problem. In 2013 IEEE International Conference on Systems, Man, and Cybernetics, pages 1672–1676, 2013. doi: 10.1109/SMC.2013.288.