Araştırma Makalesi
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İNŞAAT ZAMAN-MALİYET ÖDÜNLEŞİM OPTİMİZASYONU PROBLEMİ İÇİN DEĞİŞTİRİLMİŞ UYARLANABİLİR AĞIRLIKLI RAO-3 ALGORİTMASI

Yıl 2025, Cilt: 33 Sayı: 3, 1984 - 1996, 19.12.2025
https://doi.org/10.31796/ogummf.1718264

Öz

Değiştirilmiş Uyarlanabilir Ağırlık Yöntemi (MAWA), zaman–maliyet optimizasyon problemlerini çözmek için yaygın olarak kullanılan basit bir yöntemdir. MAWA, zaman-maliyet optimizasyonu da dahil olmak üzere çeşitli çok amaçlı optimizasyon problemlerine uygulanabilen esnek ve etkili bir yaklaşımdır. Bu tür problemler genellikle çok amaçlı optimizasyon problemleri olarak ele alınmakta olup, bu problemlerin çözümünde çoğunlukla meta-sezgisel algoritmalar kullanılmaktadır. Bu algoritmalar, çözüm uzayı sınırları içerisinde rastgele başlatılan bir çözüm popülasyonu üzerinde çalışır. MAWA, popülasyondaki tüm bireylere özgül niteliklerini dikkate almadan eşit ağırlık faktörleri atar. Ancak her çözüm, çözüm uzayındaki konumuna bağlı olarak kendine özgü uygunluk özelliklerine sahiptir. Bu çalışmada, Pareto-optimal çözümler elde etmek amacıyla Rao-3 algoritması ile MAWA'nın birleştirildiği çok amaçlı bir optimizasyon modeli sunulmuştur. Teknik literatürden alınan ve 81 ile 146 faaliyet içeren iki inşaat projesi örneği, önerilen MAWA-Rao-3 yönteminin etkinliğini değerlendirmek amacıyla incelenmiştir. Elde edilen sonuçlar, yaklaşık Pareto cepheleri veya neredeyse optimal çözümler üreten önceki modellerin sonuçlarıyla karşılaştırılmıştır. Bulgular, MAWA-Rao-3 algoritmasının inşaat mühendisliği ve yönetimi alanındaki zaman-maliyet dengeleme problemlerini çözmede etkili bir şekilde çalıştığını göstermektedir.

