Alt yüklenici seçimi için altın orandan esinlenen karşıtlık öğrenmeli Rao-1 algoritması kullanılarak zaman-maliyet-kalite ödünleşimi optimizasyonu

Öz

Arka Plan—İnşaat projeleri genellikle alt yükleniciler tarafından gerçekleştirilen iş paketlerine ayrılmakta, genel yükleniciler ise projenin genel kalitesinden ve zamanında tamamlanmasından sorumlu olmaktadır. Uygun alt yüklenicilerin projenin erken aşamalarında seçilmesi; proje süresi, maliyet performansı ve elde edilen kaliteyi doğrudan etkilediğinden kritik bir karar problemidir. Bu karar, zaman, maliyet ve kalite hedeflerinin birbiriyle çelişen yapısı nedeniyle karmaşık olup söz konusu hedeflerin eş zamanlı olarak değerlendirilmesini gerektirmektedir. İnşaat yönetiminde çok amaçlı optimizasyon tekniklerinin kullanımı giderek yaygınlaşmasına rağmen, mevcut yaklaşımların önemli bir bölümü, özellikle cezalar, teşvikler ve son teslim tarihi kısıtları gibi gerçekçi proje özellikleri dikkate alındığında, yüksek hesaplama maliyeti, yavaş yakınsama veya sınırlı çözüm çeşitliliği gibi sorunlarla karşılaşmaktadır.

Amaç—Bu çalışmanın amacı, zaman-maliyet-kalite ödünleşimini açıkça ele alan etkin bir çok amaçlı optimizasyon çerçevesi geliştirmektir. Çalışmada yakınsama davranışının ve çözüm kalitesinin iyileştirilmesi, hesaplama maliyetinin azaltılması ve proje planlamasının erken aşamasında dengeli proje planlarının belirlenmesine yönelik pratik bir karar destek yaklaşımının sunulması hedeflenmektedir.

Yöntem—Bu çalışmada, altın oran tabanlı karşıtlık öğrenme mekanizmasının standart parametresiz Rao-1 algoritmasına entegre edilmesiyle geliştirilen ve altın oran tabanlı karşıtlık Rao-1 (GROL-Rao-1) olarak adlandırılan yeni bir algoritma önerilmiştir. Alt yüklenici seçim problemi; proje süresi, toplam maliyet ve genel kaliteyi birlikte dikkate alan, son teslim tarihi, cezalar ve teşvikler gibi gerçekçi kısıtları içeren ayrık çok amaçlı bir optimizasyon modeli olarak formüle edilmiştir. Önerilen yöntem, 20 proje faaliyetinden oluşan gerçek bir vaka çalışması üzerinden doğrulanmış ve ayrık parçacık sürü optimizasyon (DPSO), dinamik karşıtlık Rao-1 (DOLRao-1), NSGA-II ve NDSII-Rao-1 algoritmaları ile karşılaştırılmıştır. Performans değerlendirmesinde amaç fonksiyonu değerlendirme sayısı, hiper hacim (HV) ve yayılım (Spread) göstergeleri kullanılmış ve istatistiksel anlamlılık testleri gerçekleştirilmiştir. Ayrıca, Pareto-optimal çözümlerin önceliklendirilmesi amacıyla kalabalıklık mesafesine dayalı sıralama yöntemi uygulanmıştır.

Bulgular—Elde edilen sonuçlar, GROL-Rao-1 algoritmasının kıyaslama algoritmalarına göre daha yüksek kaliteli ve daha iyi dağılıma sahip Pareto cepheleri ürettiğini ve hesaplama maliyetini yaklaşık %50 oranında azalttığını göstermektedir. İstatistiksel analizler, elde edilen iyileştirmelerin anlamlı olduğunu doğrulamıştır. Ayrıca, kalabalıklık mesafesine dayalı sıralama yöntemi, zaman, maliyet ve kalite hedefleri arasında dengeli çözümler sunan uzlaşık çözümlerin etkin bir şekilde belirlenmesini sağlamıştır.

