Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pick-Up Service Based on MCPSO

Algorithm 1

Pseudocode for MCPSO algorithm.

Algorithm MCPSO

Begin

 Initialize the population // master swarm and slave swarm

 Evaluate the fitness value of each particle in the population

 Repeat

  Do in parallel

   Swarm 𝑖, 1≤𝑖≤𝑁_𝑠

  End Do in parallel

  Barrier synchronization // wait for all processes to finish

   Select the fittest global individual (𝑝^𝑆_𝑔 or 𝑝^𝑀_𝑔) from all the swarms

  Do in parallel

   Swarm 𝑗, 1≤𝑗≤𝑁_𝑚

  End Do in parallel

  Barrier synchronization

   Evolve the mast swarm // update the velocity and position using Eqs. (3.1)

   Evaluate the fitness value of each particle

 Until a terminate-condition is met

End