Application of Multi-Objective Oppositional Slime Mould Algorithm for Time Cost Trade-off Optimization Problems

Öz

The Slime Mould Algorithm (SMA) is a novel meta-heuristic search technique with strong exploration capability. However, like many population-based optimization methods, the standard SMA struggles to maintain an effective balance between exploration and exploitation, particularly in multi-objective combinatorial problems such as time–cost trade-off problems (TCTP) in construction scheduling. In addition, commonly used dominance-based multi-objective approaches rely on non-dominated sorting (NDS), which may increase computational complexity and reduce diversity preservation in dense Pareto populations. To address these limitations, this study proposes a Fitness-Distance Balance-based Oppositional Slime Mould Algorithm (FDBOSMA). The proposed framework enhances the standard SMA by integrating a dominance Fitness-Distance Balance (FDB) selection mechanism together with Opposition-Based Learning (OBL) to improve diversity, strengthen global exploration and local exploitation, and mitigate premature convergence. Unlike traditional NDS-based frameworks, the FDB strategy evaluates solutions based on both fitness quality and spatial distance, aiming to preserve Pareto front distribution while reducing sorting overhead. Construction time–cost trade-off problems with 19, 29, and 146 activities from the literature were used to validate the effectiveness of the proposed approach. The FDBOSMA algorithm was compared against leading meta-heuristic algorithms, including Multi-Objective Particle Swarm Optimization (MOPSO), TLBO variants, AOA, and plain SMA. Performance was evaluated using hypervolume (HV), spread (Sp), average percent deviation (APD), and number of function evaluations (NFE). For the 19-activity case, FDBOSMA achieved an HV of 0.707 approximately 14% higher than MOPSO (0.621) while requiring only 27% of MOPSO's function evaluation budget. For the 29-activity case, FDBOSMA achieved the best HV of 0.894 and the best Sp of 0.322 among all competing algorithms, with only 1,500 NFE compared to TLBO's 4,040. For the large-scale 146-activity case, FDBOSMA achieved the highest HV of 0.630 under an equal computational budget of 40,000 NFE. Statistical validation using Wilcoxon signed-rank and Friedman tests confirmed that performance differences are significant across both small- and large-scale problem instances (p < 0.05). These results demonstrate that integrating FDB and OBL within the SMA framework significantly enhances multi-objective search performance while maintaining competitive computational efficiency, providing construction planners with well-distributed and high-quality time–cost trade-off solutions.

Anahtar Kelimeler

• Time-cost trade-off problems
• optimization
• FDB selection method
• opposition-based learning
• multi-objective slime mould algorithm

Kaynakça

1. Kaveh, A., Khanzadi, M., Alipour, M., & Naraki, M. R. (2015). CBO and CSS algorithms for resource allocation and time-cost trade-off. Periodica Polytechnica Civil Engineering, 59(3), 361–371. https://doi.org/10.3311/ppci.7788
2. Tran, H. D. (2020). Optimizing time–cost in generalized construction projects using multiple objective social group optimization and multi-criteria decision-making methods. Engineering, Construction and Architectural Management, 27(9), 2287–2313. https://doi.org/10.1108/ECAM-08-2019-0412
3. Vanhoucke, M., & Debels, D. (2007). The discrete time/cost trade-off problem: Extensions and heuristic procedures. Journal of Scheduling, 10(5), 311–326. https://doi.org/10.1007/s10951-007-0031-y
4. Hegazy, T. (1999). Optimization of construction time–cost trade-off analysis using genetic algorithms. Canadian Journal of Civil Engineering, 26(6), 685–697. https://doi.org/10.1139/l99-031
5. Kandil, A., & El-Rayes, K. (2006). Parallel genetic algorithms for optimizing resource utilization in large-scale construction projects. Journal of Construction Engineering and Management, 132(5), 491–498. https://doi.org/10.1061/(ASCE)0733-9364(2006)132:5(491)
6. Bettemir, Ö. H., & Yücel, T. (2023). Simplified solution of time-cost trade-off problem for building constructions by linear scheduling. Jordan Journal of Civil Engineering, 17(2), 293–309. https://doi.org/10.14525/jjce.v17i2.10
7. Kumar, K. M., Agrawal, D., Vishwakarma, V. K., & Eirgash, M. A. (2024). Development of time-cost trade-off optimization model for Indian highway construction projects using non-dominated sorting genetic algorithm-II methodology. Asian Journal of Civil Engineering. https://doi.org/10.1007/s42107-024-01157-y
8. Agarwal., A.K., Chauhan., S.S., Sharma., K. et al. (2024). Development of time–cost trade-off optimization model for construction projects with MOPSO technique. Asian Journal of Civil Engineering. https://doi.org/10.1007/s42107-024-01063-3

