Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

References

• Achterberg T, Kocha T, Martin A (2005) Branching rules revisited. Oper. Res. Lett. 33:42–54.Crossref, Google Scholar
• Armstrong RD, Kung DS, Sinha P, Zoltners AA (1983) A computational study of a multiple-choice knapsack algorithm. ACM Trans. Math. Software 9:184–198.Crossref, Google Scholar
• Balas E, Zemel E (1980) An algorithm for large 0–1 knapsack problems. Oper. Res. 28:1130–1154.Link, Google Scholar
• Bertsimas D, Demir R (2002) An approximate dynamic programming approach to multidimensional knapsack problems. Management Sci. 48:550–565.Link, Google Scholar
• Bonami P, Lee J (2006) BONMIN users' manual. https://projects.coin-or.org/Bonmin/.Google Scholar
• Bonami P, Biegler LT, Conn AR, Cornuejols G, Grossmann IE, Laird CD, Lee Jet al. (2005) An algorithmic framework for convex mixed integer nonlinear programs. IBM Research Report RC23771, IBM Research Division, Thomas J. Watson Research Center, Yorktown Heights, NY.Google Scholar
• Bretthauer KM, Shetty B (1995) The nonlinear resource allocation problem. Oper. Res. 43:670–683.Link, Google Scholar
• Chu PC, Beasley JE (1998) A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 4:63–86.Crossref, Google Scholar
• Coit DW, Smith AE (1996a) Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Trans. Reliability 45:254–260.Crossref, Google Scholar
• Coit DW, Smith AE (1996b) Adaptive penalty methods for genetic optimization of constrainted combinatorial problems. INFORMS J. Comput. 8:173–182.Link, Google Scholar
• Cooper MW (1981) Survey of methods of pure nonlinear integer programming. Management Sci. 27:353–361.Link, Google Scholar
• Dyer ME (1980) Calculating surrogate constraints. Math. Programming 19:255–278.Crossref, Google Scholar
• Dyer ME, Kayal N, Walker J (1984) A branch and bound algorithm for solving the multiple-choice knapsack problem. J. Comput. Appl. Math. 11:231–249.Crossref, Google Scholar
• Elhedhli S, Goffin JL (2005) Efficient production-distribution system design. Management Sci. 51:1151–1164.Link, Google Scholar
• Freville A (2004) The multidimensional 0–1 knapsack problem: An overview. Eur. J. Oper. Res. 155:1–21.Crossref, Google Scholar
• Freville A, Hanafi S (2005) The multidimensional 0–1 knapsack problem: Bounds and computational aspects. Ann. Oper. Res. 139:195–227.Crossref, Google Scholar
• Freville A, Plateau G (1994) An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem. Discrete Appl. Math. 49:189–212.Crossref, Google Scholar
• Frontline Systems (2005) Premium Solver Platform User Guide (Frontline Systems, Incline Village, NV). http://www.solver.com.Google Scholar
• Gavish B, Pirkul H (1985) Efficient algorithms for solving the multiconstraint zero-one knapsack problem to optimality. Math. Programming 31:78–105.Crossref, Google Scholar
• Gavish B, Glover F, Pirkul H (1991) Surrogate constraints in integer programming. J. Inform. Optim. Sci. 12(2):219–228.Crossref, Google Scholar
• Gerla M, Kleinrock L (1977) On the topological design of distributed computer networks. IEEE Trans. Comm. 25:48–60.Crossref, Google Scholar
• Glover F (1965) A multiphase-dual algorithm for the zero-one integer programming problem. Oper. Res. 13:879–919.Link, Google Scholar
• Hochbaum DS (1995) A nonlinear knapsack problem. Oper. Res. Lett. 17:103–110.Crossref, Google Scholar
• Hsieh Y (2002) A linear approximation for redundant reliability problems with multiple component choices. Comput. Indust. Engrg. 44:91–103.Crossref, Google Scholar
• Ibaraki T, Katoh N (1988) Resource Allocation Problems: Algorithmic Approaches (MIT Press, Cambridge, MA).Google Scholar
