Discrete Salp Swarm Algorithm for symmetric traveling salesman problem

In the Salp Swarm Algorithm (SSA), the update mechanism is inspired by the unique chain movement of the salp swarm. Numerous versions of SSA were already put forward to deal with various optimization problems, but there are very few discrete versions among them. d-opt is improved based on the 2-opt algorithm: a decreasing factor d is introduced to control the range of neighborhood search; TPALS are modified by Problem Aware Local Search (PALS) based on the characteristics of Travelling Salesman Problem (TSP); The second leader mechanism increases the randomness of the algorithm and avoids falling into the local optimal solution to a certain extent. We also select six classical crossover operators to experiment and select Subtour Exchange Crossover (SEC) and the above three mechanisms to integrate them into the SSA algorithm framework to form Discrete Salp Swarm Algorithm (DSSA). In addition, DSSA was tested on 23 known TSP instances to verify its performance. Comparative simulation studies with other advanced algorithms are conducted and from the results, it is observed that DSSA satisfactorily solves TSP.