Sonuç—Önerilen optimizasyon çerçevesi, inşaat projelerinde erken aşamadaki alt yüklenici seçimi için etkin bir karar desteği sağlamakta ve kaynak tahsisi ile proje planlamasının sağlamlığını artırmaktadır. Çalışma, inşaat yönetiminde çok amaçlı optimizasyona hesaplama açısından verimli ve karar odaklı bir yaklaşım sunmakta ve daha karmaşık ve büyük ölçekli proje uygulamalarına yönelik gelecekteki araştırmalar için bir temel oluşturmaktadır.

Anahtar Kelimeler

• İnşaat yönetimi
• Altın oran tabanlı karşıtlık öğrenme
• Çok kriterli karar verme analizi
• Çok amaçlı Rao-1 algoritması
• Zaman-maliyet-kalite ödünleşim problemi

Time cost–quality trade-off optimization for subcontractor selection using a golden ratio-inspired oppositional Rao-1 algorithm

Öz

Context—Construction projects are typically divided into work packages executed by subcontractors, while general contractors remain responsible for overall quality and timely completion. Selecting appropriate subcontractors at the early project stage is a critical decision, as it directly influences project duration, cost performance, and delivered quality. This decision is inherently complex due to the conflicting nature of time, cost, and quality objectives, which must be considered simultaneously. Although multi-objective optimization techniques have been increasingly applied in construction management, many existing approaches suffer from high computational effort, slow convergence, or limited solution diversity, particularly when realistic project features such as penalties, bonuses, and deadline constraints are incorporated.

Objective—The objective of this study is to develop an efficient multi-objective optimization framework for subcontractor selection that explicitly addresses the time–cost–quality trade-off. The study aims to improve convergence behavior and solution quality while reducing computational effort, and to provide practical decision support for identifying balanced project plans at the early planning stage.

Method—This study proposes a novel algorithm, termed the golden ratio-based oppositional Rao-1 (GROL-Rao-1), which integrates golden ratio–based opposition learning into the standard parameter-less Rao-1 algorithm to enhance search efficiency. The subcontractor selection problem is formulated as a discrete multi-objective optimization model considering project duration, total cost, and overall quality, along with realistic constraints such as deadlines, penalties, and bonuses. The proposed method is validated through a real-world case study involving 20 project activities and is compared with discrete particle swarm optimization, dynamic oppositional Rao-1, NSGA-II, and NDSII-Rao-1. Performance is evaluated using objective function evaluations, hypervolume, and spread indicators, supported by statistical significance testing. The crowded distance ranking method is also applied to prioritize Pareto-optimal solutions.

Results—The results show that GROL-Rao-1 outperforms the benchmark algorithms by producing higher-quality and better-distributed Pareto fronts while reducing computational effort by approximately 50%. Statistical analyses confirm the significance of these improvements, and the crowded distance ranking effectively identifies compromise solutions that balance time, cost, and quality objectives.

Conclusion—The proposed framework provides effective support for early-stage subcontractor selection and enhances resource allocation and planning robustness in construction projects. It contributes a computationally efficient and decision-oriented approach to multi-objective optimization in construction management and offers a foundation for future research on more complex and large-scale project applications.

Anahtar Kelimeler

• Construction management
• Golden ratio-based oppositional learning
• multi-criteria decision-making analysis
• Multi-objective Rao-1 algorithm
• Time-cost-quality trade-off problem

