gurobi: Solve an LP, QP, or MIP using the Gurobi Optimizer
In paleo13/rgurobi: Solve optimisation problems using Gurobi

Description Usage Arguments Details Value Examples

Interface to the Gurobi Optimizer, which solves linear, quadratic, and mixed integer programming problems.

1	gurobi(model, params = NULL, NumberSolutions = 1, verbose = FALSE)

`model`	`list` object with the model specification (see details).
`params`	`list` object with Gurobi parameters. Defaults to `NULL` and uses default Gurobi parameters.
`NumberSolutions`	`integer` number of solutions to return. Defaults to 1.
`verbose`	`logical` should messages be printed?

The interface can be used to solve optimization problems of the following form:

minimize x'Qx + c'x subject to Ax = b (linear constraints) l <= x <= u (bound constraints) some xj integral (integrality constraints) some xk lie within second order cones (cone constraints) Many of the model components listed here are optional.

The Gurobi Optimizer is a commercial library for solving linear, quadratic, and mixed integer programming problems. More information on Gurobi Optimization, and online documentation can be found at http://www.gurobi.com. See the package vignette for a worked example.

The gurobi function takes a pair of list variables, each consisting of multiple named components. The first argument, model, contains the optimization model to be solved. Many of model's named components are optional. The following is an enumeration of all the named components of the model argument.

model$A The linear constraint matrix. This can be dense or sparse. Sparse matrices should be built using either sparseMatrix from the Matrix package, or simple_triplet_matrix from the slam package. model$obj The linear objective vector (the c vector in the problem statement above). You must specify one value for each column of A. model$sense The senses of the linear constraints. Allowed values are '=', '<=', or '>='. You must specify one value for each row of A. model$rhs The right-hand side vector for the linear constraints (the b vector in the problem statement above). You must specify one value for each row of A. model$lb Optional. The lower bound vector. When present, you must specify one value for each column of A. When absent, each variable has a lower bound of 0. model$ub Optional. The upper bound vector. When present, you must specify one value for each column of A. When absent, the variables have infinite upper bounds. model$vtypes Optional. The variable type vector. This vector is used to capture variable integrality constraints. Allowed values are 'C' (continuous), 'B' (binary), 'I' (integer), 'S' (semi-continuous), or 'N' (semi-integer). Binary variables must be either 0 or 1. Integer variables can take any integer value between the specified lower and upper bounds. Semi-continuous variables can take any value between the specified lower and upper bounds, or a value of zero. Semi-integer variables can take any integer value between the specified lower and upper bounds, or a value of zero. When present, you must specify one value for each column of A. When absent, each variable is treated as being continuous. model$modelsense Optional. The optimization sense. Allowed values are 'min' (minimize) or 'max' (maximize). When absent, the default optimization sense is minimization. model$modelname Optional. The name of the model. The name appears in the Gurobi log, and when writing a model to a file.

A list object containing the optimal solution, with the following components: result$status The status of the optimization, returned as a string. The desired result is "OPTIMAL", which indicates that an optimal solution to the model was found. Other status are possible, for example if the model has no feasible solution or if you set a Gurobi parameter that leads to early solver termination. Status codes are documented in the Gurobi Reference Manual. result$objval The value of the objective function for the computed solution. Not populated if optimization terminated without finding a feasible solution. result$x Variable values for the best solution found. One entry per column of A. Not present if optimization terminated without finding a feasible solution. result$slack Constraint slacks. One entry per row of A. result$pi Dual multipliers for the constraints. One entry per row of A. Only returned for continuous models. result$rc Variable reduced costs. One entry per column of A. Only returned for continuous models. result$vbasis Variable basis status values for the computed optimal basis. You generally should not concern yourself with the contents of this array. If you wish to use an advanced start later, you would simply copy the vbasis and cbasis arrays into the corresponding components for the next model. This array contains one entry for each column of A. result$cbasis Constraint basis status values for the computed optimal basis. This array contains one entry for each row of A.

#
# minimize:   x +   y + 2 z
# subject to: x + 2 y + 3 z <= 4
#             x +   y       >= 1
#             x, y, z binary
model <- list()
model$A <- matrix(c(1, 2, 3, 1, 1, 0), nrow = 2, ncol=3, byrow=T)
model$obj <- c(1, 1, 2)
model$sense <- c("<=", ">=")
model$rhs <- c(4, 1)
model$vtype <- "B"
params <- list(Presolve=2, TimeLimit=100.0)
result <- gurobi(model, params)
print(result$objval)
print(result$x)