Algorithm 1 ACOE

Input: a CSP (X, D, C), maximum number of iterations Nmax, number of ants Nant

Output: bestA

1: Initialization

2: repeat

3:   for k = 1 to Nant do

4:     Construct a complete assignment Ak

5:     if cost(Ak) < cost(bestA) then

6:        bestA ← Ak

7:     end if

8:     if the condition is satisfied then

9:        bestA ← CLS(bestA)

10:    end if

11:  end for

12:  Update pheromone on each vertex

13: until cost(bestA) = 0 ∨ Nmax is reached

14: return bestA