現在位置首頁 > 博碩士論文 > 詳目
  • 同意授權
論文中文名稱:運用確定性全域最佳化方法求解工程與管理問題 [以論文名稱查詢館藏系統]
論文英文名稱:A Deterministic Global Optimization Approach for Engineering and Management Problems [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:管理學院
系所名稱:工商管理研究所
畢業學年度:100
出版年度:101
中文姓名:王佩淳
英文姓名:Pei-Chun Wang
研究生學號:95749005
學位類別:博士
語文別:英文
口試日期:2012-06-20
論文頁數:76
指導教授中文名:蔡榮發教授
口試委員中文名:翁頌舜教授;邱志洲教授;張錦特教授;郭人介教授
中文關鍵詞:全域最佳化凸化線性化管理科學
英文關鍵詞:Global optimizationConvexificationLinearizationManagement science
論文中文摘要:確定性的全域最佳化演算法普遍應用在各種工程與管理的問題,運用最佳化演算法在管理方面可量化並結構化獲得最佳決策,而在工程最佳化方面要求絕對的精確度,因此全域最佳解成為求解的重點。然而實際的工程與管理問題所建構的數學模型大部份皆為非凸規劃(nonconvex programming)模型,無法以簡單的最佳化演算法求得全域最佳解。若能將非凸規劃轉換為凸規劃(convex programming),便能以簡單的確定性最佳化演算法求得全域最佳解。因此,許多凸化(convexification)方法皆探討如何將非凸函數有效率的轉換為凸函數以確保獲得全域最佳解。然而為確保求解品質,模型中的非凸函數通常需要運用不同的凸化方法來轉換,此外,由函數轉換而產生的非線性(nonlinear)限制式需透過線性化(linearization)來達成獲得全域最佳解的目的。因此,本研究運用全域最佳化演算法求解不同的工程與管理問題以獲得全域最佳解,透過整合運用不同的凸化方法,同時將模型中包括正(posynomial)與非正(signomial)的非凸函數轉換為凸函數,接著,利用逐段線性化(piecewise linearization)方法將非線性限制式線性化,使模型成為一凸規劃模型達成確保獲取全域最佳解的目的。本研究主要具有以下優點,首先,全域最佳化演算法在工程與管理的應用方面能夠獲得滿足各條件下的精確解答以及最佳決策。第二是相較於啟發式演算法,本研究所探討的最佳化演算法可保證其解為全域最佳解。第三,本研究所探討的最佳化演算法能夠以最少的限制式與二元變數進行轉換,相較於其他確定性演算法為最有效率之演算法。第四,本研究運用多重解演算法獲取最佳的替代策略,提昇最佳化管理應用方面的決策彈性,使企業具備快速應變的能力。
論文英文摘要:Deterministic global optimization has been applied in many applications of engineering and management area. Global optimization enables management problems to obtain an optimal decision, and applications to engineering problems usually require very precise solution. Thus the global optimal solution of the applications plays critical roles. These real-world optimization problems lead to nonconvex problems. In most of the previously study on engineering and management problems involving nonconvexties, the emphasis has not been on global optimization since it is difficult to globally optimize such models. However, most nonconvex problems cannot be dealt with by conventional optimization algorithms to guarantee global optimality. Therefore, deterministic optimization approaches have been developed for convexifying the nonconvex function to obtain globally optimal solutions. This dissertation utilizes deterministic optimization approach to find the global optimum of various engineering and management problems. The presented deterministic optimization approach transforms a nonconvex program into a convex program by convexification and linearization techniques and is thus guaranteed to reach a global optimum. The advantages of this study are summarized as follows. First, deterministic global optimization applications to engineering and management problems can obtain precise solution and optimal decision. Second, the obtained solution is guaranteed to reach a global optimum thus better than heuristic algorithms. Third, compared with other deterministic methods, the presented method utilizes less additional binary variables and constraints to reformulate the problem. Then the computational efficiency can be improved greatly. Fourth, the presented approach finds alternative optimal solutions to enhance the flexibility of the decision making.
