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Mixed Logical Linear Programming, John N. Hooker, Maria A. Osorio
Mixed Logical Linear Programming, John N. Hooker, Maria A. Osorio
John Hooker
Abstract: "Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MLLP). It represents the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it eliminates integer variables when they serve no purpose, provides alternatives to the traditional continuous relaxation, and applies logic processing algorithms. This paper surveys previous work and attempts to organize ideas associated with MLLP, some old and some new, into a coherent framework. It articulates potential advantages and disadvantages of MLLP and illustrates some of them with computational experiments."
Logic Cuts For Processing Networks With Fixed Charges, John N. Hooker, Carnegie Mellon University.Engineering Design Research Center.
Logic Cuts For Processing Networks With Fixed Charges, John N. Hooker, Carnegie Mellon University.Engineering Design Research Center.
John Hooker
Abstract: "We show how some simple logical constraints can substantially accelerate the solution of mixed integer linear programming (MILP) models for the design of chemical processing networks. These constraints are easily generated in a preprocessing stage and can be applied either symbolically during a branch-and-bound search or as constraints in the MILP model. Furthermore, they represent a new class of cuts, 'logic cuts,' that generalize traditional cutting planes. A logic cut can cut off feasible points but does not change the optimal solution. We establish some elementary properties of logic cuts and use them to show that our logical constraints …