在現實生活中，設施選址是一個非常重要且需要長期投入規劃的議題，在各個產業裡皆是研究的重點之一，而在學術上稱作為有限產能設施選址問題（Capacitated facility location problem, CFLP），在有限產能下，決定各設施的地點，同時探討設施間最佳的配送量。為使一項產業順利運行，其供應鏈網路由原物料供應商、生產工廠、倉儲轉運中心以及客戶端共同組成，妥善規劃的供應鏈幫助企業有效提升營運效率並減少成本，因此多階層網路中的廠址議題被視為最具有影響力的要素之一。為追求全面性的決策，企業在評估廠址網路時也需同時考慮定量與定性因子，而這兩大因子往往相牴觸，因此設施選址可被視為多目標問題。
傳統的多目標方法需預先了解決策者對目標的偏好且僅能提供一組妥協最佳解。然而實際上在多目標問題中，存在一條無法被超越之柏拉圖無異曲線，在不犧牲任一目標下同時追求多目標妥協解。因此，基於多目標多階層有限容量選址模型，本研究首度融合非支配排序觀念於簡化群體演算法之中，提出非支配排序簡化群體演算法（Non-dominated sorting simplified swarm optimization, NSSSO），提供決策者一組無法被超越的妥協解集合，意即在多目標問題上有多個等效益的最佳妥協方案可供選擇。
本篇論文所提出的方法也與傳統上的多目標可能性線性規劃、新型多目標進化式演算法中的非支配排序遺傳演算法(Non-dominated sorting genetic algorithm II)、非支配排序粒子群演算法（Non-dominated sorting particle swarm optimizer）、多目標粒子群演算法（Multi-objective particle swarm optimization）進行比較。以實驗結果而言，本研究提出的方法所得到的柏拉圖前緣線，相較於其他方法，在曲線的接近性與多樣性兩項指標皆有不錯的成果。

Capacitated facility location is a general and important issue which needs a quite profound knowledge for long-term planning, and the problem has been widely researched in various industries to determine the facility location and related transportation strategy between facilities with certain capacity. To co-operate an industry, a supply network constructed by multi-stage: suppliers, plants, distribution centers, customers in which the location has decisive influence and should be considered simultaneously. Multiple objectives involving quantitative and qualitative factors are also pursued for more comprehensive decision making when constructing multiple facilities.
Classical multi-objective programming relies on predetermined preference by decision marker and provide a single solution. However, in multi-objective problem, there is a Pareto set of non-dominated solutions and both objective should be achieved simultaneously without sacrificing anyone. In this research, a new multi-objective evolutionary algorithm first integrating non-dominated sorting concept in Simplified swarm optimization is proposed to solve multi-objective and multi-stage capacitated facility location problem and provide decision makers a Pareto set of compromise solutions. Compare to possibilistic linear programming, Non-dominated sorting Genetic algorithm II (NSGAII), Non-dominated sorting particle swarm optimizer (NSPSO) and Multi-objective particle swarm optimization (MOPSO), numerical results show that the proposed approach can successfully obtain a perfect Pareto set in terms of quality and diversity, even regarded as a competitive approach in multi-objective problem.