論文目次:摘 要 i
ABSTRACT ii
誌 謝 iii
CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES vii
Chapter 1 Introduction 1
1.1 Research Background 1
1.2 Research Motivation and Purpose 3
1.3 Framework of the Dissertation 4
Chapter 2 Deterministic Global Optimization Approaches 7
2.1 Convexity 7
2.1.1 Convex Sets 7
2.1.2 Convex Functions 8
2.2 Convex Underestimation Techniques 11
2.3 Convexification Techniques 14
2.4 Linearization Techniques 16
2.5 Multiple Solutions 18
Chapter 3 Application to Rectangular Packing Problems 20
3.1 Introduction of Rectangular Packing Problem 20
3.2 Problem Formulation 22
3.3 Reformulation of Rectangular Packing Problems 24
3.4 Numerical Examples 27
3.5 Summary 31
Chapter 4 Application to Engineering Design Problems 33
4.1 Introduction of Engineering Design Problems 34
4.2 Convexification and Linearization Techniques for MINLP 35
4.3 Engineering Design Problems 36
4.4 Summary 45
Chapter 5 Application to Cooperative Alliance Problems 46
5.1 Introduction 47
5.2 Optimal Expansion of Incorporating Multilevel Competence sets 51
5.3 Multiple Solutions of Cooperative Alliance Problem 55
5.4 Numerical example of cooperative alliance 55
5.5 Summary 62
Chapter 6 Discussion and Conclusions 63
REFERENCES 66
論文參考文獻:[1]Abdel-Malek, L. and Areeratchakul, N. A. (2007). Quadratic programming approach to the multi-product newsvendor problem with side constraints. European Journal of Operational Research, 176(3), 1607-1619.
[2]Abdel-Malek, L., Montanari, R. and Morales, L.C. (2003). Exact, approximate, and generic iterative models for the multi-product newsboy with budget constraint. International Journal of Production Economics, 91(2), 189-198.
[3]Adjiman, C.S., Androulakis, I.P. and Floudas, C.A. (2000). Global optimization of mixed integer nonlinear problems. AICHE Journal, 46(9), 1769-1797.
[4]A1-Khayyal, F.A., Larsen, C. and Voorhis, T. A. Van. (1995). Relaxation method for nonconvex quadratically constrained quadratic programs. Journal of Global Optimization, 6(3), 215-230.
[5]Akhtar, S. Tai, K. and Ray, T. (2002). A socio-behavioural simulation model for engineering design optimization. Engineering Optimization, 34(4), 341-354.
[6]Arbib, C. and Marinelli, F. (2009). Exact and asymptotically exact solutions for a class of assortment problems. INFORMS Journal on Computing, 21(1), 13-25.
[7]Audet, C., Hansen, P., Jaumard, B. and Savard, G. (2000). A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Mathematical Programming, 87(1), 131-152.
[8]Balas, E. and Jeroslow, R. (1972). Canonical cuts on the unit hypercube. SIAM Journal of Applied Mathematics, 23(1), 61-69.
[9]Baldacci, R. and Boschetti, M. A. (2007). A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem. European Journal of Operational Research, 183(3), 1136-1149.
[10]Beale, E. M. L. and J. Tomlin, A. (1970). Special facilities in a general mathematical programming system for nonconvex problem using ordered sets of variables, in: Lawrence, J. (Ed.), Proceedings of the Fifth International Conference on Operations Research, Tavistock Publications, 447-454.
[11]Belegundu, A.D. (1982). A study of mathematical programming methods for structural optimization. Doctoral dissertation, Department of Civil and Environmental Engineering, University of Iowa City.
[12]Ben-Tal, A., Eiger, G. and Gershovitz, V. (1994). Global minimization by reducing the duality gap. Mathematical Programming, 63(1-3), 193-212.
[13]Bergamini, M. L., Aguirre, P. and Grossmann, I. (2005) Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering, 29(9), 1914-1933.
[14]Bergamini, M. L., Grossmann, I., Scenna, N. and Aguirre, P. (2008). An improved piecewise outer approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms. Computers and Chemical Engineering, 32(3), 477-493.
[15]Bergamini, M. L., Scenna, N. and Aguirre, P. (2007). Global optimal structures of heat exchanger networks by piecewise relaxation. Industrial and Engineering Chemistry Research, 46(6), 1752-1763.
