Optimization: Algorithms and applications

Optimization: Algorithms and Applications

Volumn , Issue , 2015, Pages 1-437

  Arora, Rajesh Kumar ^a  

^a INDIAN SPACE RESEARCH ORGANISATION   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85053094104     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/b18469     Document Type: Book

References (175)

1. Agnew, R.P. 1960. Differential Equations. New York: McGraw-Hill.
2. Arora, R.K., and Pradeep, K. 2003. Aerodynamic Shape Optimization of a Re-Entry Capsule. In AIAA Atmospheric Flight Mechanics Conference and Exhibit. AIAA-5394-2003, Texas.
3. Ashok, D.B., and Tirupathi, R.C. 2011. Optimization Concepts and Applications in Engineering. Cambridge, UK: Cambridge University Press.
4. Bellman, R. 1953. An Introduction to the Theory of Dynamic Programming. RAND Corp. Report.
5. Betts, J.T. 1998. Survey of Numerical Methods for Trajectory Optimization. Guidance, Control and Dynamics 21(2):193–207.
6. Burghes, D.N., and Wood, A.D. 1980. Mathematical Models in the Social, Management and Life Sciences. Hemstead, UK: Ellis Horwood.
7. Dantzig, G.B. 1949. Programming of Interdependent Activities: II Mathematical Model. Econometrica 17(3):200–211.
8. Dantzig, G.B. 1990. The Diet Problem. Interfaces 20(4):43–47.
9. Deb, K. 1995. Optimization for Engineering Design: Algorithms and Examples. Upper Saddle River, NJ: Prentice Hall.
10. Epperson, J.F. 2010. An Introduction to Numerical Methods and Analysis. Hoboken, NJ: John Wiley & Sons.
11. Gomory, R.E. 1958. Outline of an Algorithm for Integer Solutions to Linear Programs. Bulletin of American Society 64:275–278.
12. Griva, I., Nash, S.G., and Sofer, A. 2009. Linear and Nonlinear Optimization. Philadelphia: SIAM.
13. Hancock, H. 1917. Theory of Maxima and Minima. Boston: Ginn and Company.
14. Jaluria, Y. 2008. Design and Optimization of Thermal Systems. Boca Raton, FL: CRC Press.
15. Kantorovich, L.V. 1939. Mathematical Methods of Organizing and Planning Production. Leningrad State University.
16. Karush, W. 1939. Minima of Functions of Several Variables with Inequalities as Side Constraints. M.Sc. Dissertation. Illinois: University of Chicago.
17. King, J.R. 1975. Production, Planning and Control: An Introduction to Quantitative Methods. Oxford: Pergamon Press.
18. Kuhn, H.W., and Tucker, A.W. 1951. Nonlinear Programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, 481–492.
19. Pravica, D.W., and Spurr, M.J. 2010. Mathematical Modeling for the Scientific Method. Burlington, MA: Jones and Bartlett Learning.
20. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. Hoboken, NJ: John Wiley & Sons.
21. Schafer, M. 2006. Computational Engineering: Introduction to Numerical Methods. New York: Springer Science+Business Media.
22. Shepley, R.L. 1984. Differential Equations. New York: John Wiley & Sons.
23. Spivey, W.A., and Thrall, R.M. 1970. Linear Optimization. New York: Holt, Rinehart and Winston.
24. Venkataraman, P. 2009. Applied Optimization with MATLAB Programming. Hoboken, NJ: John Wiley & Sons.
25. Vinh, N.X. 1981. Optimal Trajectories in Atmospheric Flight. Amsterdam: Elsevier.
26. Watkins, D.S. 2010. Fundamentals of Matrix Computations. Hoboken, NJ: John Wiley & Sons.
27. Wismer, D.A., and Chattergy, R. 1978. Introduction to Nonlinear Optimization: A Problem Solving Approach. Amsterdam: Elsevier/North Holland.
