Monday, 14:15 - 14:40 h, Room: MA 005

 

Pedro Castro
Multiparametric disaggregation as a new paradigm for global optimization of mixed-integer polynomial programs

Coauthors: Ignacio E. Grossmann, João P. Teles

 

Abstract:
Multiparametric Disaggregation involves discretization of the domain of one of the variables appearing in a bilinear term, the basic building block to tackle higher order polynomials. Alternative numeric representation systems can be employed (e.g., decimal, binary) with the user specifying the accuracy level for the approximation. With this, the original MINLP can be approximated by an upper bounding MILP, which might be easier to solve to global optimality.
In this work, we propose a lower bounding relaxation MILP, where a truncation error is defined for the parameterized variables. Since the higher the chosen accuracy, the tighter the formulation, we can easily construct a global optimization algorithm starting with 1 significant digit (first iteration) and ending when the optimality gap is lower than a given tolerance.
Starting with Disjunctive Programming models, we show that the new relaxation, although looser,
leads to a better performance than the one from piecewise McCormick relaxations (using univariate
and uniform domain partitioning). The primary cause is the linear vs. exponential increase in
problem size for an order of magnitude reduction in optimality gap.

 

Talk 3 of the invited session Mon.2.MA 005
"Global mixed-integer nonlinear optimization II" [...]
Cluster 14
"Mixed-integer nonlinear programming" [...]

 

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