[16]Björk, K. J., Lindberg, P. O. and Westerlund, T. (2003). Some convexifications in global optimization of problems containing signomial terms. Computers and Chemical Engineering, 27(5), 669-679.
[17]Björk, K.J. and Westerlund, T. (2002). Global optimization of heat exchanger network synthesis problems with and without the isothermal mixing assumption. Computers and Chemical Engineering, 26(11), 1581-1593.
[18]Bomze, I.M. (1998). On standard quadratic Optimization Problems. Journal of global optimization, 13(4), 369-387.
[19]Bomze, I.M. and Klerk, E. D. (2002). Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. Journal of global optimization, 24(2), 163-185.
[20]Bomze, I.M., Locatelli, M. and Tardella, F. (2008). New and old bounds for standard quadratic optimization: dominance, equivalence and incomparability. Mathematical Programming, 115(1), 31-64.
[21]Boyd, S. P. and Vandenberghe, L. (2003). Convex Optimization. Cambridge University Press.
[22]Cello, C. A. (2000). Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Inderstry, 41(2), 113-127.
[23]Camponogara, E., Castro, M. P., Plucenio, A. and Pagano, D. J. (2011) Compressor scheduling in oil fields: Piecewise-linear formulation, valid inequalities, and computational analysis. Optimization and Engineering, 12(1-2), 153-174.
[24]Chen, T.Y. (2002). Expanding competence sets for the consumer decision problem. European Journal of Operational Research, 138(3), 622-648.
[25]Chen, T. Y. and Chen, H. C. (2009). Mixed-discrete structural optimization using a rank-niche evolution strategy. Engineering Optimization, 41(1), 3080-3091.
[26]Clautiaux, F., Carlier, J. and Moukrim, A. (2007). A new exact method for the two-dimensional orthogonal packing problem. European Journal of Operational Research, 183(3), 1136-1149.
[27]Clautiaux, F., Jouglet, A., Carlier, J. and Moukrim, A. (2008). A new constraint programming approach for the orthogonal packing problem. Computers and Operations Research, 35(3), 944-959.
[28]Das, S. K. and Abdel-Malek, L. (2003). Modeling the flexibility of order quantities and lead-times in supply chains. Journal of Production Economics, 85(2), 171-181.
[29]Erbatur, F., Hasancebi, O., Tutuncu, I. and Killic, H. (2000). Optimal design of planar and space structures with genetic algorithms. Computers and Structures, 75(2), 209-224.
[30]Farias, I. R. (2004). Semi-continuous cuts for mixed-integer programming, in: Bienstock, D. and Nemhauser, G.L. (Eds.), Integer Programming and Combinatorial Optimization (IPCO), Lecture Notes in Computer Science, 3064, 163-177. Springer, Berlin.
[31]Farias, I. R., Johnson, E. L. and Nemhauser, G. L. (2001). Branch-and-cut for combinatorial optimization problems without auxiliary binary variables. Knowledge Engineering Review, 16(1), 25-39.
[32]Farias, I. R., Zhao, M. and Zhao, H. (2008). A special ordered set approach for optimizing a discontinuous separable piecewise linear function. Operations Research Letters, 36(2), 234-238.
[33]Fekete, S. P. and Schepers, J. (2004). A combinatorial characterization of higher-dimensional orthogonal packing. Mathematics of Operations Research, 29(2), 353-368.
[34]Fekete, S. P., Schepers, J. and Veen, J. (2007). An exact algorithm for higher-dimensional orthogonal packing. Operations Research, 55(3), 569-587.
[35]Feng, J.W., Yu, P.L. (1998). Minimum spanning table and optimal expansion of competence set. Journal of Optimization Theory and Applications, 99(3), 655-679.
[36]Fesanghary, M., Mahdavi, M., Minary-Jolandan, M. and Alizadeh, Y. (2008). Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. Computer Methods in Applied Mechanics and Engineering, 197(33-40), 3080-3091.
[37]Floudas, C. A. (1999). Recent advances in global optimization for process synthesis, design and control: Enclosure of all solutions. Computers and Chemical Engineering, 23(1), S963-S974.