28. Deb, K. 1995. Optimization for Engineering Design: Algorithms and Examples. Upper Saddle River, NJ: Prentice Hall.
29. Dennis, J.E., and Schnabel, R.B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Upper Saddle River, NJ: Prentice Hall.
30. Kincaid, D., and Cheney, W. 2009. Numerical Analysis: Mathematics of Scientific Computing. Providence, RI: American Mathematical Society.
31. King, R.M., and Mody, N.A. 2011. Numerical and Statistical Methods for Biomedical Engineering: Applications in MATLAB. Cambridge, UK: Cambridge University Press.
32. Philips, D.T., Ravindran, A., and Solberg, J.J. 1976. Operations Research: Principles and Practice. New York: John Wiley & Sons.
33. Reklaitis, G.V., Ravindran, A., and Ragsdell, K.M. 1983. Engineering Optimization: Methods and Applications. New York: John Wiley & Sons.
34. Andreas, A., and Wu-Shey, L. 2007. Practical Optimization: Algorithms and Engineering Applications. New York: Springer Science+Business Media.
35. Ashok, D.B., and Tirupathi, R.C. 2011. Optimization Concepts and Applications in Engineering. Cambridge, UK: Cambridge University Press.
36. Cauchy, A.L. 1847. Methode generale pour la resolution des systemes d’equations simultanees. Comptes Rendus de l’Académie des Sciences 25:536–538.
37. Colville, A.R. 1968. A Comparative Study on Nonlinear Programming Codes, Report 320-2949, IBM. New York Scientific Centre.
38. Dennis, J.E., and Schnabel, R.B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Upper Saddle River, NJ: Prentice Hall.
39. Fletcher, R., and Powell, M.J.D. 1963. A Rapidly Convergent Descent Method for Minimization. The Computer Journal 6:163–168.
40. Fletcher, R., and Reeves, C.M. 1964. Function Minimization by Conjugate Gradients. The Computer Journal 7(2):149–154.
41. Freudenstein, F., and Roth, B. 1963. Numerical Solutions of Systems of Nonlinear Equations. Journal of ACM 10(4):550–556.
42. Griva, I., Nash, S.G., and Sofer, A. 2009. Linear and Nonlinear Optimization. Philadelphia: SIAM.
43. Haftka, R.T., and Gurdal, Z.A. 1992. Elements of Structural Optimization. Dordrecht, the Netherlands: Kluwer.
44. Levenberg, K. 1944. A Method for the Solution of Certain Nonlinear Problems in Least Squares. Quarterly Applied Mathematics 2(2):164–168.
45. Marquardt, D. 1963. An Algorithm for Least Squares Estimation of Nonlinear Parameters. SIAM Journal of Applied Mathematics 11(2):431–441.
46. Nelder, J.A., and Mead, R. 1965. A Simplex Method for Function Minimization. Computer Journal 7(2):308–313.
47. Nowak, U., and Weimann, L. 1991. A Family of Newton Codes for Systems of Highly Nonlinear Equation. TR 91-10. Berlin: Konard Zuse Zentrumf. Informationstechn.
48. Powell, M.J.D. 1970. A Hybrid Method for Nonlinear Equations. Chapter 6. In: Numerical Methods for Nonlinear Algebraic Equations. P. Rabinowitz (ed.), Gordon and Breach, 87–114.
49. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. Hoboken, NJ: John Wiley & Sons.
50. Reklaitis, G.V., Ravindran, A., and Ragsdell, K.M. 1983. Engineering Optimization: Methods and Applications. New York: John Wiley & Sons.
51. Rosenbrock, H.H. 1960. An Automatic Method for Finding the Greatest or Least Value of a Function. The Computer Journal 3(3):175–184.
52. Shanno, D.F. 1970. Conditioning of Quasi-Newton Methods for Function Minimization. Mathematics of Computation 24:647–656.
