A New Ant Colony Optimization Algorithm to Solve the Periodic Capacitated Arc Routing Problem with Continuous Moves

Algorithm 1

The complete ACO algorithm for the PCARP-CM.

Algorithm: ACO for the PCARP-CM

1:  procedure ACO(cars, arcs, cities)

2:  Select an initial point

  Iteration

  Spread pheromones for the first iteration

3:  Do until reaching the Stopping Criteria

4:     For each ant // ()

5:       For each car // ()

6:         If car 1 then evaluate the initial point end if

7:         Load possible ending points in the last day for car

8:         Generate the graph for the problem

9:         For each day // ()

10:           Computes the visibility for each possible move

11:           Draw the next city to be visited considering

            the probabilities from the equation (12)

12:           Update the sparse graphs

13:         Next day

14:       Nest car

15:       Apply the Local Search Procedure

16:       Save the solution if it is the best one

17:       Computes the quantity of pheromones to be spread by the ant in each

        arc, car and day using the equation (13)

18:     Next ant

19:     Update the pheromones using the variation and for in the

      equation (14)

20:  Loop

21:  Return the best solution found