[38]Floudas, C. A. (2000a). Deterministic Global Optimization: Theory, Methods and Application. Kluwer Academic Publishers, Boston.
[39]Floudas, C. A. (2000b). Global optimization in design and control of chemical process systems. Journal of Process Control, 10(2-3), 125-134.
[40]Floudas, C. A., Akrotirianakis, I. G., Caratzoulas, S., Meyer, C. A. and Kallrath, J. (2005). Global optimization in the 21st century: Advances and challenges. Computers and Chemical Engineering, 29(6), 1185-1202.
[41]Floudas, C. A. and Gounaris, C. E. (2008). A review of recent advances in global optimization. Journal of Global Optimization, 45(1), 3-38.
[42]Floudas, C. A. and Pardalos, P. (2004). Frontiers in Global Optimization, Kluwer Academic Publishers, Boston.
[43]Floudas, C. A. and Visweswaran, V. (1995). Quadratic optimization. In: Horst, R. and Pardalos P. M.(eds.), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, 217-269.
[44]Goyal, V. and Ierapetritou, M. G. (2004). Computational studies using a novel simplicial-approximation based algorithm for MINLP optimization. Computers and Chemical Engineering, 28(9), 1771-1780.
[45]Guu, S. M. and Liou, Y. C. (1998). On a quadratic optimization problem with equality constraints. Journal of Optimization Theory and Applications, 98(3), 733-741.
[46]Hifi, M. and Ouafi, R. (1998). A best-first branch-and-bound algorithm for orthogonal rectangular packing problems. International Transactions Operational Research, 5(5), 345-356.
[47]Hirschberger, M. (2005). Computation of efficient compromise arcs in convex quadratic multicriteria optimization. Journal of Global Optimization, 31(3), 535-546.
[48]Hopper, E. and Turton, B. C. H. (2001). An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research, 128(1), 34-57.
[49]Horst, R. and Pardalos, P. M. (1995). Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht.
[50]Horst, R. and Thoai, N. V. (1996). A new algorithm for solving the general quadratic programming problem. Computational Optimization and Applications, 5(1), 39-48.
[51]Horst, R. and Tuy, H. (2003). Global Optimization: Deterministic Approaches, 3rd edition, Springer, Berlin.
[52]Hsu, Y.L. and Liu, T.C. (2007). Developing a fuzzy proportional-derivative controller optimization engine for engineering design optimization problems. Engineering Optimization, 39(6), 679-700.
[53]Hu, Y.C. (2007). Grey relational analysis and radial basis function network for determining costs in learning sequences. Applied Mathematics and Computation, 184(2), 291-299.
[54]Hu, Y.C., Tzeng, G.H. and Chen, C.M. (2004). Deriving two-stage learning sequences from knowledge in fuzzy sequential pattern mining. Information Sciences, 159(1-2), 69-86.
[55]Huang, W., Chen, D. and Xu, R. (2007). A new heuristic algorithm for rectangle packing. Computers and Operations Research, 34(11), 3270-3280.
[56]Huang, J.J., Tzeng, G.H. and Ong, C.S. (2006). Optimal fuzzy-criteria expansion of competence sets using multi-objectives evolutionary algorithms. Expert Systems and Applications, 30(4), 739-745.
[57]Jaberipour, M. and Khorram, E. (2010). Two improved harmony search algorithms for solving engineering optimization problem. Communication in Nonlinear Science and Numerical Simulation, 15(11), 3316-3331.
[58]Keha, A. B., Farias, I. R. and Nemhauser, G. L. (2004). Models for representing piecewise linear cost functions. Operations Research Letters, 32(1), 44-48.
[59]Keha, A. B., Farias, I. R. and Nemhauser, G. L. (2006). A branch-and-cut algorithm without binary variables for nonconvex piecewise linear optimization. Operations Research, 54(5), 847-858.
[60]Kim, S. and Kojima, M. (2003). Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP Relaxations. Computational Optimization and Applications, 26(2), 143-154.
[61]Klerk, E. and Pasechnik, D. V. (2007). A linear programming reformulation of the standard quadratic optimization problem. Journal of Global Optimization, 37(1), 75-84.