53. Venkataraman, P. 2009. Applied Optimization with MATLAB Programming. Hoboken, NJ: John Wiley & Sons.
54. Barnes, E.R. 1986. A Variation on Karmarkar’s Algorithm for Solving Linear Programming Problems. Mathematical Programming 36:174–182.
55. Dantzig, G.B. 1963. Linear Programming and Extensions. Princeton, NJ: Princeton University Press.
56. Fishback, P.E. 2010. Linear and Nonlinear Programming with MAPLE: An Interactive Applications-Based Approach. Boca Raton, FL: CRC Press.
57. Griva, I., Nash, S.G., and Sofer, A. 2009. Linear and Nonlinear Optimization. Philadelphia: SIAM.
58. Karmarkar, N. 1984. A New Polyline-Time Algorithm for Linear Programming, Combinatorica 4(4):373–395.
59. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. Hoboken, NJ: John Wiley & Sons.
60. Spivey, W.A., and Thrall, R.M. 1970. Linear Optimization. New York: Holt, Rinehart and Winston.
61. Vanderbei, R.J., Meketon, M.S., and Freedman, B.A. 1986. A Modification of Karmarkar’s Linear Programming Problem. Algorithmica 1:395–407.
62. Davis, L. 1987. Genetic Algorithm and Simulated Annealing. London: Pitman.
63. Deb, K. 1995. Optimization for Engineering Design: Algorithms and Examples. Upper Saddle River, NJ: Prentice Hall.
64. Dorigo, M. 1992. Optimization, Learning and Natural Algorithms, PhD dissertation, Dipartimento di Elettronica, Politecnico di Milano. Italy.
65. Dorigo, M., Maniezzo, V., and Colorni, A. 1996. Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transactions on Systems, Man, and Cybernetics B 26(1):29–41.
66. Gendreau, M., and Potvin, J.Y. 2010. Handbook of Metaheuristics, International Series in Operations Research and Management Science, Vol. 146. Heidelberg and New York: Springer Science+Business Media.
67. Glover, F. 1986. Future Paths for Integer Programming and Links to Artificial Intelligence. Computers and Operations Research 13:533–549.
68. Goldberg, D.E. 1989. Genetic Algorithms in Search Optimization and Machine Learning. Reading, MA: Addison-Wesley.
69. Goldberg, D.E., Deb, K., and Thierens, D. 1993. Towards a Better Understanding of Mixing in Genetic Algorithms. Journal of the Society of Instrument and Control Engineers 32(1):10–16.
70. Hartl, D.L. 1991. Basic Genetics. Burlington, MA: Jones & Bartlett.
71. Holland, J.H. 1992. Adaptation in Natural and Artificial Systems. Cambridge, MA: MIT Press.
72. Kennedy, J., and Eberhart, R. 2001. Swarm Intelligence. San Diego: Academic Press.
73. Laarhoven, P.J.M.V., and Aarts, E.H.L. 1987. Simulated Annealing: Theory and Applications. Dordrecht: Kluwer.
74. Laskari, E.C., Parsopoulos, K.E., and Vrahatis, M.N. 2002. Particle Swarm Optimization for Minmax Problems. Evolutionary Computation Proceedings 2:1576–1581.
75. Merkle, D., Middendorf, M., and Schmeck, H. 2002. Ant Colony Optimization for Resource-Constrained Project Scheduling. IEEE Transactions on Evolutionary Computation 6(4):333–346.
76. Michalewicz, Z. 1996. Genetic Algorithm + Data Structures = Evolution Programs. Heidelberg and New York: Springer-Verlag.
77. Mitchell, M. 1996. An Introduction to Genetic Algorithms. Cambridge, MA: MIT Press.
78. Pham, D.T., and Karaboga, D. 2000. Intelligent Optimization Techniques: Genetic Algorithm, Tabu Search, Simulated Annealing and Neural Networks. Heidelberg and New York: Springer Science+Business Media.
