Journals / Endüstri Mühendisliği / 2017 / Cilt: 28 - Sayı: 1

A SURVEY ON FINDING REPRESENTATIVE POINTS FOR MULTI-OBJECTIVE INTEGER PROGRAMS AND QUALITY MEASURES

ÇOK AMAÇLI TAMSAYI PROGRAMLAMA PROBLEMLERİ İÇİN TEMSİLİ ÇÖZÜM ÜRETEN YAKLAŞIMLARIN VE KALİTE ÖLÇÜLERİNİN İNCELENMESİ

Pages
19–39
Publication Date
2017-05-31
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this study, we review the quality measures used to evaluate the representative sets and the approaches that generate representative points.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The number of nondominated points of multi-objective integer programming problems increases exponentially with the problem size.
📊
Key Findings & Data:Instead of generating all nondominated points, it is reasonable to generate a set of points that represents the nondominated set with a desired quality level.
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Conclusion & Impact:In this study, we review the quality measures used to evaluate the representative sets and the approaches that generate representative points.
🔬Design:Review & Systematic Survey
📍Scope:Comprehensive Sample
⚙️Variables:Baskın nokta · temsili baskın nokta · kalite ölçüleri

Abstract

The number of nondominated points of multi-objective integer programming problems increases exponentially with the problem size. Therefore, finding all nondominated points is computationally hard and not practical for the decision maker. Instead of generating all nondominated points, it is reasonable to generate a set of points that represents the nondominated set with a desired quality level. In this study, we review the quality measures used to evaluate the representative sets and the approaches that generate representative points.

Özet

Çok amaçlı tamsayı programlama problemlerinde baskın noktaların sayısı problemin büyüklüğüne bağlı olarak üssel bir büyüme gösterir. Bu nedenle, bu problemler için tüm baskın noktaları bulmak zordur ve karar verici için pratik bir yaklaşım da değildir. Tüm baskın noktalar yerine, bu noktaları belirli kalite ölçülerine göre iyi temsil eden noktalar bulmak önemlidir. Bu çalışmamızda, temsili kümenin değerlendirilmesinde kullanılan kalite ölçülerini ve bu kalite ölçülerine göre tüm baskın nokta kümesini iyi temsil eden noktalar bulan yaklaşımları inceleyeceğiz.

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Cite This Article

LOKMAN, B. (2017). A SURVEY ON FINDING REPRESENTATIVE POINTS FOR MULTI-OBJECTIVE INTEGER PROGRAMS AND QUALITY MEASURES. Endüstri Mühendisliği, Cilt: 28 - Sayı: 1, 19–39. https://ajindex.com/articles/70696

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References (14)

  1. Aktaş, E., Özaydın, Ö., Ülengin, F., Önsel, Ş., Ağaran, B. 2011. “İstanbul’da İtfaiye İstasyonu Yerlerinin Seçimi İçin Yeni Bir Model,” Endüstri Mühendisliği Dergisi, sayı 22 (4), s. 2-12
  2. Armann, R. 1987. “Solving Multiobjective Programming Problems by Discrete Representation,” Optimization, vol. 20, p. 483-492
  3. Aytuğ, H., Sayın, S. 2009. “Using Support Vector Machines to Learn the Efficient Set in Multiple Objective Discrete Optimization,” European Journal of Operational Research, vol. 193, p. 510-519
  4. Bazgan, C., Jamain, F., Vanderpooten, D. 2015. “Approximate Pareto Sets of Minimal Size for Multi-Objective Optimization Problems,” Operation Research Letters, vol. 43, p. 1-6
  5. Boland, N., Charkhgard, H., Savelsbergh, M. 2015. “A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method,” INFORMS Journal on Computing, vol. 27 (4), p. 735-754
  6. Boland, N., Charkhgard, H., Savelsbergh, M. 2016. “The L-Shape Search Method for Triobjective Integer Programming,” Mathematical Programming Computation, vol. 8 (2), p. 217-251
  7. Burkard, R. E., Hamacher, H., Rote, G. 1991. “Sandwich Approximation of Univariate Convex Functions with an Application to Separable Convex Programming,” Naval Research Logistics, vol. 38 (6), p. 911-924
  8. Ceyhan, G. 2014. “Generating Representative Nondominated Point Subsets in Multiobjective Integer Programs,” Yüksek Lisans Tezi, Orta Doğu Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Ankara
  9. Chen, J., Li, J., Xin, B. 2017. “DMOEA-εC: Decomposition-Based Multi-Objective Evolutionary Algorithm with the ε-Constraint Framework,” IEEE Transactions on Evolutionary Computation, DOI 10.1109/TEVC.2017.2671462
  10. Czyzżak, P., Jaszkiweicz, A. 1998. “Pareto Simulated Annealing - a Metaheuristic Technique for Multiple-Objective Combinatorial Optimization,” Journal of Multi-Criteria Decision Analysis, vol. 7, p. 34-47
  11. Dächert, K., Klamroth, K. 2015. “A Linear Bound on the Number of Scalarizations Needed to Solve Discrete Tricriteria Optimization Problems,” Journal of Global Optimization, vol. 61 (4), p. 643-676
  12. Deb, K. 2001. Multiobjective Optimization Using Evolutionary Algorithms, Chichester, Wiley, U. K
  13. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T. 2002. “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, p. 182-197
  14. Diakonikolas, I., Yannakakis, M. 2009. “Small Approximate Pareto Sets for Biobjective