Kaynakça

1. J. Mbachu, “Conceptual framework for the assessment of subcontractors’ eligibility and performance in the construction industry”, Construction Management and Economics, 26(5), 471-484, 2008. https://doi.org/10.1080/01446190801918730.
2. G. Polat, B. Kaplan, B. N. Bingol, “Subcontractor selection using genetic algorithm”, Procedia Engineering, 123, 432-440, 2015. https://doi.org/10.1016/j.proeng.2015.10.081.
3. S. Kale, D. Arditi, “General contractors’ relationships with subcontractors: A strategic asset”, Construction Management and Economics, 19(5), 541-549, 2001. https://doi.org/10.1080/01446193.2001.9709630.
4. S. Monghasemi, M. R. Nikoo, M. A. Khaksar Fasaee, J. Adamowski, “A novel multi criteria decision making model for optimizing time–cost–quality trade-off problems in construction projects”, Expert Systems with Applications, 42(6), 3089-3104, 2015. https://doi.org/10.1016/j.eswa.2014.11.032.
5. H. Dolio, “Analysis of pre-qualification criteria in contractor selection and their impacts on project success”, Construction Management and Economics, 27(12), 1245-1263, 2009. https://doi.org/10.1080/01446190903394541.
6. H. Zhang, H. Li, “Simulation-based optimization for dynamic resource allocation”, Automation in Construction, 13(3), 409-420, 2004. https://doi.org/10.1016/j.autcon.2003.12.005.
7. D.-H. Tran, M.-Y. Cheng, M.-T. Cao, “Hybrid multiple objective artificial bee colony with differential evolution for the time–cost–quality trade-off problem”, Knowledge-Based Systems, 74, 176-186, 2015. https://doi.org/10.1016/j.knosys.2014.11.018.
8. A. Afshar, A. Kaveh, O. Shoghli, “Multi-objective optimization of time–cost–quality using multi-colony ant algorithm”, Asian Journal of Civil Engineering, 8(2), 113-124, 2007.

