LogMIP (acronym of Logical Mixed Integer Programming) is a solver for generalized disjunctive programs (GDP). The problem formulation corresponds to the one proposed by Raman & Grossmann (1994), which is a continuous-discrete optimization problem that can be formulated in the following form:

are continuous variables,

are binary variables (0-1),

are Boolean variables, to establish whether a disjunction term is true or false

logic relationships between Boolean variables,

objective function, which can be linear or non-linear,

linear or non-linear inequalities independent of the discrete choices,

mixed-integer inequalities that can contain linear or non-linear continuous terms,

Integer inequalities

fixed cost terms.
 

Small Examples

LogMIP has two main components:

a language for the disjunction definitions.

disjunctive program solvers.

Those components are linked to GAMS (a computer system for the specification and solution of mathematical programs). Both parts are supersets of GAMS language and solvers respectively. LogMIP is not independent of GAMS, it uses the declarations and definitions made into GAMS language format for the specifications and solution of a disjunctive problem.