Bi-objective Machine Scheduling Using Enhanced Simulated Annealing and Bee Algorithm Approaches
Main Article Content
Abstract
Many industrial systems involve multiple criteria and objectives, and they are very complex problems in computational science, such as task scheduling. We propose bi-criteria and bi-objective scheduling problems, which are solved by two nature-inspired evolutionary algorithms, such as Simulated Annealing (SA) and Bee Algorithm (BA). This problem is characterized by scheduling a batch of tasks on multiple machines, and it is fundamental because the solution should focus on the simultaneous optimization of two conflicting objectives: the makespan minimization and the total tardiness minimization. This problem is NP-Hard, and therefore, two evolutionary methods were used to search for solutions intelligently in this huge, very complex space. In this research, A mathematical model of the scheduling problem was developed based on the above objectives. Here, we proposed a tailored tune-up of SA and BA, both of which have been specifically developed and implemented to solve the proposed model for integrated scheduling and delivery, geared for the bifunctional nature of the problem. Quantitative results indicate that the Bee Algorithm (BA) achieves a more diverse Pareto front, with an average improvement of approximately 12–18 % in solution diversity compared to Simulated Annealing (SA). In contrast, SA converges faster, reducing computational time by about 30–40 % for large problem instances (n ≥ 80). Overall, BA provides better trade-offs between objectives, while SA offers superior computational efficiency. The results showed that both algorithms can generate solutions that are balanced and time-efficient.
Downloads
Article Details
Section
How to Cite
References
Al-Kayiem, H.H., 2010. Study on the thermal accumulation and distribution inside a parked car cabin. American Journal of Applied Sciences, 7(6), pp. 784–789.
Al-Nuaimi, A., 2015. Local search algorithms for multiobjective scheduling problem. Journal of Al-Rafidain University College for Sciences, pp. 201–217. https://doi.org/10.55562/jrucs.v36i2.255
Ali, F.H., 2020. Optimal and near optimal solutions for multi objective function on a single machine. In: 2020 International Conference on Computer Science and Software Engineering (CSASE). https://doi.org/10.1109/CSASE48920.2020.9142053
Bakar, M.R., Abbas, I.T., Kalal, M.A., AlSattar, H.A., Bakhayt, A.G. and Kalaf, B.A., 2017. Solution for multi-objective optimisation master production scheduling problems based on swarm intelligence algorithms. Journal of Computational and Theoretical Nanoscience, 14(11), pp. 5184–5194.
Błażewicz, J., Ecker, K.H., Pesch, E., Schmidt, G. and Węglarz, J., 2007. Handbook on scheduling: From theory to applications. Berlin: Springer.
Burmeister, S.C., Guericke, D. and Schryen, G., 2024. A memetic NSGA-II for the multi-objective flexible job shop scheduling problem with real-time energy tariffs. Flexible Services and Manufacturing Journal, 36, pp. 1530–1570.
Celik, E. and Topaloglu, S., 2021. A novel simulated annealing-based optimization approach for cluster-based task scheduling. Cluster Computing, 24(4), pp. 2927–2956.
Chen, B., Zeng, Z. and Zhang, Y., 2014. A new local search-based multiobjective optimization algorithm. IEEE Transactions on Evolutionary Computation, 19(1), pp. 50–73.
Chong, C.S., Low, M.Y.H., Sivakumar, A.I. and Gay, K.L., 2006. A bee colony optimization algorithm to job shop scheduling. In: Proceedings of the Winter Simulation Conference, pp. 1954–1961.
Colombo, F., 2014. Mathematical programming algorithms for network optimization problems. PhD thesis. Università degli Studi di Milano.
Davidović, T., Ramljak, D. and Šelmić, M., 2015. Bee colony optimization—Part I: The algorithm overview. YUJOR, 25(1), pp. 33–56.
Doctor, S., Venayagamoorthy, G.K. and Gudise, V.G., 2004. Optimal PSO for collective robotic search applications. In: Proceedings of the Congress on Evolutionary Computation, pp. 1390–1395.
Festa, P., 2014. A brief introduction to exact, approximation, and heuristic algorithms for solving hard combinatorial optimization problems. In: International Conference on Transparent Optical Networks, pp. 1–20.
Gulati, R. and Singh, N., 2014. A literature review of bee colony optimization algorithms. In: Innovative Applications of Computational Intelligence on Power, Energy and Controls (CIPECH), pp. 499–504.
Ibrahim, M.H., 2022. Solving multi-objectives function problem using branch and bound and local search methods. International Journal of Nonlinear Analysis and Applications, pp. 1649–1658.