79. Reimann, M., Doerner, K., and Hartl, R.F. 2004. D-Ants: Savings Based Ants Divide and Conquer the Vehicle Routing Problems. Computers & Operations Research 31(4):563–591.
80. Shmygelska, A., and Hoos, H.H. 2005. An Ant Colony Optimization Algorithm for the 2D and 3D Hydrophobic Polar Protein Folding Problem. BMC, Bioinformatics 6:30.
81. Byrd, R.H., Gilbert, J.C., and Nocedal, J. 2000. A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming. Mathematical Programming 89(1):149–185.
82. Byrd, R.H., Schnabel, R.B., and Shultz, G.A. 1988. Approximate Solution of the Trust Region Problem by Minimization over Two-Dimensional Subspaces. Mathematical Programming 40(3):247–263.
83. Coleman, T.F., and Verma, A. 2001. A Preconditioned Conjugate Gradient Approach to Linear Equality Constrained Minimization. Computational Optimization and Applications 20(1):61–72.
84. Griva, I., Nash, S.G., and Sofer, A. 2009. Linear and Nonlinear Optimization. Philadelphia: SIAM.
85. Han, S.P. 1977. A Globally Convergent Method for Nonlinear Programming. Journal of Optimization Theory and Applications 22(3):297–309.
86. Haug, E.J., and Arora, J.S. 1979. Applied Optimal Design: Mechanical and Structural Systems. New York: John Wiley & Sons.
87. Horowitz, B., Guimaraes, L.J.N., and Afonso, S.M.B. 2008. A Concurrent Efficient Global Optimization Algorithm Applied to Engineering Problems. AIAA 2008-6010.
88. Moré, J.J., and Sorensen, D.C. 1983. Computing a Trust Region Step. SIAM Journal on Scientific and Statistical Computing 3:553–572.
89. Nocedal, J., and Wright, S.J. 2006. Numerical Optimization. Springer Series in Operations Research. New York: Springer Science+Business Media.
90. Powell, M.J.D. 1978. The Convergence of Variable Metric Methods for Nonlinearly Constrained Optimization Calculations. Nonlinear Programming 3. New York: Academic Press.
91. Ragsdell, K.M., and Philips, D.T. 1976. Optimal Design of a Class of Welded Structures Using Geometric Programming. ASME Journal of Engineering for Industries 98(3):1021–1025.
92. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. Hoboken, NJ: John Wiley & Sons.
93. Reklaitis, G.V., Ravindran, A., and Ragsdell, K.M. 1983. Engineering Optimization: Methods and Applications. New York: John Wiley & Sons.
94. Sandgren, E. 1990. Nonlinear Integer and Discrete Programming in Mechanical Design Optimization. ASME Journal of Mechanical Design 112:223–229.
95. Thygeson, J.R., and Grossmann, E.D. 1970. Optimization of a Continuous Through-Circulation Dryer. American Institute of Chemical Engineers Journal 16:749–754.
96. Adimurthy, V., Ramanan, R.V., and Pankaj, P. 2012. Optimization in Aerospace Dynamics. Bangalore, India: ISRO.
97. Arora, R.K., and Pradeep, K. 2003. Aerodynamic Shape Optimization of a Re-Entry Capsule. AIAA Atmospheric Flight Mechanics Conference and Exhibit. AIAA-5394-2003.
98. Binh, T., and Korn, U. 1997. MOBES: A Multi-Objective Evolution Strategy for Constrained Optimization Problems. Proceedings of the Third International Conference on Genetic Algorithms 176–182.
99. Chankong, V., and Haimes, Y.Y. 1983. Multiobjective Decision Making: Theory and Methodology. Amsterdam: North Holland.