9. Feng, C. W., Liu, L., & Burns, S. A. (1997). Using genetic algorithms to solve construction time–cost trade-off problems. Journal of Computing in Civil Engineering, 11(3), 184–189. https://doi.org/10.1061/(ASCE)0887-3801(1997)11:3(184)
10. Yang, I.-T. (2007). Performing complex project crashing analysis with the aid of a particle swarm optimization algorithm. International Journal of Project Management, 25(6), 637–646. https://doi.org/10.1016/j.ijproman.2006.11.001
11. Eirgash, M. A., & Toğan, V. (2023). A novel oppositional teaching-learning strategy based on the golden ratio to solve the time-cost-environmental impact trade-off optimization problems. Expert Systems with Applications, 119995.
12. Toğan, V., Sulub, A. S., Eirgash, M. A., & Mostofi, F. (2026). Project scheduling to minimize time and cost in large-scale construction projects with repulsion-based improved arithmetic optimization. Journal of Construction Engineering and Management, 152(3), 04025277. https://doi.org/10.1061/JCEMD4.COENG-17269
13. Son, P. V. H., & Khoi, L. N. Q. (2022). Utilizing artificial intelligence to solve the time–cost–quality trade-off problem. Scientific Reports, 12, 20112. https://doi.org/10.1038/s41598-022-24668-7
14. Sulub, A. S., Mostofi, F., & Toğan, V. (2024). Utilizing arithmetic optimization algorithm for optimizing time and cost in construction projects. Journal of Construction Engineering and Management Innovation, 7(4), 336–353. https://doi.org/10.31462/jcemi.2024.04336353
15. Luong, D.-L., Tran, D.-H., & Nguyen, P. T. (2018). Optimizing multi-mode time–cost–quality trade-off of construction project using opposition multiple objective difference evolution. International Journal of Construction Management, 0(0), 1–13.
16. Ozcan-Deniz, G., Zhu, Y., & Ceron, V. (2012). Time, cost, and environmental impact analysis on construction operation optimization using genetic algorithms. Journal of Management in Engineering, 28(3), 265–272.
17. Son, P. V. H., & Khoi, L. N. Q. (2023). Adaptive opposition slime mold algorithm for time–cost–quality–safety trade-off for construction projects. Asian Journal of Civil Engineering, 24, 1927–1942. https://doi.org/10.1007/s42107-023-00612-6
18. Eirgash, M. A., & Toğan, V. (2024). A dual opposition learning-based multi-objective Aquila Optimizer for trading-off time-cost-quality-CO₂ emissions of generalized construction projects. Engineering Computations.
19. Tran, D.-H., Luong, D. L., Duong, M. T., Le, T. N., & Pham, A. D. (2018). Opposition multiple objective symbiotic organisms search (OMOSOS) for time, cost, quality, and work continuity. Journal of Computational Design and Engineering, 5(2), 160–172. https://doi.org/10.1016/j.jcde.2017.11.008
20. Li, S., Chen, H., & Wang, M. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2020.03.055
21. Abdel-Basset., M, Chang., V, Mohamed., R. (2020). A hybrid novel Slime mould algorithm with whale optimization algorithm for tackling the image segmentation problem of chest X-ray images, Applied Soft Computing, 95, 106642
22. Naik, M. K., Panda, R., & Abraham, A. (2021). Adaptive opposition slime mould algorithm. Soft Computing, 25(22). https://doi.org/10.1007/s00500-021-06140-2
23. Eirgash, M. A., Toğan, V., & Dede, T. (2019). A multi-objective decision-making model based on TLBO for the time–cost trade-off problems. Structural Engineering and Mechanics, 71(2), 139-151.
24. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
25. Kahraman, H. T., Aras, S., & Gedikli, E. (2020). Fitness-distance balance (FDB): A new selection method for meta-heuristic search algorithms. Knowledge-Based Systems, 190.
26. Kahraman, H. T., Bakir, H., Duman, S., Katı, M., Aras, S., & Guvenc, U. (2022). Dynamic FDB selection method and its application: Modeling and optimizing of directional overcurrent relays coordination. Applied Intelligence, 52(5), 4873–4908.
27. Bakir, H., Guvenc, U., Kahraman, H. T., & Duman, S. (2022). Improved Lévy flight distribution algorithm with FDB-based guiding mechanism for AVR system optimal design. Computers & Industrial Engineering, 168, 108032.
28. Bakir, H., Duman, S., Guvenc, U., & others. (2023). Improved adaptive gaining-sharing knowledge algorithm with FDB-based guiding mechanism for optimization of optimal reactive power flow problem. Electrical Engineering, 105, 3121–3160. https://doi.org/10.1007/s00202-023-01803-9
29. Toğan, V., & Eırgash, M. A. (2019). Time-Cost Trade-Off Optimization with a New Initial Population Approach. Teknik Dergi, 30(6), 9561-9580. https://doi.org/10.18400/tekderg.410934
30. Ghohanı Arab, H., Mahallatı Rayenı, A., & Ghasemı, M. R. (2021). An Effective Improved Multi-objective Evolutionary Algorithm (IMOEA) for Solving Constraint Civil Engineering Optimization Problems. Teknik Dergi, 32(2), 10645-10674. https://doi.org/10.18400/tekderg.541640
31. Tizhoosh, H. R. (2005). Opposition-based learning: A new scheme for machine intelligence. In International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies.
32. Mahdavi, S., Rahnamayan, S., & Deb, K. (2018). Opposition-based learning: A literature review. Swarm and Evolutionary Computation, 39, 1–23.
33. Rahnamayan, S., Tizhoosh, H. R., & Salama, M. M. A. (2007). Quasi-oppositional differential evolution. In Proceedings of the IEEE Congress on Evolutionary Computation (pp. 22229–2236). Singapore. https://doi.org/10.1109/CEC.2007.4424748
34. Sakellaropoulos S, Chassiakos AP (2004) Project time-cost analysis under generalized precedence relations. Adv Eng Softw 35(10-11):715–724. https://doi.org/10.1016/j.advengsoft.2004.03.017
35. Toğan V, Dede T, Başağa HB (2021) Handbook of AI-based Metaheuristics. 1st ed. Boca Raton, New York: Taylor & Francis Group. https://doi.org/10.1201/9781003162841
36. Bettemir, Ö. H., and M. T. Birgonul. 2025. “Solution of discrete time–cost trade-off problem with adaptive search domain.” Eng. Constr. Archit.Manage. 32 (2): 1032–1052. https://doi.org/10.1108/ECAM-06-2022-0601.
37. Sulub, A. S., Eirgash, M. A., and Toğan, V. (2025). An arithmetic optimization algorithm based on opposition jumping rate for time–cost trade-off optimization problems. Asian J. Civ. Eng. 26, 867–886 https://doi.org/10.1007/s42107-024-01227-1
38. Habibi, F., Barzinpour, F., & Sadjadi, S. J. (2017). A multi-objective optimization model for project scheduling with time-varying resource requirements and capacities. Journal of Industrial and Systems Engineering, 10 (special issue on scheduling), 92-118.
39. Akbarzadeh, M. R., Naeim, B., Asgari, A., & Estekanchi, H. E. (2026). Framework for multi-hazard parameterized fragility-based uncertainty quantification and sensitivity analysis of offshore wind turbines. Soil Dynamics and Earthquake Engineering, 201, 109963. https://doi.org/10.1016/j.soildyn.2025.109963.