9. T. Wang, M. Abdallah, C. Clevenger, S. Monghasemi, “Time–cost–quality trade-off analysis for planning construction projects”, Engineering, Construction and Architectural Management, 28(1), 82-100, 2021. https://doi.org/10.1108/ECAM-12-2017-0271.
10. S. Li, H. Chen, M. Wang, A. A. Heidari, S. Mirjalili, “Slime mould algorithm: A new method for stochastic optimization”, Future Generation Computer Systems, 111, 300-323, 2020. https://doi.org/10.1016/j.future.2020.03.055.
11. L. Abualigah, D. Yousri, M. Abd Elaziz, A. A. Ewees, M. A. A. Al-Qaness, A. H. Gandomi, “Aquila Optimizer: A novel meta-heuristic optimization algorithm”, Computers & Industrial Engineering, 157, 107250, 2021. https://doi.org/10.1016/j.cie.2021.107250.
12. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, 6(2), 182-197, 2002. https://doi.org/10.1109/4235.996017.
13. E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, V. G. da Fonseca, “Performance assessment of multiobjective optimizers: An analysis and review”, IEEE Transactions on Evolutionary Computation, 7(2), 117-132, 2003. https://doi.org/10.1109/TEVC.2003.810758.
14. R. V. Rao, “Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems”, International Journal of Industrial Engineering Computations, 11(1), 107-130, 2020. https://doi.org/10.5267/j.ijiec.2019.6.002.
15. M. A. Eirgash, V. Toğan, M. K. Trivedi, K. Sharma, “A modified oppositional teaching-learning-based optimization model for solving construction time–cost–quality trade-off problems”, 7th International Project and Construction Management Conference (IPCMC2022), Istanbul: Türkiye, 20-22 October 2022, 100-112.
16. M. Yılmaz, T. Dede, “Multi-objective time–cost trade-off optimization for the construction scheduling with Rao algorithms”, Structures, 48, 798-808, 2023. https://doi.org/10.1016/j.istruc.2023.01.006.
17. V. Togan, A. S. Sulub, M. A. Eirgash, F. Mostofi, “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, 2026. https://doi.org/10.1061/JCEMD4.COENG-17269.
18. H. R. Tizhoosh, “Opposition-based learning: A new scheme for machine intelligence”, International Conference on Computational Intelligence for Modelling, Control and Automation. Vienna, Austria, 28-30 November 2005, 695-701. https://doi.org/10.1109/cimca.2005.1631345.
19. M. A. Eirgash, V. Toğan, “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, 224, 119995, 2023. https://doi.org/10.1016/j.eswa.2023.119995.
20. D. Diakoulaki, G. Mavrotas, L. Papayannakis, “Determining objective weights in multiple criteria problems: The CRITIC method”, Computers & Operations Research, 22(7), 763-770, 1995. https://doi.org/10.1016/0305-0548(94)00059-H.
21. C. L. Hwang, K. Yoon, Multiple attribute decision making: Methods and applications, Berlin, Heidelberg, NY, USA, Springer - Verlag, 1981.
22. J. E. Kelley, M. R. Walker, “Critical-path planning and scheduling”, Eastern Joint IRE-AIEE-ACM Computer Conference, Boston Massachusetts, USA, 1-3 December 1959, 160-173. https://doi.org/10.1145/1460299.1460318
23. J. W. Fondahl, A non-computer approach to the critical path method for construction industry, 2nd Edition, Department of Civil Engineering Stanford University, Stanford, California, USA, 1962.
24. S. E. Elmaghraby, Activity Networks: Project Planning and Control by Network Models, New York, USA, Wiley, 1977.
25. C-W. Feng, L. A. Liu, S. A. Burns, “Using genetic algorithms to solve construction time-cost trade-off problems”, Journal of Computing in Civil Engineering, 11(3), 184-189, 1997. https://doi.org/10.1061/(ASCE)0887-3801(1997)11:3(184).
26. K. P. Anagnostopoulos, L. Kotsikas, “Experimental evaluation of simulated annealing algorithms for the time-cost trade-off problem”, Applied Mathematics and Computation, 217(1), 260-270, 2010. https://doi.org/10.1016/j.amc.2010.05.056.
27. A. Dhawan, K. Sharma, M. K. Trivedi, “Simulated annealing-based time–cost trade-off model for construction projects”, Artificial Intelligence and Sustainable Computing, H. M. Dubey, M. Pandit, L. Srivastava, B. K. Panigrahi, eds., Singapore, Springer; 2022. Ch. 4, 33-43. https://doi.org/10.1007/978-981-16-1220-6_4.
28. Y. Xiong, Y. P. Kuang, “Applying an ant colony optimization algorithm-based multiobjective approach for time–cost trade-off”, Journal of Construction Engineering and Management, 134(2), 153-156, 2008. https://doi.org/10.1061/(ASCE)0733-9364(2008)134:2(153).
29. M. A. Eirgash, V. Toğan, T. Dede, “A multi-objective decision-making model based on TLBO for the time–cost trade-off problems”, Structural Engineering and Mechanics, 71(2), 139-151, 2019. https://doi.org/10.12989/sem.2019.71.2.139.