100. Chernyi, G.G. 1961. Introduction to Hypersonic Flow. New York: Academic Press.
101. Deb, K. 2002. Multi-Objective Optimization Using Evolutionary Algorithms. Hoboken, NJ: John Wiley & Sons.
102. Knowles, J.D., and Corne, D.W. 2000. Approximating the Non-Dominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2):149–172.
103. Miettinen, K. 1999. Nonlinear Multiobjective Optimization. Dordrecht: Kluwer.
104. Parsopoulos, K.E., and Vrahatis, M.N. 2002. Particle Swarm Optimization in Multiobjective Problems. Proceedings of the ACM 2002 Symposium on Applied Computation: 603–607.
105. Statnikov, R.B., and Matusov, J.B. 1995. Multicriteria Optimization and Engineering, Springer.
106. Veldhuizen, D.A.V. 1999. Multiobjective Evolutionary Algorithms: Classification, Analyzes, and New Innovations. PhD dissertation, Air Force Institute of Technology, Wright-Patterson AFB.
107. Zitzler, E., Deb, K., and Thiele, L. 2000. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2):173–195.
108. Abuo-El-Ata, M., Fergany, H., and El-Wakeel, M. 2003. Probabilistic Multi-Item Inventory Model with Varying Order Cost Under Two Restrictions: A Geometric Programming Approach. International Journal of Production Economics 83(3):223–231.
109. Beightler, C.S., Philips, D.T., and Wilde, D.J. 1967. Foundations of Optimization. Upper Saddle River, NJ: Prentice Hall.
110. Cao, B.Y. 2002. Fuzzy Geometric Programming. Dordrecht: Kluwer Academic.
111. Chen, T.Y. 1992. Structural Optimization Using Single-Term Posynomial Geometric Programming. Computer and Structures 45(5):911–918.
112. Chiang, M. 2005. Geometric Programming for Communication Systems. Hanover, MA: NOW Publishers.
113. Chu, C., and Wong, D.F. 2001. VLSI Circuit Performance Optimization by Geometric Programming. Annals of Operations Research 105:37–60.
114. Dawson, J., Boyd, S., Hershenson, M., and Lee, T.H. 2001. Optimal Allocation of Local Feedback in Multistage Amplifiers via Geometric Programming. IEEE Transactions on Circuits and Systems 48(1):1–11.
115. Dembo, R.S. 1976. A Set of Geometric Programming Test Problems and Their Solutions. Mathematical Programming 10:192–213.
116. Dembo, R.S. 1978. Dual to Primal Conversion in Geometric Programming. Journal of Optimization Theory and Applications 26:243–252.
117. Dey, S., and Roy, T.K. 2013. Optimization of Structural Design Using Geometric Programming. International Journal of Engineering Research and Technology 2(8).
118. Duffin, R.J., Peterson, E.L., and Zener, C. 1967. Geometric Programming. New York: John Wiley & Sons.
119. Fang, S.C., Rajasekara, J.R., and Tsao, H.S.J. 1997. Entropy Optimization and Mathematical Programming. Dordrecht: Kluwer Academic.
120. Hajela, P. 1986. Geometric Programming Strategies for Large Scale Structural Synthesis. AIAA Journal 24(7):1173–1178.
121. Hoburg, W., and Abbeel, P. 2012. Geometric Programming for Aircraft Design Optimization. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Hawaii. AIAA 2012-1680.
122. Jefferson, T.R., and Scott, C.H. 1979. Avenues of Geometric Programming— Applications. NZOR 7-1.
123. Ojha, A.K., and Biswal, K.K. 2010. Posynomial Geometric Programming Problems with Multiple Parameters. Journal of Computing 2(1).
124. Phillips, D.T., Ravindran, A., and Solberg, J.J. 1976. Operations Research—Principles and Practice. John Wiley & Sons.
125. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. New Jersey: John Wiley & Sons.
126. Stoecker, W.F. 1971. Design of Thermal System. New York: McGraw-Hill.
127. Allison, J.T., and Papalambros, P.Y. 2008. Consistency Constraint Allocation in Augmented Lagrangian Coordination. Distance Education and Training Council (DETC), 49823.