[62]Kojima, M. and Tunce, L. (2000). Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization. Mathematical Programming, 89(1), 79-111.
[63]Konno, H. and Yamamoto, R. (2005). Global optimization versus integer programming in portfolio optimization under nonconvex transaction costs. Journal of Global Optimization, 32(2), 207-219.
[64]Lau, R.S.M. (1996). Strategic flexibility: a new reality for world class manufacturing. SAM Advanced Management Journal, 61(2), 11-15.
[65]Lee, J. and Wilson, D. (2001). Polyhedral methods for piecewise linear functions: the lambda method. Discrete Applied Mathematics, 108(3), 269-285.
[66]Lee, K. S. and Geem, Z. W. (2005). A new meta-heuristic algorithm for continuous engineering optimization: Harmony search theory and practice. Computer Methods in Applied Mechanics and Engineering, 194(36-38), 3902-3933.
[67]Lee, S. and Grossmann, I. E. (2000). New algorithms for nonlinear generalized disjunctive programming. Computers and Chemical Engineering, 24(9-10), 2125-2141.
[68]Leung, T. W., Chan, C. K. and Troutt, M. D. (2003). Application of a mixed simulated annealing-genetic algorithm heuristic for the two-dimensional orthogonal packing problem. European Journal of Operational Research, 145(3), 530-542.
[69]Li, H.L. (1999). Incorporating competence sets of decision makers by deduction graph. Operations Research, 47(2), 209-220.
[70]Li, J.M., Chiang, C.I. and Yu, P.L. (2000). Optimal multiple stage expansion of competence set. European Journal of Operational Research, 120(3), 511-524.
[71]Li, H.L. and Yu, P.L. (1994). Optimal competence set expansion using deduction graphs. Journal of Optimization Theory and Applications, 80(1), 75-91.
[72]Li, H. L., Chang, C. T. and Tsai, J. F. (2002). Approximately global optimization for assortment problems using piecewise linearization techniques. European Journal of Operational Research, 140(3), 584-589.
[73]Li, M. S., Gabriel, A., Shim, Y. and Azarm, S. (2011). Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Networks and Spatial Economics, 11(1), 159-191.
[74]Li, H. L. and Papalambros, P. (1985). A production system for use of global optimization knowledge. ASME Journal of Mechanical Design, 107(2), 277-284.
[75]Li, H. L. and Tsai, J. F. (2001). A fast algorithm for assortment optimization problems. Computers and Operations Research, 28(12), 1245-1252.
[76]Li, H. L. and Tsai, J. F. (2005). Treating free variables in generalized geometric global optimization programs. Journal of Global Optimization, 33(1), 1-13.
[77]Li, H. L. and Tsai, J. F. (2008). A distributed computation algorithm for solving portfolio problems with integer variables. European Journal of Operational Research, 186(2), 882-891.
[78]Li, H. L., Tsai, J. F. and Floudas, C. A. (2008). Convex underestimation for posynomial functions of positive variables. Optimization Letters, 2(3), 333-340.
[79]Liberti, L. and Pantelides, C. C. (2003). Convex envelops of monomials of odd degree. Journal of Global Optimization, 25(2), 157-168.
[80]Lin, M. H., Tsai, J. F. and Wang, P. C. (2012). Solving Engineering optimization problems by a deterministic global optimization approach. Applied Mathematics and Information Sciences, 6(7S), 21S-27S.
[81]Lin, C.C. (2006a). Competence set expansion using an efficient 0-1 programming model. European Journal of Operational Research, 170(3), 950-956.
[82]Lin, C.M. (2006). Multiobjective fuzzy competence set expansion problem by multistage decision-based hybrid genetic algorithms. Applied Mathematics and Computation, 181(2), 1402-1416.
[83]Lin, C. C. (2006b). A genetic algorithm for solving the two-dimensional assortment problem. Computers and Industrial Engineering, 50(1), 175-184.
[84]Lin, X., Floudas, C. A. and Kallrath, J. (2005). Global solution approach for a nonconvex MINLP problem in product portfolio optimization. Journal of Global Optimization, 32(2), 417-431.
[85]LINGO Release 9.0. LINDO System Inc., Chicago, 2004.