30. S. Aminbakhsh, R. Sönmez, “Discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem”, Expert Systems with Applications, 51, 177-185, 2016. https://doi.org/10.1016/j.eswa.2015.12.041.
31. A. S. Sulub, F. Mostofi, V. Togan, “Utilizing the arithmetic optimization algorithm for optimizing time and cost in construction projects”, Journal of Construction Engineering and Management Innovation, 7(4), 336-353, 2024. https://doi.org/10.31462/jcemi.2024.04336353.
32. A. S. Sulub, M. A. Eirgash, V. Togan, “An arithmetic optimization algorithm based on opposition jumping rate for time–cost trade-off optimization problems”, Asian Journal of Civil Engineering, 26, 867–886, 2025. https://doi.org/10.1007/s42107-024-01227-1.
33. K. Khalili-Damghani, M. Tavana, A. R. Abtahi, F. J. S. Arteaga, “Solving multi-mode time–cost–quality trade-off problems under generalized precedence relations”, Optimization Methods & Software, 30(5), 965-1001, 2015. https://doi.org/10.1080/10556788.2015.1005838.
34. A. J. Babu, N. Suresh, “Project management with time, cost, and quality considerations”, European Journal of Operational Research, 88(2), 320-327, 1996. https://doi.org/10.1016/0377-2217(94)00202-9.
35. D. B. Khang, Y. M. Myint, “Time, cost and quality trade-off in project management: a case study”, International Journal of Project Management, 17(4), 249-256, 1999. https://doi.org/10.1016/S0263-7863(98)00043-X.
36. B. Pollack-Johnson, M. J. Liberatore, “Incorporating quality considerations into project time/cost tradeoff analysis and decision making”, IEEE Transactions on Engineering Management, 53(4), 534-542, 2006. https://doi.org/10.1109/TEM.2006.883705.
37. H. R. Tareghian, S. H. Taheri, “A solution procedure for the discrete time, cost and quality tradeoff problem using electromagnetic scatter search”, Applied Mathematics and Computation, 190(2), 1136-1145, 2007. https://doi.org/10.1016/j.amc.2007.01.100.
38. K. El-Rayes, A. A. Kandil, “Time-cost-quality trade-off analysis for highway construction”, Journal of Construction Engineering and Management, 131(4), 477-486, 2005. https://doi.org/10.1061/(ASCE)0733-9364(2005)131:4(477).
39. B. Paryzad, K. Eshghi, “A new approach in fuzzy optimization of time–cost–quality trade-off problem”, Optimality, 1(1), 34-45, 2024. https://doi.org/10.22105/opt.v1i1.42.
40. K. C. Lam, S. T. Ng, T. Hu, M. Skitmore, S. O. Cheung, “Decision support system for contractor pre-qualification—artificial neural network model”, Engineering, Construction and Architectural Management, 7(3), 251-266, 2000. https://doi.org/10.1108/eb021150.
41. E. Fallah-Mehdipour, O. Bozorg-Haddad, M. M. R. Tabari, M. A. Mariño, “Extraction of decision alternatives in construction management projects: Application and adaptation of NSGA-II and MOPSO”, Expert Systems with Applications, 39(3), 2794-2803, 2012. https://doi.org/10.1016/j.eswa.2011.08.139.
42. S. Aminbakhsh, A. M. Abdulsattar, “Optimizing three-dimensional trade-off problem of time–cost–quality over multi-mode projects with generalized logic”, Buildings, 14(6), 1676, 2024. https://doi.org/10.3390/buildings14061676.
43. K. Sharma, M. K. Trivedi, “AHP and NSGA-II-based time–cost–quality trade-off optimization model for construction projects”, Artificial Intelligence and Sustainable Computing, H. M. Dubey, M. Pandit, L. Srivastava, B. K. Panigrahi, Eds., Singapore, Springer, 2022. Ch. 5, 45-63. https://doi.org/10.1007/978-981-16-1220-6_5.
44. D. L. Luong, D. H. Tran, P. T. Nguyen, “Optimizing multi-mode time–cost–quality trade-off of construction project using opposition multiple objective difference evolution”, International Journal of Construction Management, 21(3), 271-283, 2021. https://doi.org/10.1080/15623599.2018.1526630.
45. D. T. Nguyen, D. T. V. Doan, N. N. C. Tran, D. H. Tran, “A novel multiple objective whale optimization for time–cost–quality tradeoff in non-unit repetitive projects”, International Journal of Construction Management, 23(5), 843-854, 2023. https://doi.org/10.1080/15623599.2021.1938939.
46. P. V. H. Son, L. N. Q. Khoi, “Application of slime mold algorithm to optimize time, cost and quality in construction projects”, International Journal of Construction Management, 24(13), 1375-1386, 2024. https://doi.org/10.1080/15623599.2023.2174660.
47. M. Yılmaz, T. Dede, “Optimizing multiobjective time–cost–quality problems in construction projects: Efficacy of strength Pareto-based Rao algorithms”, Journal of Construction Engineering and Management, 151(5), 04025036, 2025. https://doi.org/10.1061/JCEMD4.COENG-15551.
48. M. Reyes-Sierra, C. A. Coello Coello, “Multi-objective particle swarm optimizers: A survey of the state-of-the-art”, International Journal of Computational Intelligence Research, 2(3), 287-308, 2006.