128. Anderson, V.L., and McLean, R.A. 1974. Design of Experiments: A Realistic Approach. New York: Marcel Dekker.
129. Balesdent, M., Berend, N., and Depince, P. 2010. Optimal Design of Expendable Launch Vehicles using Stage-Wise MDO Formulation. 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Texas. AIAA 2010-9324.
130. Cornell, J.A., and Khuri, A.I. 1996. Response Surfaces: Design and Analyses. Marcel Dekker.
131. Dapeng, W., Gary, W.G., and Naterer, G.F. 2007. Extended Collaboration Pursuing Method for Solving Larger Multidisciplinary Design Optimization Problems. AIAA Journal 45(6):1208–1221.
132. Fletcher, R. 1981. Practical Methods of Optimization: Constrained Optimization. New York: John Wiley & Sons.
133. Geyer, P. 2009. Component-Oriented Decomposition for Multidisciplinary Design Optimization in Building Design. Advanced Engineering Informatics 23(1):12–31.
134. Goldberg, D.E. 1989. Genetic Algorithm in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley.
135. He, Y., and McPhee, J. 2005. Multidisciplinary Optimization of Multi-Body Systems with Application to the Design of Rail Vehicles. Multi-Body System Dynamics 14(2):111–135.
136. Herskovits, J. 2004. A Mathematical Programming Algorithms for Multidisciplinary Design Optimization. 10th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Texas. AIAA 2004-4502.
137. IIT Mumbai. 2004. Workshop on Optimization Based Design/Multidisciplinary Design Optimization (Course Notes), Trivandrum.
138. Kodiyalam, S., and Sobieszczanski-Sobieski, J. 2000. Bi-Level Integrated System Synthesis with Response Surfaces. AIAA Journal 38(8):1479–1485.
139. Kroo, I., and Manning, V. 2000. Collaborative Optimization: Status and Directions. 8th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Texas. AIAA 2000-4721.
140. Manokaran, K., Vidya, G., and Sivaramakrishnan, A.E. 2009. Wing Planform Design Optimization for Reusable Launch Vehicle. Journal of Aircraft 46(2):726–730.
141. Martins, J.R.R.A., and Lambe, A.B. 2013. Multidisciplinary Design Optimization: A Survey of Architectures. AIAA Journal 51(9):2049–2075.
142. McAllister, C.D., and Simpson, T.W. 2003. Multidisciplinary Robust Design Optimization of an Internal Combustion Engine. Journal of Mechanical Design 125(1):124–130.
143. Sobieszczanski-Sobieski, J., Agte, J.S., and Sandusky, R.R., Jr. 2000. Bi-Level Integrated System Synthesis. AIAA Journal 38(1):164–172.
144. Sobieszczanski-Sobieski, J., and Haftka, R.T. 1996. Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments. 34th AIAA Aerospace Sciences Meeting and Exhibit, Reno. AIAA 96-0711.
145. Tedford, N.P., and Martins, J.R.R.A. 2006. On the Common Structure of MDO Problems: A Comparison of Architectures. 11th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, Texas. AIAA 2006-7080.
146. Tedford, N.P., and Martins, J.R.R.A. 2010. Benchmarking Multidisciplinary Design Optimization Algorithms. Optimization and Engineering 11:159–183.
147. Xiaoqian Chen Li Yan, Wencai Luo, Ling Xu, Young Zhao, and Zhenguo Wang. 2006. Research on Theory and Application of Multidisciplinary Design Optimization of Flight Vehicles. 2nd AIAA MDO Specialist Conference, VA. AIAA 2006-1721.
148. Yoder, S., and Brockman, J. 1996. A Software Architecture for Collaborative Development and Solution of MDO Problems (Multidisciplinary Design Optimization). AIAA, NASA and ISSMO Symposium on Multidisciplinary Analysis and Optimization, VA. AIAA 96-4103.
