Column enumeration based decomposition techniques for a class of non-convex MINLP problems
We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are computed via subproblems. These problems can be linear, mixed integer linear, (non-)convex nonlinear, or mixed integer nonlinear. However, the important property of the subproblems is that we can compute their exact global optimum quickly. The proposed technique will be illustrated solving a cutting problem with optimum nonlinear programming subproblems.
KeywordsMINLP Column enumeration Decomposition Packing
Unable to display preview. Download preview PDF.
- Adjiman C.S., Androulakis I.P. and Floudas C.A. (1997). Global optimization of MINLP problems in process synthesis and design. Comput. Chem. Eng. 21(Suppl. S): S445–S450 Google Scholar
- Floudas, C.A.: Deterministic Global Optimization: Theory, Algorithms and Applications, vol. 37 of Nonconvex Optimization and Its Applications, pp. 309–554. Kluwer Academic Publishers (2000)Google Scholar
- Kallrath, J.: Online Storage Systems and Transportation Problems with Applications: Optimization Models and Mathematical Solutions, vol. 91 of Applied Optimization, pp. 92–104. Kluwer Academic Publishers, Norwell, MA (2004)Google Scholar
- Lindo Systems: Lindo API: User’s Manual. Lindo Systems, Inc., Chicago (2004)Google Scholar
- Lenstra J.K. and Rinnooy Kan A.H.G. (1979). Complexity of Packing, Covering and Partitioning Problems. In: Schrijver, A. (eds) Packing and Covering in Combinatorics, pp 275–291. Mathematisch Centrum, Amsterdam Google Scholar
- Liberti, L., Maculan, N. (eds.): Global Optimization: From Theory to Implementation, vol. 84 of Nonconvex Optimization and Its Applications, pp. 223–232. Springer (2006)Google Scholar
- Pintér, J.D.: Continuous global optimization software: A brief review. Optima, 52, 1–8 (1996a). See also http://plato.la.asu.edu/gom.html
- Pintér J.D. Global Optimization in Action: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications, vol. 6 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers (1996b)Google Scholar
- Pardalos P.M., Resende M.G.C. (eds.): Handbook of Applied Optimization pp. 337–351. Oxford University Press (2002)Google Scholar
- Schrage L. (2006). Optimization Modeling with LINGO. LINDO Systems, Inc., Chicago, IL Google Scholar
- 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. Int. Trans. Oper. Res. 5(1): 45–57 Google Scholar