R6 Class for Sparse Linear Programs

Collects the constraints of a linear program in long form and hands them to lpSolve::lp() in triplet form, which keeps memory linear in the number of non-zero coefficients. Constraints are tagged with the block they belong to, so a program can be assembled once and solved over a subset of its blocks.

Details

Two tables describe a program.

variables has one row per decision variable: an id_var giving its column in the program, a block naming the group it belongs to, and whatever further key columns the caller needs to identify it. Nothing about the meaning of a variable is known here; the subclass supplies it.

constraints has one row per non-zero coefficient: block, id_row, id_var, coefficient, plus the dir and rhs of the row it belongs to, which are constant within an id_row. Coefficients are summed over duplicated (id_row, id_var) pairs and exact zeroes are dropped, since lpSolve::lp() matches constraint rows to dir/rhs by the order of the row indices it is given, and cannot represent an empty row.

All variables are non-negative: lpSolve::lp() has no notion of variable bounds, so a quantity that may take either sign has to be split into two variables.

lpSolve is a suggested dependency, since most of the package does not solve linear programs. It has to be installed before a program can be constructed.

See also

trans_rate_lp

Active bindings

variables

The decision variables, one row each.

constraints

The constraint coefficients, one row per non-zero entry.

block_summary

Rows and coefficients per constraint block.

n_var

Number of decision variables.

n_row

Number of constraint rows.

status

The lpSolve::lp() status of the last solve; 0 is success.

objective

The objective value of the last solve.

values

The solved value of every variable, joined to its keys.

Methods

Public methods

• lp_problem$new()

• lp_problem$add_constraints()

• lp_problem$solve()

• lp_problem$print()

• lp_problem$clone()

---

lp_problem$new()

Initialize a program over a fixed set of decision variables. Fails if the suggested lpSolve package is not installed, since nothing could be solved.

Usage

lp_problem$new(variables)

Arguments

variables

A data.table with id_var (1:n, in order) and block, plus any key columns identifying each variable.

Returns

A new lp_problem object

---

lp_problem$add_constraints()

Add one block of constraint rows.

Usage

lp_problem$add_constraints(block, constraints)

Arguments

block

Name of the block, used to subset the program when solving.

constraints

A data.table with id_row, id_var, coefficient, dir and rhs. id_row only has to be unique within this call; it is renumbered to stay unique across blocks. dir and rhs must be constant within an id_row.

Returns

The lp_problem object, invisibly

---

lp_problem$solve()

Solve the program and store the solution.

Usage

lp_problem$solve(objective, direction = "min", blocks = NULL)

Arguments

objective

A data.table with id_var and coefficient; variables it does not mention do not enter the objective.

direction

"min" or "max".

blocks

Constraint blocks to include; all of them when NULL.

Returns

The lp_problem object, invisibly

---

lp_problem$print()

Print a summary of the program.

Usage

lp_problem$print(...)

Arguments

...

Ignored.

---

lp_problem$clone()

The objects of this class are cloneable with this method.

Usage

lp_problem$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.