149. Yushin Kim, Yong-Hee Jeon, and Dong-Ho Lee. 2006. Multi-Objective and Multi-Disciplinary Design Optimization of Supersonic Fighter Wing. Journal of Aircraft 43(3):817–824.
150. Balas, E. 1965. An Additive Algorithm for Solving Linear Programs with Zero-One Variables. Operations Research 13(4):517–546.
151. Bricker, D.L. 1999. Notes on Balas’ Additive Algorithm. Ames: University of Iowa Press.
152. Dakin, R.J. 1965. A Tree-Search Algorithm for Mixed-Integer Programming Problems. Computer Journal 8(3):250–255.
153. Garfinkel, R.S., and Nemhauser, G.L. 1972. Integer Programming. New York: John Wiley & Sons.
154. Gomory, R.E. 1960. An Algorithm for the Mixed Integer Problem. Rand Report, R.M. 25797.
155. Gomory, R.E., and Baumol, W.J. 1960. Integer Programming and Pricing. Econometrica 28(3):521–550.
156. Kennedy, J., and Eberhart, R.C. 2001. Swarm Intelligence. San Diego: Academic Press.
157. Land, A.H., and Doig, A. 1960. An Automatic Method for Solving Discrete Programming Problems. Econometrica 28:497–520.
158. Laskari, E.C., Parsopoulos, K.E., and Vrahatis, M.N. 2002. Particle Swarm Optimization for Integer Programming. Evolutionary Computation Proceedings 2:1576–1581.
159. Rao, S.S. 2009. Engineering Optimization: Theory and Practice. Hoboken, NJ: John Wiley & Sons.
160. Shenoy, G.V., Srivastava, U.K., and Sharma, S.C. 1986. Operations Research for Management. New Delhi: New Age International Publishers.
161. Wismer, D.A., and Chattergy, R. 1978. Introduction to Nonlinear Optimization: A Problem Solving Approach. Amsterdam: North Holland.
162. Bellman, R.E. 1957. Dynamic Programming. Princeton, NJ: Princeton University Press.
163. Bertsekas, D.P. 1987. Dynamic Programming: Deterministic and Stochastic Models. Upper Saddle River, NJ: Prentice Hall.
164. Denardo, E.V. 1982. Dynamic Programming Models and Applications. Upper Saddle River, NJ: Prentice Hall.
165. Dreyfus, S. 2010. Modern Computational Applications of Dynamic Programming. Journal of Industrial and Systems Engineering 4(3):152–155.
166. Edwin, J.E., and Gruber, M.J. 1971. Dynamic Programming Application in Finance. The Journal of Finance 26(2):473–506.
167. George, R.E. 1963. Nuclear Rocket Thrust Optimization using Dynamic Programming. AIAA Journal 1(5):1159–1166.
168. Hadley, G. 1964. Nonlinear and Dynamic Programming. Reading, MA: Addison-Wesley.
169. Hillier, F.S., and Lieberman, G.J. 2010. Introduction to Operations Research. New York: McGraw-Hill.
170. Howard, R.A. 1960. Dynamic Programming and Markov Processes. John Wiley & Sons.
171. Leondes, C.T., and Smith, F.T. 1970. Optimization of Interplanetary Orbit Transfers by Dynamic Programming. Journal of Spacecraft and Rockets 7(5):558–564.
172. Powell, W.B. 2010. Approximate Dynamic Programming: Solving the Curses of Dimensionality. Hoboken, NJ: John Wiley & Sons.
173. Puterman, M.L. 2005. Markov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboken, NJ: John Wiley & Sons.
174. Smith, D.K. 1991. Dynamic Programming: A Practical Introduction. Ellis Horwood.
175. Sniedovich, M. 1992. Dynamic Programming. New York: Marcel Dekker.