New operators for integer permutation-based particle swarm optimizer

This paper introduces new operators to particle swarm paradigm (PSO) that could lead to a stunt flocking in solving a class of combinatorial optimization problem. The term "\´stunt flocking" is analogous to clustering around an optimal solution in domain of the problem considered. Instead of looking at PSO as using individuality and sociality, we adopt the viewpoint of exploration (selecting among all available options and observing outcomes) and exploiting (consistently choosing the global best option). Accordingly, we define two new operators, namely: exploration and exploiting operators for a permutation-based particle swarm algorithm. For exploiting operator we use an order-based imitation function to simulate imitation of the global best option. However, exploration operator is carried out as a result of two lower level operations: recalling the best solution in the memory of each particle and random shuffling of some elements in the permutation that represents each particle. Traveling sales person (TSP) and quadratic assignment (QA) problems are considered here for testing the algorithm. Matlab subcommands are used to illustrate how these operators can take place in programming code. Results of implementing the proposed technique to the mentioned problems agree to great extent with the known optimal solutions