Keywords:-
Article Content:-
Abstract
Integer programming is not new subject in optimization. However, given its practical applicability, we face computational difficulties in solving the large-scale problems. In this paper we solve a class of mixed-integer nonlinear programming problem by adopting a strategy of releasing non-basic variables from their bounds found in the optimal continuous solution in such a way to force the appropriate non-integer basic variables to move to their neighborhood integer points.
References:-
References
Duran, M.A., and Grossmann, I. E. 1986a. An Outer-Approximation Algorithm for A Class of Mixed-Integer Nonlinear Programs. Mathematical Programming 36, 307-339.
Kocis, G. R; and Grossmann, I.E. 1988. Global Optimizzation of Nonconvex MINLP Prolems in Process Synthesis. Ind. Eng. Chem 27, 1407-1422.
Floudas, C.A. 1989. Global Optimum Search for Nonconvex NLP and MINLP Problems. Computers Chem. Eng. 13, 1117-1132.
Ryoo, H. S., and Sahinidis, N.V. 1995. Global Optimization of Nonconvex NLPs and MINLPs with Applications in Process Design. Computers Chem. Vol.19. No. 5, 551-566.
Grossman, I. E., and Floudas, C. A. 1987. Active Constraint Strategy for Flexibility Analysis in Chemical Proses. Comput.Chem. engng, Vol. 11, No. 6, 675 - 693.
Harjunkoski, I; Westerlund, T; and Porn, R. 1999. Numerical and Environmental Considerations on a Complex Industrial Mixed Integer Non-Linear Programming (MINLP) Problem. Comput. & Chem. Eng.,23, 1545-1561.
Kallrath, J. 2005. Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization. Annals of Operations Research 140, 339-373.
Cai. X., et al. 2001. Solving Large Non-Convex Water Resources Management Models Using Genenalized Benders Decomposition. INFORMS, Vol. 49, No. 2, 235–245
Bragalli, C; et al. 2006. An MINLP Solution Method for a Water Network Problem. Springer: Lecture Notes in Computer Science vol. 4168. 696-707.
Martin, A; Moller, M; and Moritz, S. 2006. Mixed Integer Models for the Stationary Case of Gas Network Optimization. Math. Program., 105,563-582.
Grossman, I.E., and Sahinidis, N.V (eds). 2002. Special Issu on Mixed Integer Programming and Its Application to Engineering, Part I, Optim. Eng., 3 (4)
Kravanja, S., and Zula, T. 2010. The MINLP Approach to Structural Synthesis. Challenges, Opportunities and Solutions in Structural Engineering and Construction. Taylor & Francis Group, London,
Fugenschuh, A, et al. 2010. Mixed-Integer Nonlinear Problems in Transportation Applications. 2nd International Conference on Engineering Optimization. September 6-9, 2010, Lisbon, Portugal
Guerra, A., Newman, A.M., and Leyffer, S. 2011. Concrete Structure Design Using Mixed-Integer Nonlinear Programming with Complementarity Constraints. SIAM J. Optim, Vol 21, No.3, 833-863.
Junoh, A. K, et al. 2012. Classification of Examination Marks According to Bloom’s Taxonomy by Using Binary Linear Programming, IACSIT Press, Singapore, IPCSIT, vol. 36, 20-25
Tambunan, H. 2016. Mathematical Model for Mapping Students Cognitive Capability, International Journal of Evaluation and Research in Education 5(3), 221-226.
Tambunan, H & Mawengkang, H. 2018. Integer Linear Programming Approach for Detection Learning Outcomes Achievement. Far East Journal of Mathematical and Sciences, 5(1), 95-109.
Mawengkang, H., and Murtagh, B. A. 1986. Solving Nonlinear Integer Programs with Large-Scale Optimization Software. Annals of Operations Research 5425-437
Duran, M. A. and Grossmann, I.E. 1986b. A Mixed-Integer Nonlinear Programming Algorithm for Process Systems Synthesis. AIChE Journal Vol 32, No.4, 592-606
Fletcher, R., and Leyffer, S. 1994. Solving Mixed Integer Nonlinear Programs by Outer Approximation. Mat. Program, 66, 327-349.
Kesavan, P; et al. 2004. Outer Approximation Algorithms for Separable Nonconvex. Math. Program, Ser. A 100, 517–535
Geoffrion, A. M. 1972. A Generalized Benders Decomposition, J. Op-tim. Theory Appl, 10 (4), 237–260.
Westerlund, T; and Petersson, F. 1995. A Cutting Plane Method for Solving Convex MINLP Problems. Computers Eng., 19, 131-136.
Gupta, O.K; and Ravindran, V. 1985. Branch and Bound Experiments in Convex Nonlinear Integer Programming. Mangement Science, 31, 1533-1546.
Belotti, P.,Lee, J.,Liberti,L., Margot,F., and Wachter,A. 2009. Branching and Bounds Tightening Techniques for non-Convex MINLP, Optimization Methods and Software, 24(4):597-634,
Liberti, L., Nannicini, G., and Mladenovic,N, 2009. A Good Recipe for Solving MINLPs. In: V. Maniezzo, T. Stutzle, S.Voss (eds.) Metaheuristics: Hybridizing metaheuristics and Mathematical Programming. Annals of Information Systems. Springer, vol. 10,. 231-245.
Scraf, H.E. (1986). Testing for Optimality In the Absence of Convexity. @ Cambridge University Press. 117-133.
Tambunan, H., and Mawengkang, H. 2016. Solving Mixed Integer Non-Linear Programming Using Active Constraint. Global Journal of Pure and Applied Mathematics. Vol. 12, Number 6, 5267–5281