On the Complexities of the Design of Water Distribution Networks

Pseudocode 1

(1) Set up parameters and initialize the number of iterations to zero.

(2) Generate a random population of 𝑀 particles: {𝑋_𝑖(𝑘)}^𝑀_𝑖=1

(3) Evaluate the fitness of the particles and set the local best location for each

 particle equal to its current location.

(4) Form the Pareto front and make a list of particles belonging to the front.

(5) Build the singular point.

(6) Find the closest particle to the singular point and establish it as swarm leader.

(7) While not in termination-condition, do the following:

 (a) Execute from i = 1 to number of particles.

   Start

    (i) Change the position of the particle:

       Determine the inertia parameter 𝜔(𝑘), according to (3.8).

     Calculate the new velocity, 𝑉_𝑖(𝑘+1), for particle 𝑖 according to (3.4) or (3.5).

     Set a new position, 𝑋_𝑖(𝑘+1), for particle 𝑖 according to (3.7).

    (ii) Calculate the new fitness function vector for particle 𝑖 in its new position.

    (iii) If the new fitness function vector for particle 𝑖 dominates the fitness

     function vector that the particle had before moving to the new position;

     then set the new position as the best position currently found by particle i.

    (iv) If particle 𝑖 is in the list of particles belonging to the Pareto front then:

       if the new fitness function vector may also be a point on the

       Pareto front and this new position has at least one of its

       neighbors located further than the minimal permissible distance

       from any of the objectives, then add a new particle j (a clone of i)

       with 𝑃_𝑘 and 𝑃_𝑘best located at the current position of i;

    else

       try to add (if possible) the particle i (at its new position) to the

       Pareto front; if the particle is added, remove from the list any

       dominated solution; dominated clones are eliminated from the swarm.

    (v) If particle 𝑖 is closer to the singular point than any other particle in the

     swarm, then set particle 𝑖 as the leader of the swarm with regard to the

     singular point.

    (vi) If particle 𝑖 is not currently the leader of the swarm, but coincides in

      position with the leader, then re-generate particle 𝑖 randomly.

   End

  (b) Increase the iteration number.

(8) Show the Pareto front and related results.