Abstract
In this paper, we present a constraint-partitioning approach for finding local optimal solutions of large-scale mixed-integer nonlinear programming problems (MINLPs). Based on our observation that MINLPs in many engineering applications have highly structured constraints, we propose to partition these MINLPs by their constraints into subproblems, solve each subproblem by an existing solver, and resolve those violated global constraints across the subproblems using our theory of extended saddle points. Constraint partitioning allows many MINLPs that cannot be solved by existing solvers to be solvable because it leads to easier subproblems that are significant relaxations of the original problem. The success of our approach relies on our ability to resolve violated global constraints efficiently, without requiring exhaustive enumerations of variable values in these constraints. We have developed an algorithm for automatically partitioning a large MINLP in order to minimize the number of global constraints, an iterative method for determining the optimal number of partitions in order to minimize the search time, and an efficient strategy for resolving violated global constraints. Our experimental results demonstrate significant improvements over the best existing solvers in terms of solution time and quality in solving a collection of mixed-integer and continuous nonlinear constrained optimization benchmarks.
Research supported by National Science Foundation Grant IIS 03-12084.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont (1999)
Bongartz, I., Conn, A.R., Gould, N., Toint, P.L.: CUTE: Constrained and unconstrained testing environment. ACM Trans. on Mathematical Software 21(1), 123–160 (1995)
Conn, A.R., Gould, N., Toint, P.L.: Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization. Mathematical Programming 73, 73–110 (1996)
Duran, M.A., Grossmann, I.E.: An outer approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming 36, 306–307 (1986)
Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Brooks Cole Publishing Company (2002)
Geoffrion, A.M.: Generalized Benders decomposition. J. Optim. Theory and Appl. 10(4), 237–241 (1972)
Gill, P.E., Murray, W., Saunders, M.: SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM Journal on Optimization 12, 979–1006 (2002)
Gould, N.I.M., Orban, D., Toint, P.L.: An interior-point â„“1-penalty method for nonlinear optimization. Technical report, RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK (2003)
Harjunkoski, I., Westerlund, T., Pörn, R., Skrifvars, H.: Different transformations for solving non–convex trim loss problems by MINLP. European Journal of Operations Research 105, 594–603 (1998)
Holmberg, K.: On the convergence of the cross decomposition. Mathematical Programming 47, 269–316 (1990)
Leyffer, S.: Mixed integer nonlinear programming solver (2002), http://www-unix.mcs.anl.gov/~leyffer/solvers.html
Leyffer, S.: MacMINLP: AMPL collection of MINLP problems (2003), http://www-unix.mcs.anl.gov/~leyffer/MacMINLP/
Rardin, R.L.: Optimization in Operations Research. Prentice-Hall, Englewood Cliffs (1998)
Sahinidis, N.V.: BARON: A general purpose global optimization software package. Journal of Global Optimization 8(2), 201–205 (1996)
Wah, B., Chen, Y.X.: Fast temporal planning using the theory of extended saddle points for mixed nonlinear optimization. Artificial Intelligence (accepted for publication) (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wah, B.W., Chen, Y. (2005). Solving Large-Scale Nonlinear Programming Problems by Constraint Partitioning. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_51
Download citation
DOI: https://doi.org/10.1007/11564751_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29238-8
Online ISBN: 978-3-540-32050-0
eBook Packages: Computer ScienceComputer Science (R0)