Khan, K.A. and Khan, A.S., 2012. A comparison of BA, GA, PSO, BP and LM for training feed forward neural networks in e-learning context. International Journal of Intelligent Systems and Applications.
Khare, A. and Rangnekar, S., 2013. A review of particle swarm optimization and its applications in solar photovoltaic system. Applied Soft Computing, 13(5), pp. 2997–3006.
Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P., 1983. Optimization by simulated annealing. Science, 220(4598), pp. 671–680.
Lalwani, S., Sharma, H. and Dashora, Y., 2013. A comprehensive survey: Applications of multi-objective particle swarm optimization algorithm. Transactions on Combinatorics, 2(1), pp. 39–101.
Maraveas, C., 2022. Applications of IoT for optimized greenhouse environment and resources management. Computers and Electronics in Agriculture, 198, P. 106993.
Marini, F. and Walczak, B., 2015. Particle swarm optimization (PSO): A tutorial. Chemometrics and Intelligent Laboratory Systems, 149, pp. 153–165.
Meissner, M., Schmuker, M. and Schneider, G., 2006. Optimized particle swarm optimization and its application to artificial neural network training. BMC Bioinformatics, 7(1), P. 125.
Meng, L., Zhang, C., Zhang, B., Gao, K., Ren, Y. and Sang, H., 2023. MILP modelling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times. Swarm and Evolutionary Computation, P. 101374.
Möhring, R.H., Schulz, A.S. and Uetz, M., 2003. Solving project scheduling problems by minimum cut computations. Management Science, 49(3), pp. 330–350.
Mou, J., Song, W. and Chen, Q., 2017. Multi-objective inverse scheduling optimization of single-machine shop system with uncertain due-dates. Cluster Computing, 20(1), pp. 371–390.
Mousa, A.A., El-Shorbagy, M.A. and Abd-El-Wahab, A., 2012. Local search-based hybrid particle swarm optimization algorithm for multiobjective optimization. Swarm and Evolutionary Computation, 3, pp. 1–14.
Onwunalu, J.E. and Durlofsky, L.J., 2010. Application of a particle swarm optimization algorithm for determining optimum well location and type. Computational Geosciences, 14(1), pp. 183–198.
Pham, D.T., Castellani, M., Ghanbarzadeh, A. and Koç, E., 2007. The bees algorithm: A novel tool for complex optimization problems. International Journal of Manufacturing Research, 2(4), pp. 454–472.
Pinedo, M.L., 2016. Scheduling: Theory, algorithms, and systems. 5th ed. Cham: Springer.
Poli, R., 2007. An analysis of publications on particle swarm optimization applications. Journal of Artificial Evolution and Applications.
Teodorovic, D., 2006. Bee colony optimization: Principles and applications. In: Neural Network Applications Conference, pp. 151–156.
Thomas, H., Cormen, T., Leiserson, C. and Rivest, R., 2009. Introduction to algorithms. 3rd ed.
Umar, M.F., 2025. Predicting the durability properties of concrete with recycled plastic aggregate. Journal of Engineering, 31(10), pp. 1–22. https://doi.org/10.31026/j.eng.2025.10.01
Wang, Y., Li, J. and Zhang, H., 2022. A hybrid particle swarm optimization and simulated annealing algorithm for job shop scheduling. European Journal of Operational Research, 299(3), pp. 1021–1035.
Wu, C.C., 2007. Heuristic algorithms for solving maximum lateness scheduling problem with learning considerations. Computers & Industrial Engineering, 52(1), pp. 124–132.
Wu, R., Luo, E., Li, X., Tang, H. and Li, Y., 2025. Hybrid artificial bee colony algorithm with Q-learning for distributed scheduling. Swarm and Evolutionary Computation.
Yousif, S.F., Ali, F.H. and Alshaikhli, K.F., 2023. Using local search methods for solving two multi-criteria machine scheduling problems, Al-Mustansiriyah Journal of Science, 34(4), pp. 96–103. https://doi.org/10.23851/mjs.v34i4.1430
Yousif, S.F., 2024. Solving maximum early jobs time and range of lateness jobs times problem. Iraqi Journal of Science, pp. 923–937. https://doi.org/10.24996/ijs.2024.65.2.28
Zhang, W., 2024. Enhancing multi-objective evolutionary algorithms with machine learning for scheduling problems. Frontiers in Industrial Engineering, 2, P. 1337174.
Zhang, Y., 2015. A comprehensive survey on particle swarm optimization algorithm and its applications. Mathematical Problems in Engineering, P. 931256.