The clp package provides a Go interface to the COIN-OR Linear Programming (CLP) library, part of the COIN-OR (COmputational INfrastructure for Operations Research) suite.

Linear programming (LP) is a method for maximizing or minimizing a linear expression subject to a set of constraints expressed as inequalities. As an example that's simple enough to solve by hand, what roll of three six-sided dice has the largest total value if no two dice are allowed have the same value and the difference in value between the first and second largest dice must be smaller than the difference in value between the second and third largest dice? From an LP standpoint, the objective function we need to maximize to answer that question is a + b + c, where each variable represents the value on one die. The first constraint is that each die be six sided:

• 1 ≤ a ≤ 6
• 1 ≤ b ≤ 6
• 1 ≤ c ≤ 6

The second constraint is that the three dice all have different values. We specify this by imposing a total order, a > b > c, which we express as

• 1 ≤ a - b ≤ ∞
• 1 ≤ b - c ≤ ∞

The third constraint is that the difference in value between the first and second largest dice (a − b) is smaller than the difference in value between the second and third largest dice (b − c). To put this in a suitable format for LP, we rewrite a − b < b − c as

• -∞ ≤ a - 2b + c ≤ -1

These constraints translate directly to Go using the clp package's API:

package main

import (
        "fmt"
        "github.com/lanl/clp"
        "math"
)

func main() {
        // Set up the optimization problem.
        pinf := math.Inf(1)
        ninf := math.Inf(-1)
        simp := clp.NewSimplex()
        simp.EasyLoadDenseProblem(
                //         A    B    C
                []float64{1.0, 1.0, 1.0},
                [][2]float64{
                        // LB UB
                        {1, 6}, // 1 ≤ a ≤ 6
                        {1, 6}, // 1 ≤ b ≤ 6
                        {1, 6}, // 1 ≤ c ≤ 6
                },
                [][]float64{
                        // LB  A    B    C    UB
                        {1.0, 1.0, -1.0, 0.0, pinf},  // 1 ≤ a - b ≤ ∞
                        {1.0, 0.0, 1.0, -1.0, pinf},  // 1 ≤ b - c ≤ ∞
                        {ninf, 1.0, -2.0, 1.0, -1.0}, // -∞ ≤ a - 2b + c ≤ -1
                })
        simp.SetOptimizationDirection(clp.Maximize)

        // Solve the optimization problem.
        simp.Primal(clp.NoValuesPass, clp.NoStartFinishOptions)
        soln := simp.PrimalColumnSolution()

        // Output the solution.
        fmt.Printf("Die 1 = %.0f\n", soln[0])
        fmt.Printf("Die 2 = %.0f\n", soln[1])
        fmt.Printf("Die 3 = %.0f\n", soln[2])
}

The output is the expected

Die 1 = 6
Die 2 = 5
Die 3 = 3

clp has been tested only on Linux. The package requires a CLP installation to build. To check if CLP is installed, ensure that the following command produces a list of libraries, typically along the lines of -lClp -lCoinUtils …, and, more importantly, issues no error messages:

pkg-config --libs clp

Once CLP installation is confirmed, you're ready to install the clp package. As clp has opted into the Go module system, installation is in fact unnecessary if your program or package has done likewise. Otherwise, install the clp package with go get:

go get github.com/lanl/clp

Pre-built documentation for the clp API is available online at https://pkg.go.dev/github.com/lanl/clp.

Copyright © 2011, Triad National Security, LLC. All rights reserved.

This software was produced under U.S. Government contract 89233218CNA000001 for Los Alamos National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. Department of Energy/National Nuclear Security Administration. All rights in the program are reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear Security Administration. The Government is granted for itself and others acting on its behalf a nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare derivative works, distribute copies to the public, perform publicly and display publicly, and to permit others to do so. NEITHER THE GOVERNMENT NOR TRIAD NATIONAL SECURITY, LLC MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LIABILITY FOR THE USE OF THIS SOFTWARE. If software is modified to produce derivative works, such modified software should be clearly marked, so as not to confuse it with the version available from LANL.

clp is provided under a BSD 3-clause license. See the LICENSE file for the full text.

This package is part of the LANL Go Suite, represented internally to LANL as LA-CC-11-056.

Scott Pakin, pakin@lanl.gov