Kaynakça

  • Abualigah. L, Diabat. A, Mirjalili. S, Elaziz. M.A, Gandomi. A.H, (2021a). The arithmetic optimization algorithm, Computer Methods in Applied mechanics and Engineering, 376, 113609. https://doi.org/10.1016/j.cma.2020.113609
  • Abualigah. L, Yousri. D, Abd Elaziz. M, Ewees. A.A, Al-qaness. M. A., Gandomi. A. H. (2021b). Aquila optimizer: A novel meta-heuristic optimization algorithm, Computers & Industrial Engineering., 157,107250. https://doi.org/10.1016/j.cie.2021.107250
  • Afshar, A., Ziaraty, A., Kaveh. A and Sharifi. F. (2009). Nondominated archiving multicolumn ant algorithm in time–cost trade-off optimization. Journal Construction Engineering and Management, 135, 7, 668-674.
  • 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 Civil Engineering. 25, 4529–4539, https://doi.org/10.1007/s42107-024-01063-3
  • Albayrak, G. (2020). “Novel hybrid method in time–cost trade-off or resource-constrained construction projects”. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44 (4), 1295-1307. https://doi.org/10.1007/s40996-020-00437-2
  • Aminbakhsh, S., and Sönmez, R. (2016). Applied discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem.” Expert System with Applications, 51, 177-185.
  • Basseur, M,. Zitzler, E. (2006). A preliminary study on handling uncertainty in indicator-based multiobjective optimization. In: Lecture Notes in Computer Science. Springer Berlin Heidelberg. 3907, p. 727–39. https://doi.org/10.1007/11732242_71.
  • Bettemir, Ö. H. (2009). Optimization of time-cost-resource trade-off problems in project scheduling using meta-heuristic algorithms. Doctoral dissertation, Middle East Technical University, Turkey.
  • Bettemir, Ö. H., and Birgönül, T. (2016). Network analysis algorithm for the solution of discrete time-cost trade-off problem. KSCE Journal of Civil Engineering, 21, No. 4, pp. 1047-1058.
  • Bettemir, Ö.H. and Birgonul, M.T. (2023), “Solution of discrete time–cost trade-off problem with adaptive search domain”, Engineering, Construction and Architectural Management, 0969-9988. https://www.emerald.com/insight/0969-9988.htm
  • Deb., K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Transaction and Evolution Computing, 6(2), 182–197.
  • Dede, T., (2018). Decision-Making Process Techniques Used in the Optimization of Construction Projects, Engineering Sciences, NWSAENS, 13, 2, 128-136.
  • Eirgash, M. A., and Dede, T. (2018). “A multi-objective improved teaching learning-based optimization algorithm for time-cost trade-off problems.” Journal of Construction Engineering, Management and Innovation, 1(3), 118-128.
  • Eirgash, M. A., Toğan, V., and 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
  • Eirgash., M.A. (2025). Influence of jumping rate on opposition-based jaya algorithm for discrete time cost trade-off optimization problems, Uludağ University Journal of The Faculty of Engineering, 30(1), 35-50.
  • Elbeltagi, E., Hegazy, T., and Grierson, D. (2005). “Comparison among Five Evolutionary-Based Optimization Algorithms.” Advanced Engineering Informatics, Vol. 19, pp. 43–53.
  • Eshtehardian, E., Afshar, A., and Abbasnia, R. (2008). “Time–cost optimization: using GA and fuzzy sets theory for uncertainties in cost.” Construction Management and Economics, Vol. 26, No. 7, pp.
  • Feng, C-W., Liu, L., and Burns, S. A. (1997) “Using genetic algorithms to solve construction time-cost trade-off problems.” Journal of Computing in Civil Engineering, Vol. 11, No. 3, pp.184-189.
  • Hamdy, M,. Nguyen, A.T,. Hensen, J.L.M. (2016). A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems. Energy Building;121(6):57–71. https://doi.org/10.1016/j.enbuild.2016.03.035.
  • Jia, H. Rao, H. Wen., C. Mirjalili, S. (2023). “Crayfsh optimization algorithm”, Artificial Intelligence Review, https://doi.org/10.1007/s10462-023-10567-4
  • Kelly, J. E. (1961). “Critical path planning and scheduling: Mathematical basis” Operational Research., 9(3), 167–179.
  • Kim, I.Y. and de Week, O.L.(2005). Adaptive weighted-sum method for bi-objective, Journal of Construction Division, 91(1), 45-68, 1965
  • 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. 25, 5975–5988, https://doi.org/10.1007/s42107-024-01157-y
  • 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
  • Liu, L., Burns, S., and Feng, C. (1995). “Construction time–cost trade-off analysis using LP/IP hybrid model.” Journal of Construction Engineering and Management., 121(4), 446–454.
  • Meyer, W.L., Shaffer, L.R. (1965). Extending CPM for Multiform Project Time-Cost Curves. Optimization: Pareto front generation. Structural and Multidisciplinary Optimization 29(2), pp. 149-158.
  • Parveen, S. ve Saha, S. K., (2012). GA Based Multi-Objective Time-Cost Optimization in a Project with Resources Consideration, International Journal of Modern Engineering Research, IJMER, 2, 6, 2012, 4352-4359.
  • Rao, R. V. (2020). Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems. international journal of industrial engineering computations, 11 (1): 107–130. https://doi.org/10.5267/j.ijiec.2019.6.002.
  • Rao, R. V., & Keesari, H. S. (2020). Rao algorithms for multi objective optimization of selected thermodynamic cycles. Engineering with Computers. https://doi.org/10.1007/s00366-0 20-01008-9.
  • Rao, R. V., Savsani, V. J., and Vakharia, D. P. (2011). “Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems.” Computuer Aided Design, Vol. 43, No. 3, pp. 303-315.
  • Senouci AB, Mubarak SA. (2016). Multiobjective optimization model for scheduling of construction projects under extreme weather. Journal of Civil Engineering Management, 22(3): 373–81.
  • Sönmez, R., and Bettemir, O. H. (2012). “A hybrid genetic algorithm for the discrete time-cost trade-off problem.” Expert Systems with Applications, Vol. 39, No. 13, pp. 11428-11434.
  • Sulub, A.S., Eirgash, M.A. & Toğan, V. (2024). An arithmetic optimization algorithm based on opposition jumping rate for time cost trade-off optimization problems. Asian Journal of Civil Engineerin, 26, 867–886 https://doi.org/10.1007/s42107-024-01227-1
  • Toğan, V. and Eirgash, M.A. (2019). Time-Cost Trade-off Optimization of Construction Projects using Teaching Learning Based Optimization. KSCE Journal of Civil Engineering, 23(1), 10–20. https://doi.org/10.1007/s12205-018-1670-6
  • Toğan, V. Berberoğlu, N. Başağa, H.B. (2020). New adaptive weight formulations for time-cost optimization. Structures, 28, 2291-2299.
  • Vanhoucke, M., Debels, D. (2007). The discrete time/cost trade-off problem: extensions and heuristic procedures. Journal of Scheduling, 10(5), 311-326.
  • Ya-ping, K. and Ying, X.(2006). Construction Time-Cost Trade-off Analysis Using Ant Colony Optimization Algorithm," 2006 International Conference on Management Science and Engineering, Lille, France, pp. 2039-2044, doi: 10.1109/ICMSE.2006.314128.
  • Zhang, H., and Xing, F. (2010). “Fuzzy-multi-objective particle swarm optimization for time–cost–quality trade-off in construction. “Automation in Construction, 19, 8, 1067-1075.
  • Zhang, Y., and Ng, S. (2012). “An ant colony system based decision support system for construction time-cost optimization.” Journal of Civil Engineering and Management, Vol. 18, No. 4, pp. 580-589
  • Zheng, D. X. M., Ng, S. T., and Kumaraswamy, M. M. (2004). “Applying a genetic algorithm-based multiobjective approach for time-cost optimization.” Journal of Construction Engineering and Management, 130, 2, 168 - 176.
  • Zheng, D., Ng, S., and Kumaraswamy, M. (2005). “Applying Pareto ranking and niche formation to genetic algorithm-based multiobjective time–cost optimization.” Journal of Construction Engineering and Management, 131, 1. 81–91.

MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS

Yıl 2025, Cilt: 33 Sayı: 3, 1984 - 1996, 19.12.2025
https://doi.org/10.31796/ogummf.1718264

Öz

The Modified Adaptive Weight Approach (MAWA) represents a straightforward method commonly applied to solve time–cost optimization problems. MAWA is a flexible and effective approach that can be applied to various multi-objective optimization problems, including time–cost optimization in construction projects. These algorithms operate on a population of potential solutions that are randomly initialized within the boundaries of the solution space. MAWA assigns uniform weight factors to all individuals in the population without accounting for their specific characteristics. However, each solution possesses unique fitness attributes relative to its position in the solution space. In this study, a multi-objective optimization model combining the Rao-3 algorithm with the MAWA is introduced to generate a set of Pareto-optimal solutions. Two construction project case studies, drawn from existing technical literature and comprising 81 to 146 activities, are analyzed to evaluate the effectiveness of the proposed MAWA-Rao-3 method. The results are benchmarked against those from previously established models that produced approximate Pareto fronts or near-optimal solutions. The findings demonstrate that the MAWA-Rao-3 algorithm performs efficiently in addressing time-cost trade-off problems within the field of construction engineering and management.

Kaynakça

  • Abualigah. L, Diabat. A, Mirjalili. S, Elaziz. M.A, Gandomi. A.H, (2021a). The arithmetic optimization algorithm, Computer Methods in Applied mechanics and Engineering, 376, 113609. https://doi.org/10.1016/j.cma.2020.113609
  • Abualigah. L, Yousri. D, Abd Elaziz. M, Ewees. A.A, Al-qaness. M. A., Gandomi. A. H. (2021b). Aquila optimizer: A novel meta-heuristic optimization algorithm, Computers & Industrial Engineering., 157,107250. https://doi.org/10.1016/j.cie.2021.107250
  • Afshar, A., Ziaraty, A., Kaveh. A and Sharifi. F. (2009). Nondominated archiving multicolumn ant algorithm in time–cost trade-off optimization. Journal Construction Engineering and Management, 135, 7, 668-674.
  • 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 Civil Engineering. 25, 4529–4539, https://doi.org/10.1007/s42107-024-01063-3
  • Albayrak, G. (2020). “Novel hybrid method in time–cost trade-off or resource-constrained construction projects”. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44 (4), 1295-1307. https://doi.org/10.1007/s40996-020-00437-2
  • Aminbakhsh, S., and Sönmez, R. (2016). Applied discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem.” Expert System with Applications, 51, 177-185.
  • Basseur, M,. Zitzler, E. (2006). A preliminary study on handling uncertainty in indicator-based multiobjective optimization. In: Lecture Notes in Computer Science. Springer Berlin Heidelberg. 3907, p. 727–39. https://doi.org/10.1007/11732242_71.
  • Bettemir, Ö. H. (2009). Optimization of time-cost-resource trade-off problems in project scheduling using meta-heuristic algorithms. Doctoral dissertation, Middle East Technical University, Turkey.
  • Bettemir, Ö. H., and Birgönül, T. (2016). Network analysis algorithm for the solution of discrete time-cost trade-off problem. KSCE Journal of Civil Engineering, 21, No. 4, pp. 1047-1058.
  • Bettemir, Ö.H. and Birgonul, M.T. (2023), “Solution of discrete time–cost trade-off problem with adaptive search domain”, Engineering, Construction and Architectural Management, 0969-9988. https://www.emerald.com/insight/0969-9988.htm
  • Deb., K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Transaction and Evolution Computing, 6(2), 182–197.
  • Dede, T., (2018). Decision-Making Process Techniques Used in the Optimization of Construction Projects, Engineering Sciences, NWSAENS, 13, 2, 128-136.
  • Eirgash, M. A., and Dede, T. (2018). “A multi-objective improved teaching learning-based optimization algorithm for time-cost trade-off problems.” Journal of Construction Engineering, Management and Innovation, 1(3), 118-128.
  • Eirgash, M. A., Toğan, V., and 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
  • Eirgash., M.A. (2025). Influence of jumping rate on opposition-based jaya algorithm for discrete time cost trade-off optimization problems, Uludağ University Journal of The Faculty of Engineering, 30(1), 35-50.
  • Elbeltagi, E., Hegazy, T., and Grierson, D. (2005). “Comparison among Five Evolutionary-Based Optimization Algorithms.” Advanced Engineering Informatics, Vol. 19, pp. 43–53.
  • Eshtehardian, E., Afshar, A., and Abbasnia, R. (2008). “Time–cost optimization: using GA and fuzzy sets theory for uncertainties in cost.” Construction Management and Economics, Vol. 26, No. 7, pp.
