Solving Large-Scale Nonlinear Programming Problems by Constraint Partitioning
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.
KeywordsProblem Instance Constraint Function Master Problem Global Constraint Local Optimal Solution
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- 5.Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Brooks Cole Publishing Company (2002)Google Scholar
- 8.Gould, N.I.M., Orban, D., Toint, P.L.: An interior-point ℓ1-penalty method for nonlinear optimization. Technical report, RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK (2003)Google Scholar
- 11.Leyffer, S.: Mixed integer nonlinear programming solver (2002), http://www-unix.mcs.anl.gov/~leyffer/solvers.html
- 12.Leyffer, S.: MacMINLP: AMPL collection of MINLP problems (2003), http://www-unix.mcs.anl.gov/~leyffer/MacMINLP/
- 13.Rardin, R.L.: Optimization in Operations Research. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
- 15.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)Google Scholar