DSPopt.jl

DSPopt.jl is an interface to a parallel decomposition mixed-integer programming solver DSP. This package allows users to define block structures in optimization model written in StructJuMP and solve the block-structured problem using the parallle solver DSP.

This package can model and solve (by interfacing DSP) the following optimization problems:

• Two-stage stochastic (mixed-integer) quadratic constrained programming (TSSP)
• The Wasserstein-based distributionally robust variant of TSSP
• Block-structured (mixed-integer) linear programming

Intallation

NOTE: You need to install solver DSP first. This package provides an interface only.

] add DSPopt

Examples

This is one simple example of stochastic form. Please find more examples in ./examples particularly for block form.

using MPI
using StructJuMP
using DSPopt

# Comment out this line if you want to run in serial
MPI.Init()

# Initialize DSPopt.jl with the communicator.
DSPopt.parallelize(MPI.COMM_WORLD)

xi = [[7,7] [11,11] [13,13]]

# create StructuredModel with number of scenarios
m = StructuredModel(num_scenarios = 3)

@variable(m, 0 <= x[i=1:2] <= 5, Int)
@objective(m, Min, -1.5 * x[1] - 4 * x[2])
for s = 1:3
    # create a StructuredModel linked to m with id s and probability 1/3
    blk = StructuredModel(parent = m, id = s, prob = 1/3)
    @variable(blk, y[j=1:4], Bin)
    @objective(blk, Min, -16 * y[1] + 19 * y[2] + 23 * y[3] + 28 * y[4])
    @constraint(blk, 2 * y[1] + 3 * y[2] + 4 * y[3] + 5 * y[4] <= xi[1,s] - x[1])
    @constraint(blk, 6 * y[1] + y[2] + 3 * y[3] + 2 * y[4] <= xi[2,s] - x[2])

    # Quadratic constraints supported from DSP version 2.0.0 or higher
    @constraint(blk, const_quad, w[1]^2 <= 1600)
    if s == 1
        @constraint(blk, const_quad2, 2 * w[1]^2 + 2 * w[2]^2 <= 400)
    elseif s == 2
        @constraint(blk, const_quad2, 5 * w[1] - w[2]^2 -2 * w[3]^2 >= -100)
    end
end

# The Wasserstein ambiguity set of order-2 can be imposed with the size limit of 1.0.
DSPopt.set(WassersteinSet, 2, 1.0)

status = optimize!(m, 
    is_stochastic = true, # Needs to indicate that the model is a stochastic program.
    solve_type = DSPopt.DW, # see instances(DSPopt.Methods) for other methods
)

# Comment out this line if you want to run in serial
MPI.Finalize()

Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, under contract number DE-AC02-06CH11357.