  • Feng, C-W., Liu, L., and Burns, S. A. (1997) “Using genetic algorithms to solve construction time-cost trade-off problems.” Journal of Computing in Civil Engineering, Vol. 11, No. 3, pp.184-189.
  • Hamdy, M,. Nguyen, A.T,. Hensen, J.L.M. (2016). A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems. Energy Building;121(6):57–71. https://doi.org/10.1016/j.enbuild.2016.03.035.
  • Jia, H. Rao, H. Wen., C. Mirjalili, S. (2023). “Crayfsh optimization algorithm”, Artificial Intelligence Review, https://doi.org/10.1007/s10462-023-10567-4
  • Kelly, J. E. (1961). “Critical path planning and scheduling: Mathematical basis” Operational Research., 9(3), 167–179.
  • Kim, I.Y. and de Week, O.L.(2005). Adaptive weighted-sum method for bi-objective, Journal of Construction Division, 91(1), 45-68, 1965
  • 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. 25, 5975–5988, https://doi.org/10.1007/s42107-024-01157-y
  • 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
  • Liu, L., Burns, S., and Feng, C. (1995). “Construction time–cost trade-off analysis using LP/IP hybrid model.” Journal of Construction Engineering and Management., 121(4), 446–454.
  • Meyer, W.L., Shaffer, L.R. (1965). Extending CPM for Multiform Project Time-Cost Curves. Optimization: Pareto front generation. Structural and Multidisciplinary Optimization 29(2), pp. 149-158.
  • Parveen, S. ve Saha, S. K., (2012). GA Based Multi-Objective Time-Cost Optimization in a Project with Resources Consideration, International Journal of Modern Engineering Research, IJMER, 2, 6, 2012, 4352-4359.
  • Rao, R. V. (2020). Rao algorithms: Three metaphor-less simple algorithms for solving optimization problems. international journal of industrial engineering computations, 11 (1): 107–130. https://doi.org/10.5267/j.ijiec.2019.6.002.
  • Rao, R. V., & Keesari, H. S. (2020). Rao algorithms for multi objective optimization of selected thermodynamic cycles. Engineering with Computers. https://doi.org/10.1007/s00366-0 20-01008-9.
  • Rao, R. V., Savsani, V. J., and Vakharia, D. P. (2011). “Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems.” Computuer Aided Design, Vol. 43, No. 3, pp. 303-315.
  • Senouci AB, Mubarak SA. (2016). Multiobjective optimization model for scheduling of construction projects under extreme weather. Journal of Civil Engineering Management, 22(3): 373–81.
  • Sönmez, R., and Bettemir, O. H. (2012). “A hybrid genetic algorithm for the discrete time-cost trade-off problem.” Expert Systems with Applications, Vol. 39, No. 13, pp. 11428-11434.
  • Sulub, A.S., Eirgash, M.A. & Toğan, V. (2024). An arithmetic optimization algorithm based on opposition jumping rate for time cost trade-off optimization problems. Asian Journal of Civil Engineerin, 26, 867–886 https://doi.org/10.1007/s42107-024-01227-1
  • Toğan, V. and Eirgash, M.A. (2019). Time-Cost Trade-off Optimization of Construction Projects using Teaching Learning Based Optimization. KSCE Journal of Civil Engineering, 23(1), 10–20. https://doi.org/10.1007/s12205-018-1670-6
  • Toğan, V. Berberoğlu, N. Başağa, H.B. (2020). New adaptive weight formulations for time-cost optimization. Structures, 28, 2291-2299.
  • Vanhoucke, M., Debels, D. (2007). The discrete time/cost trade-off problem: extensions and heuristic procedures. Journal of Scheduling, 10(5), 311-326.
  • Ya-ping, K. and Ying, X.(2006). Construction Time-Cost Trade-off Analysis Using Ant Colony Optimization Algorithm," 2006 International Conference on Management Science and Engineering, Lille, France, pp. 2039-2044, doi: 10.1109/ICMSE.2006.314128.
  • Zhang, H., and Xing, F. (2010). “Fuzzy-multi-objective particle swarm optimization for time–cost–quality trade-off in construction. “Automation in Construction, 19, 8, 1067-1075.
  • Zhang, Y., and Ng, S. (2012). “An ant colony system based decision support system for construction time-cost optimization.” Journal of Civil Engineering and Management, Vol. 18, No. 4, pp. 580-589
  • Zheng, D. X. M., Ng, S. T., and Kumaraswamy, M. M. (2004). “Applying a genetic algorithm-based multiobjective approach for time-cost optimization.” Journal of Construction Engineering and Management, 130, 2, 168 - 176.
  • Zheng, D., Ng, S., and Kumaraswamy, M. (2005). “Applying Pareto ranking and niche formation to genetic algorithm-based multiobjective time–cost optimization.” Journal of Construction Engineering and Management, 131, 1. 81–91.
Toplam 41 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İnşaat Yapım Mühendisliği, Mimari Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Mohammad Azim Eirgash 0000-0001-5399-115X