[86]Lodi, A., Martello, S. and Monaci, M. (2002a). Two-dimensional packing problems: A survey. European Journal of Operational Research, 141(2), 241-252.
[87]Lodi, A., Martello, S. and Vigo, D. (2002b). Recent advances on two-dimensional bin packing problems. Discrete Applied Mathematics, 123(1-3), 379-396.
[88]Lodi, A., Martello, S. and Vigo, D. (2004). Models and bounds for two-dimensional level packing problems. Journal of Combinatorial Optimization, 8(3), 363-379.
[89]Loh, H. T. and Papalambros, P. Y. (1991). A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems,” ASME Journal of Mechanical Design, 113(3), 325-334.
[90]Long, C.E., Polisetty, P.K. and Gatzke, E.P. (2006). Nonlinear model predictive control using deterministic global optimization. Journal of Process Control, 16(6), 635-643.
[91]Lu, H. C., Li, H. L., Gounaris, C. E. and Floudas, C. A. (2010). Convex relaxation for solving posynomial programs. Journal of Global Optimization, 46(1), 147-154.
[92]Lundell, A. (2009). Transformation techniques for signomial functions in global optimization, Ph. D. Thesis, Ăbo, Akademi University.
[93]Lundell, A. and Westerlund, T. (2009). Convex underestimation strategies for signomial functions. Optimization Methods and Software, 24(4-5), 505-522.
[94]Mahdavi, M., Fesanghary, M. and Damangir, E. (2007). An improved harmony search algorithm for solving optimization problems. Applied Mathematics and Computation, 188(2), 1567-1579.
[95]Maranas, C. and Floudas, C. A. (1995). Finding all solutions of nonlinearly constrained systems of equations. Journal of Global Optimization, 7(2), 143-182.
[96]Maranas, C. D. and Floudas, C. A. (1997). Global optimization in generalized geometric programming. Computers and Chemical Engineering, 21(4), 351-369.
[97]Markowitz, H. M. (1995). The general mean-variance portfolio selection problem. In: Howison, S. K., Kelly, F. P. and Wilmott, P. (eds.) Mathematical Models in Finance. Chapman and Hall, London, 93-99.
[98]McCormick, G. P. (1976). Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems. Mathematical Programming, 10(1), 147-175.
[99]Meyer, C. A. and Floudas, C. A. (2003). Trilinear monomials with positive or negative domains: Facets of convex and concave envelopes. In: Floudas, C. A. and Pardalos, P. M. (eds.) Frontiers in Global Optimization. Kluwer, Santorini, 327-352.
[100]Nema, S., Goulermas, J., Sparrow, G. and Cook, P. (2008). A hybrid Particle swarm branch-and-bound (HPB) optimizer for mixed discrete nonlinear programming. IEEE Transactions on Systems, Man and Cybernetics, 38(6), 1411-1424.
[101]Neumaier, A. (2004). Complete Search in Continuous Global Optimization and Constraint Satisfaction. In: A. Iserles(Ed.) Acta Numerica, Cambridge Unviersity Press, Cambridge, 13, 271-369.
[102]Pedberg, M. (2000). Approximating separable nonlinear functions via mixed zero-one programs. Operations Research Letters, 27(1), 1-5.
[103]Pedamallu, C. S. and Ozdamar, L. (2008) Investigating a hybrid simulated annealing and local search algorithm for constrained optimization. European Journal of Operational Research, 185(3), 1230-1245.
[104]Pörn, R., Björk, K. J. and Westerlund, T. (2008). Global solution of optimization problems with signomial parts. Discrete Optimization, 5(1), 108-120.
[105]Pörn, R., Harjunkoski, I. and Westerlund, T. (1999). Convexification of different classes of non-convex MINLP problems. Computers and Chemical Engineering, 23(3), 439-448.
[106]Rao, S. S. and Xiong, Y. (2005). A hybrid genetic algorithm for mixed-discrete design optimization. ASME Journal of Mechanical Design, 127(6), 1100-1112.
[107]Rao, S. S. (1996). Engineering optimization, John Wiley & Sons, New York.