• Karwan MH, Rardin RL, Sarin S (1987) A new surrogate dual multiplier search procedure. Naval Res. Log. 34:431–450.Crossref, Google Scholar
• Kellerer H, Pferschy U, Pisinger D (2004) Knapsack Problems (Springer, Berlin).Crossref, Google Scholar
• Liang Y-C, Smith A (2004) An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans. Reliability 53:417–423.Crossref, Google Scholar
• Marsten RE, Morin TL (1978) A hybrid approach to discrete mathematical programming. Math. Programming 14:21–40.Crossref, Google Scholar
• Martello S, Toth P (2003) An exact algorithm for the two-constraint 0–1 knapsack problem. Oper. Res. 51:826–835.Link, Google Scholar
• Martello S, Pisinger D, Toth P (1999) Dynamic programming and strong bounds for the 0–1 knapsack problem. Management Sci. 45:414–424.Link, Google Scholar
• Mathur K, Salkin HM, Morito S (1983) A branch and search algorithm for a class of nonlinear knapsack problems. Oper. Res. Lett. 2:155–160.Crossref, Google Scholar
• Nakagawa Y (2003) An improved surrogate constraints method for separable nonlinear integer programming. J. Oper. Res. Soc. Japan 46:145–163.Google Scholar
• Nakagawa Y (2004) A difficulty estimation method for multidimensional nonlinear 0–1 knapsack problems using entropy. IEICE Trans. Fundamentals J87-A:406–408.Google Scholar
• Nakagawa Y, Iwasaki A (1999) Modular approach for solving nonlinear knapsack problems. IEICE Trans. Fundamentals Electronics E82-A:1860–1864.Google Scholar
• Nakagawa Y, Miyazaki S (1981) Surrogate constraints algorithm for reliability optimization problems with two constraints. IEEE Trans. Reliability R-30:175–180.Crossref, Google Scholar
• Nakagawa Y, Hikita M, Kamada H (1984) Surrogate constraints algorithm for reliability optimization problems with multiple constraints. IEEE Trans. Reliability R-33:301–305.Crossref, Google Scholar
• Nauss MR (1978) The 0–1 knapsack problem with multiple choice constraints. Eur. J. Oper. Res. 2:125–131.Crossref, Google Scholar
• Ng KYK, Sancho NGF (2001) A hybrid dynamic programming depth-first search algorithm with an application to redundancy allocation. IIE Trans. 33:1047–1058.Crossref, Google Scholar
• Osorio MA, Glover F, Hammer P (2002) Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions. Ann. Oper. Res. 117:71–93.Crossref, Google Scholar
• Petersen CC (1967) Computational experience with variants of the Balas algorithm applied to the selection of R&D projects. Management Sci. 13:736–750.Link, Google Scholar
• Puchinger J, Raidl G, Pferschy U (2010) The multidimensional knapsack problem: Structure and algorithms. INFORMS J. Comput. 22:250–265.Link, Google Scholar
• Ralphs TK (2006) Parallel branch and cut. Talbi E-G, ed. Parallel Combinatorial Optimization (John Wiley & Sons, Hoboken, NJ), 53–101.Crossref, Google Scholar
• Shannon C (1948) A mathematical theory of communication. Bell System Tech. J. 27:379–423.Crossref, Google Scholar
• Sinha P, Zoltners AA (1979) The multiple-choice knapsack problem. Oper. Res. 27:503–515.Link, Google Scholar
• Takaoka T (1998) A new measure of disorder—Entropy. Computing Theory ‘98: Proc. 4th Australasian Theory Symposium (CATS ‘98), (Springer-Verlag, New York), 77–85.Google Scholar
• Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Programming, Ser. A 99:563–591.Crossref, Google Scholar
• Vasquez M, Vimont Y (2005) Improved results on the 01 multidimensional knapsack problem. Eur. J. Oper. Res. 165:70–81.Crossref, Google Scholar
• Watanabe S (1960) Information theoretical analysis of multivariate correlation. IBM J. Res. Development 4:66–82.Crossref, Google Scholar