Invited Session Mon.2.MA 005

Monday, 13:15 - 14:45 h, Room: MA 005

Cluster 14: Mixed-integer nonlinear programming [...]

Global mixed-integer nonlinear optimization II


Chair: Ignacio E. Grossmann



Monday, 13:15 - 13:40 h, Room: MA 005, Talk 1

Brage Rugstad Knudsen
Mixed integer optimization of the late-life performance of shale-gas wells

Coauthors: Andrew R. Conn, Bjarne Foss


Efficient shale-gas recovery requires a large number of wells in order to maintain a sustainable total gas supply. The wells and the production pads are often widely spread over a large geographical area, and interconnected by comprehensive surface gathering lines. We present a discrete time mixed integer nonlinear program (MINLP) for optimal scheduling of shale-gas multi-well pads. The MINLP model is formulated by using a dynamic reservoir proxy model and a nonlinear well model for each well, and we show how shut-ins may be efficiently scheduled to prevent liquid loading and boost late-life rates for these types of wells. Furthermore, by using a simplified well model and performing a linear reformulation, we do a preliminary comparison of solving the scheduling problem as an MILP compared to the MINLP.



Monday, 13:45 - 14:10 h, Room: MA 005, Talk 2

Gonzalo Guillén-Gosálbez
Solving mixed-integer linear-fractional programming problems via an exact MILP reformulation

Coauthors: Pedro Copado, Ignacio Grossmann


We present a method to solve mixed-integer linear-fractional programming (MILFP) problems in which
the objective function is expressed as a ratio of two linear functions and the equality and
inequality constraints are all linear. Our approach extends the transformation of Charnes and
Cooper (1962), originally devised for linear-fractional programs with continuous variables, to
handle the mixed-integer case. In essence, we reformulate the MILFP into an equivalent mixed-integer
linear program (MILP) that makes use of auxiliary continuous variables. The solution of this MILP,
which can be obtained by standard branch-and-cut methods, provides the global optimum of the
original MILFP. Numerical results show that our strategy outperforms the most widely used
general-purpose mixed-integer nonlinear programming solution methods (i.e., outer approximation
- available in DICOPT -, nonlinear branch and bound - SBB -, and extended cutting plane,
alphaBB) as well as the branch-and-reduce global optimization algorithm implemented in BARON.

Charnes, A., Cooper, W. W. (1962). Naval Research Logistics Quarterly, 9: 181-196.



Monday, 14:15 - 14:40 h, Room: MA 005, Talk 3

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

Coauthors: Ignacio E. Grossmann, João P. Teles


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.


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