Yusuf Baltaci 0000-0002-0461-2130

Gönderilme Tarihi 12 Haziran 2025
Kabul Tarihi 27 Kasım 2025
Yayımlanma Tarihi 19 Aralık 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 33 Sayı: 3

Kaynak Göster

APA Eirgash, M. A., & Baltaci, Y. (2025). MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, 33(3), 1984-1996. https://doi.org/10.31796/ogummf.1718264
AMA Eirgash MA, Baltaci Y. MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS. ESOGÜ Müh Mim Fak Derg. Aralık 2025;33(3):1984-1996. doi:10.31796/ogummf.1718264
Chicago Eirgash, Mohammad Azim, ve Yusuf Baltaci. “MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 33, sy. 3 (Aralık 2025): 1984-96. https://doi.org/10.31796/ogummf.1718264.
EndNote Eirgash MA, Baltaci Y (01 Aralık 2025) MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 33 3 1984–1996.
IEEE M. A. Eirgash ve Y. Baltaci, “MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS”, ESOGÜ Müh Mim Fak Derg, c. 33, sy. 3, ss. 1984–1996, 2025, doi: 10.31796/ogummf.1718264.
ISNAD Eirgash, Mohammad Azim - Baltaci, Yusuf. “MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 33/3 (Aralık2025), 1984-1996. https://doi.org/10.31796/ogummf.1718264.
JAMA Eirgash MA, Baltaci Y. MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS. ESOGÜ Müh Mim Fak Derg. 2025;33:1984–1996.
MLA Eirgash, Mohammad Azim ve Yusuf Baltaci. “MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, c. 33, sy. 3, 2025, ss. 1984-96, doi:10.31796/ogummf.1718264.
Vancouver Eirgash MA, Baltaci Y. MODIFIED ADAPTIVE WEIGHT RAO-3 ALGORITHM FOR CONSTRUCTION TIME-COST TRADE-OFF OPTIMIZATION PROBLEMS. ESOGÜ Müh Mim Fak Derg. 2025;33(3):1984-96.

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