OPL (pronounced Opal) is a Linear Programming syntax based off of OPL Studio.
The entire purpose of this gem is to allow you to write your linear programs or optimization problems in a simple, human-understandable way. So instead of 30 lines of code to set up a problem (as in the rglpk documentation), you can set up your problem like so:
maximize(
"x + y",
subject_to([
"x <= 10",
"y <= 3"
]))
I try to keep the tests up to date, so take a look in there for more examples. Run tests with
rspec tests.rb
A quick view at functionality:
Summation and Forall constraints:
maximize(
"sum(i in (0..3) x[i])",
subject_to([
"forall(i in (0..3), x[i] <= 3)"
]))
Easy specification of variable types:
lp = maximize(
"10x1 + 6x2 + 4x3",
subject_to([
"x1 + x2 + x3 <= 100",
"10x1 + 4x2 + 5x3 <= 600",
"2x1 + 2x2 + 6x3 <= 300",
"x1 >= 0",
"x2 >= 0",
"x3 >= 0"
],[
"BOOLEAN: x1",
"INTEGER: x3"
]
))
Access to epsilon for strict inequalities:
lp = maximize(
"x + y + z",
subject_to([
"x + z < 2",
"y <= 4",
],[
"INTEGER: y",
"EPSILON: 0.03"
]
))
BE WARNED - When you specify a variable as INTEGER or BOOLEAN, you will be using the Branch & Cut method to solve the problem. This is very inefficient, and some seemingly easy problems can take forever to solve. You may have to formulate your problem in a clever way. Here is an example.
This problem would take B&C hours to solve:
lp = maximize(
"x + y + x[3]",
subject_to([
"x + x[3] <= 2.5",
"y <= 4"
],[
"INTEGER: x, y",
]
))
But if we just use some common sense, we can make this model:
lp = maximize(
"x + y + x[3]",
subject_to([
"x <= 2.5",
"x[3] <= 2.5",
"x + x[3] <= 2.5",
"y <= 4"
],[
"INTEGER: x, y",
]
))
Which is solvable in a few milliseconds and clearly does not affect the result.
Use ruby data matrices:
d = [[3,5,3],[1,2,3],[2,5,9]]
lp = maximize(
"sum(i in [1,2], j in (0..1), d[i][j+1]*x[i-1][j])",
subject_to([
"forall(i in (1..2), x[i-1][1] <= 100)",
"forall(i in (0..2), j in (0..2), x[i][j] <= 200)"
],[
"NONNEGATIVE: x",
"DATA: {d => #{d}}"
]
))
Sudoku wrapper:
problem = [
[0,0,0,2,6,0,7,0,1],
[6,8,0,0,7,0,0,9,0],
[1,9,0,0,0,4,5,0,0],
[8,2,0,1,0,0,0,4,0],
[0,0,4,6,0,2,9,0,0],
[0,5,0,0,0,3,0,2,8],
[0,0,9,3,0,0,0,7,4],
[0,4,0,0,5,0,0,3,6],
[7,0,3,0,1,8,0,0,0]
]
sudoku = OPL::Sudoku.new problem
sudoku.solve
sudoku.format_solution
sudoku.print_solution