[108]Rosen, J. B. and Marcia, R. F. (2004). Convex quadratic approximation. Computational Optimization and Applications, 28(2), 173-184.
[109]Ryoo, H. S. and Sahinidis, N. V. (2001). Analysis of bounds for multilinear functions. Journal of Global Optimization, 19(4), 403-424.
[110]Saaty, T.L. (1980). The Analytic Hierarchy Process, McGraw Hill, New York.
[111]Saaty, T.L. (1996). Decision Making with Dependence and Feedback: The Analytic Network Process, RWS Publications, Pittsburgh.
[112]Sanchez, R. and Heene, A. (1997). Reinventing strategic management: new theory and practice for competence-based competition. European Management Journal, 15(3), 303-317.
[113]Sandgren, E. (1990). Nonlinear integer and discrete programming in mechanical design optimization. ASME Journal of Mechanical Design, 112(2), 223-230.
[114]Sandgren, E. and Vanderplaats, G. N. (1993). Optimum design of trusses with sizing and shape variables. Structural Optimization, 6(2), 79-85.
[115]Shee, D.Y. (2006). An analytic framework for competence set expansion: lessons learned from an SME. Total Quality Management, 17(8), 981-997.
[116]Sherali, H. D. and Tuncbilek, C. H. (1995). A reformulation-convexification approach for solving nonconvex quadratic programming problems. Journal of Global Optimization, 7(1), 1-13.
[117]Sherali, H. D. and Tuncbilek, C. H. (1997). New reformulation linearization/ convexification relaxations for univariate and multivariate polynomial programming problems. Operations Research Letters, 21(1), 1-9.
[118]Shi, D.S. and Yu, P.L. (1996). Optimal expansion and design of competence sets with asymmetric acquiring costs. Journal of Optimization Theory and Applications, 88(3), 643-658.
[119]Shi, D.S. and Yu, P.L. (1999). Optimal expansion of competence sets with intermediate skills and compound nodes. Journal of Optimization Theory and Applications, 102(3), 643-657.
[120]Shimizu, K. and Hitt, M.A. (2004). Strategic flexibility: Organizational preparedness to reverse ineffective strategic decisions. Academy of Management Executive, 18(4), 44 -59.
[121]Silva, E., Alvelos, F. and Valério, J. M. (2010). An integer programming model for two- and three-stage two-dimensional cutting stock problems. European Journal of Operational Research, 205(3), 699-708.
[122]So, M. A., Zhang, J. and Ye, Yinyu. (2007). On approximating complex quadratic optimization problems via semidefinite programming relaxations. Mathematical Programming, series B, 110(1), 93-110.
[123]Stolpe, M. (2007). On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1programs. Optimization and Engineering, 8(2), 163-192.
[124]Stoyan, Y.G. and Yaskov, G.N. (1998) Mathematical model and solution method of Optimization problem of placement of rectangles and circles taking into account special constraints. International Transactions Operational Research, 5(1), 45-57.
[125]Su, C. L. and Hsieh, S. (2010). Using CPSO for the engineering optimization problems. WSEAS Transactions on Mathematics, 9(8), 628-637.
[126]Thoai, N. V. (2000). Duality bound method for the general quadratic programming problem with quadratic constraints. Journal of Optimization Theory and Applications, 107(2), 331-354.
[127]Tsai, J. F. (2005). Global optimization of nonlinear fractional programming problems in engineering design. Engineering Optimization, 37(4), 399-409.
[128]Tsai, J. F. (2007). An optimization approach for supply chain management models with quantity discount policy. European Journal of Operational Research, 177(2), 982-994.
[129]Tsai, J.F., Lin, M. H. and Hu, Y. C. (2008). Finding multiple solutions to general integer linear programs. European Journal of Operational Research, 184(2), 802-809.
[130]Tsai, J. F., Lin, M. H. and Hu, Y. C. (2007). On generalized geometric programming problems with non-positive variables. European Journal of Operational Research, 178(1), 10-19.
[131]Tsai, J. F. and Li, H. L. (2006). A Global Optimization Method for Packing Problems. Engineering Optimization, 38(6), 687-700.
[132]Tsai, J. F., Li, H. L. and Hu, N. Z. (2002). Global optimization for signomial discrete programming problems in engineering design. Engineering Optimization, 34(6), 613-622.