中文摘要 I
ABSTRACT II
致謝 III
LIST OF CONTENTS IV
LIST OF TABLES VI
LIST OF FIGURES VII
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 RESEARCH FRAMEWORK 4
CHAPTER 2 LITERATURE REVIEW 6
2.1 MULTI-OBJECTIVE FACILITY LOCATION PROBLEM 6
2.2 OZGEN AND GULSUN’S FACILITY LOCATION MODEL 8
2.3 MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS (MOEAS) 12
CHAPTER 3 METHODOLOGY 16
3.1 NON-DOMINATED SORTING CONCEPT 16
3.2 SIMPLIFIED SWARM OPTIMIZATION (SSO) 19
3.3 PERFORMANCE METRIC OF MOEAS 20
CHAPTER 4 THE PROPOSED ALGORITHM 22
4.1 SOLUTION REPRESENTATION 22
4.2 ADJUSTED MECHANISM FOR INFEASIBLE SOLUTION 23
4.3 FITNESS FUNCTION 25
4.4 NON-DOMINATED SORTING SIMPLIFIED SWARM OPTIMIZATION (NSSSO) 26
4.5 THE PROCEDURE FOR SOLVING MULTI-MOCFLP BY NSSSO 28
CHAPTER 5 EXPERIMENTAL RESULTS 30
5.1 EXPERIMENTAL DATA 30
5.1.1 Multi-objective Test Problems 30
5.1.2 Multi-MOCFLP Datasets 30
5.2 DESIGN OF EXPERIMENTS 31
5.3 RESULTS DISCUSSION OF MULTI-OBJECTIVE TEST PROBLEMS 39
5.4 RESULT DISCUSSION OF MULTI-MOCFLP 42
5.4.1 Compared to Ozgen and Gulsun’s Result 43
5.4.2 Compared to Other MOEAs 45
5.4.3 Statistical Verification 55
CHAPTER 6 CONCLUSIONS & FUTURE DIRECTION 58
6.1 CONCLUSION 58
6.2 FUTURE DIRECTION 59
REFERENCES 61
APPENDICES 66

1. D. Ozgen, B. Gulsun, Combining possibilistic linear programming and fuzzy AHP for solving the multi-objective capacitated multi-facility location problem, Information Sciences, 268 (2014) 185-201.
2. M.T. Melo, S. Nickel, F. Saldanha-da-Gama, Facility location and supply chain management – A review, European Journal of Operational Research, 196 (2009) 401-412.
3. A. Klose, A. Drexl, Facility location models for distribution system design, European Journal of Operational Research, 162 (2005) 4-29.
4. M.A. Badri, Combining the analytic hierarchy process and goal programming for global facility location-allocation problem, International Journal of Production Economics, 62 (1999) 237-248.
5. A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P.N. Suganthan, Q. Zhang, Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation, 1 (2011) 32-49.
6. H.R. Cheshmehgaz, H. Haron, A. Sharifi, The review of multiple evolutionary searches and multi-objective evolutionary algorithms, Artificial Intelligence Review, 43 (2015) 311-343.
7. G. Cornu´ejols, G. Nemhauser, L. Wolsey, The uncapacitated facility location problem, in: I.P.M.a.R. Francis (Ed.) Discrete Location Theory, John Wiley and Sons, Inc, New York, 1990, pp. 119-171.
8. W.-C. Yeh, A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems, Expert Systems with Applications, 36 (2009) 9192-9200.
9. D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., 1989.
10. J. Kennedy, Particle Swarm Optimization, in: C. Sammut, G.I. Webb (Eds.) Encyclopedia of Machine Learning, Springer US, Boston, MA, 2010, pp. 760-766.
11. R. Sridharan, The capacitated plant location problem, European Journal of Operational Research, 87 (1995) 203-213.
12. G. Şahin, H. Süral, A review of hierarchical facility location models, Computers & Operations Research, 34 (2007) 2310-2331.
13. E. Fernández, J. Puerto, Multiobjective solution of the uncapacitated plant location problem, European Journal of Operational Research, 145 (2003) 509-529.
14. F. Altiparmak, M. Gen, L. Lin, T. Paksoy, A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers & Industrial Engineering, 51 (2006) 196-215.
15. G. Zhou, H. Min, M. Gen, A genetic algorithm approach to the bi-criteria allocation of customers to warehouses, International Journal of Production Economics, 86 (2003) 35-45.
16. A. Cakravastia, I.S. Toha, N. Nakamura, A two-stage model for the design of supply chain networks, International Journal of Production Economics, 80 (2002) 231-248.
17. X. Tang, J. Zhang, The multi-objective capacitated facility location problem for green logistics, in: 2015 4th International Conference on Advanced Logistics and Transport (ICALT), 2015, pp. 163-168.
18. N. Wichapa, P. Khokhajaikiat, Solving multi-objective facility location problem using the fuzzy analytical hierarchy process and goal programming: a case study on infectious waste disposal centers, Operations Research Perspectives, 4 (2017) 39-48.
