Simplex-Swift

This package contains a basic implementation of the Simplex algorithm.

Usage

1. Solving maximization problem

For example, given a function with constraints:

F = 7X₁ + 8X₂ + 10X₃

2X₁ + 3X₂ + 2X₃ ≤ 1000

X₁ + X₂ + 2X₃ ≤ 800

We need to maximize F(X₁ X₂ X₃).

let function    : [Double] = [7, 8, 10]
let constraint1 : [Double] = [2, 3, 2, 1000]
let constraint2 : [Double] = [1, 1, 2, 800]

if let solution = SimplexSolver.maximize(function: function, constraints: [constraint1, constraint2], maximumIterationsCount: 10) {
    let x1 = solution[0]  // 200
    let x2 = solution[1]  // 0
    let x3 = solution[2]  // 300
    let f  = solution[3]  // 4400
}

The maximum value of the function F(X₁ X₂ X₃) is 4400 when X₁ = 200, X₂ = 0, X₃ = 300.

2. Solving minimization problem

Another example, given a function with constraints:

F = 3X₁ + 9X₂

2X₁ + X₂ ≥ 8

X₁ + 2X₂ ≥ 8

Minimize F(X₁ X₂).

let function    : [Double] = [3, 9]
let constraint1 : [Double] = [2, 1, 8]
let constraint2 : [Double] = [1, 2, 8]

if let solution = SimplexSolver.minimize(function: function, constraints: [constraint1, constraint2], maximumIterationsCount: 10) {
    let x1 = solution[0]  // 8
    let x2 = solution[1]  // 0
    let f  = solution[2]  // 24
}

The minimum value of the function F(X₁ X₂) is 24 when X₁ = 8, X₂ = 0.