[133]Tsai, J. F. and Lin, M. H. (2008). Global optimization of signomial mixed-integer nonlinear programming problems with free variables. Journal of Global Optimization, 42(1), 39-49.
[134]Tsai, J. F. and Lin, M. H. (2011). An efficient global approach for posynomial geometric programming problems. INFORMS Journal on Computing, 23(3), 1-10.
[135]Tsai, J.F., Wang, P. C. and Lin, M. H. (2011). An efficient deterministic optimization approach for rectangular packing problems. Optimization, DOI:10.1080/02331934.2011.625029
[136]Tsai, J. F., Hsieh, P. L. and Huang, Y. H. (2009). An optimization algorithm for cutting stock problems in the TFT-LCD industry. Computers and Chemical Engineering, 57(3), 913-919.
[137]Tsai, J.F., Wang, P. C. and Lin, M. H. (2012). Optimal expansion of competence sets with multilevel skills. Computers and Industrial Engineering, 62(3), 770-776.
[138]Tuy, H. and Hoai-Phuong, N. T. (2007). A robust algorithm for quadratic programming under quadratic constraints. Journal of Global Optimization, 37(4), 557-569.
[139]Twarmalani, M. and Sahinidis, N. V. (2005). A polyhedral branch and cut approach to global optimization. Mathematical Programming, 103(2), 225-249.
[140]Upadhyay, A. and Kalyanaraman, V. (2000). Optimum design of fibre composite stiffened panels using genetic algorithms. Engineering Optimization, 33(2), 201-220.
[141]Vielma, J. P., Ahmed, S. and Nemhauser, G. L. (2010). Mixed-integer models for nonseparable piecewise linear optimization: unifying framework and extensions. Operations Research, 58(2), 303-315.
[142]Vielma, J. P., Keha, A. B. and Nemhauser, G. L. (2008). Nonconvex, lower semicontinuous piecewise linear optimization. Discrete Optimization, 5(2), 467-488.
[143]Vielma, J. P. and Nemhauser, G. L. (2011). Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Mathematical Programming, 128(1-2), 49-72.
[144]Wei, L., Oon, W.C., Zhu, W. and Lim, A. (2011). A skyline heuristic for the 2D rectangular packing and strip packing problems, European Journal of Operational Research, 215(2), 337-346.
[145]Westerlund, T. (2007). Some Transformation Techniques in Global Optimization. In: L. Liberti and N. Maculan(Eds.), Global Optimization, from Theory to Implementations, Springer, New York,.
[146]Westerlund, T. and Pettersson, F. (1995). An extended cutting plane method for solving convex MINLP problems. Computers and Chemical Engineering, 19(1), 131-136.
[147]Westerlund, T., Skrifvars, H., Harjunkoski, I. and Pörn, R. (1998). An extended cutting plane method for a class of non-convex MINLP problems. Computers and Chemical Engineering, 22(3), 357-365.
[148]Wilson, D. (1998). Polyhedral methods for piecewise linear functions, Ph.D. Thesis, University of Kentucky.
[149]Wäscher, G., Hausner, H. and Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research, 183(3), 1109-1130.
[150]Yu, P. L. (2006). Working knowledge mining by principles for deep knowledge. International Journal of Information Technology and Decision, 5(4), 729-738.
[151]Yu, P. L. and Chen, Y. C. (2007). Competence Set Analysis and Effective Problem Solving, in: Shi, Y. et al. (Eds.) Advances in Multiple Criteria Decision Making and Human Systems Management. IOS press, Amsterdam, 229-250.
[152]Yu, P. L. and Chianglin, C. Y. (2006). Decision traps and competence dynamics in changeable spaces. International Journal of Information Technology and Decision, 5(1), 5-18.
[153]Yu, P. L. and Zhang, D. (1992). Optimal expansion of competence sets and decision support. Information Systems and Operational Research, 30(2), 68-85.
[154]Zhang, X., Ling, C. and Qi, L. (2011). Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints. Journal of Global Optimization, 49(2), 293-311.
論文全文使用權限:同意授權於2014-08-06起公開