Comparison of PSO, FA, and BA for Discrete Optimization Problems

Swarm intelligence (SI) is widely applied for optimizing both continuous and discrete problems. Many papers have investigated them for continuous optimizations since most swarm-based algorithms are designed based on continuous movements, which are simply calculated using vector-based mathematical operations. It is quite easy to select the best SI algorithm for a given continuous problem. However, it is quite hard to pick an optimum SI algorithm for a discrete problem since the individual movement is difficult to develop. Therefore, in this paper, three SI algorithms: particle swarm optimization (PSO), firefly algorithm (FA), and bat algorithm (BA), are compared to solve some cases of traveling salesman problem (TSP). Evaluation on four TSP cases show that FA is the most effective and efficient since it dynamically evolves some individuals' groups and balances the exploitative-explorative movements.

I. Introduction

In the last decade, meta-heuristic-based algorithms have been broadly used to solve optimization problems, especially in the engineering area [1]. The algorithms based on metaheuristic are commonly divided into two groups: evolutionary algorithm (EA) and swarm intelligence (SI). EA is designed to solve both discrete and continuous problems of optimization, such as genetic algorithm (GA) [2]–[6] and harmony search algorithm (HS) [7]. Meanwhile, most SI algorithms are commonly designed to tackle the problems of continuous functions, such as cuckoo search (CS) [8], FA [9]–[17], and krill herd algorithm (KH) [18]–[21], although some special SI algorithms are developed to handle the discrete ones, such as bee colony optimization (BCO) [22], [23].