19. T.L. Saaty, Decision making with the analytic hierarchy process, International journal of services sciences, 1 (2008) 83-98.
20. C.-H. Cheng, D.-L. Mon, Evaluating weapon system by analytical hierarchy process based on fuzzy scales, Fuzzy sets and systems, 63 (1994) 1-10.
21. Z. Ayağ, R.G. Özdemir, A fuzzy AHP approach to evaluating machine tool alternatives, Journal of intelligent manufacturing, 17 (2006) 179-190.
22. C.A.C. Coello, G.B. Lamont, D.A.V. Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation), Springer-Verlag, 2006.
23. Q. Zhang, H. Li, MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition, IEEE Transactions on Evolutionary Computation, 11 (2007) 712-731.
24. P.-C. Chang, S.-H. Chen, J.-C. Hsieh, A Global Archive Sub-Population Genetic Algorithm with Adaptive Strategy in Multi-objective Parallel-Machine Scheduling Problem, in, Springer Berlin Heidelberg, Berlin, Heidelberg, 2006, pp. 730-739.
25. J.D. Schaffer, Multiple objective optimization with vector evaluated genetic algorithms, in: Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1985, Lawrence Erlbaum Associates. Inc., Publishers, 1985.
26. E. Zitzler, K. Deb, L. Thiele, Comparison of Multiobjective Evolutionary Algorithms: Empirical Results, Evol. Comput., 8 (2000) 173-195.
27. H. Ishibuchi, T. Murata, A multi-objective genetic local search algorithm and its application to flowshop scheduling, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 28 (1998) 392-403.
28. C.M. Fonseca, P.J. Fleming, Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 28 (1998) 26-37.
29. N. Srinivas, K. Deb, Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms, Evolutionary Computation, 2 (1994) 221-248.
30. E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3 (1999) 257-271.
31. K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II, in, Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, 2000.
32. X. Li, A non-dominated sorting particle swarm optimizer for multiobjective optimization, in: Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI, Springer-Verlag, Chicago, IL, USA, 2003, pp. 37-48.
33. C.A.C. Coello, G.T. Pulido, M.S. Lechuga, Handling multiple objectives with particle swarm optimization, IEEE Transactions on Evolutionary Computation, 8 (2004) 256-279.
34. E. Alba, B. Dorronsoro, M. Giacobini, M. Tomassini, Decentralized cellular evolutionary algorithms, (2004).
35. E. Zitzler, Evolutionary algorithms for multiobjective optimization: Methods and applications, (1999).
36. J.M. Bader, Hypervolume-based search for multiobjective optimization: theory and methods, Johannes Bader, 2010.
37. R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on, IEEE, 1995, pp. 39-43.
38. W.-C. Yeh, Simplified swarm optimization in disassembly sequencing problems with learning effects, Computers & Operations Research, 39 (2012) 2168-2177.
39. W.-C. Yeh, Optimization of the Disassembly Sequencing Problem on the Basis of Self-Adaptive Simplified Swarm Optimization, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 42 (2012) 250-261.
40. W.-C. Yeh, Orthogonal simplified swarm optimization for the series–parallel redundancy allocation problem with a mix of components, Knowledge-Based Systems, 64 (2014) 1-12.
41. D.A. Van Veldhuizen, G.B. Lamont, Multiobjective evolutionary algorithm research: A history and analysis, in, Citeseer, 1998.
42. D.R.M. Fernandes, C. Rocha, D. Aloise, G.M. Ribeiro, E.M. Santos, A. Silva, A simple and effective genetic algorithm for the two-stage capacitated facility location problem, Computers & Industrial Engineering, 75 (2014) 200-208.
43. C.-M. Lai, W.-C. Yeh, Y.-C. Huang, Entropic simplified swarm optimization for the task assignment problem, Applied Soft Computing, 58 (2017) 115-127.
44. D.S. Liu, K.C. Tan, S.Y. Huang, C.K. Goh, W.K. Ho, On solving multiobjective bin packing problems using evolutionary particle swarm optimization, European Journal of Operational Research, 190 (2008) 357-382.