A novel swarm intelligence optimization technique is proposed called dragonfly algorithm (DA). The main inspiration of the DA algorithm originates from the static and dynamic swarming behaviours of dragonflies in nature. Two essential phases of optimization, exploration and exploitation, are designed by modelling the social interaction of dragonflies in navigating, searching for foods, and avoiding enemies when swarming dynamically or statistically. The paper also considers the proposal of binary and multi-objective versions of DA called binary DA (BDA) and multi-objective DA (MODA), respectively. The proposed algorithms are benchmarked by several mathematical test functions and one real case study qualitatively and quantitatively. The results of DA and BDA prove that the proposed algorithms are able to improve the initial random population for a given problem, converge towards the global optimum, and provide very competitive results compared to other well-known algorithms in the literature. The results of MODA also show that this algorithm tends to find very accurate approximations of Pareto optimal solutions with high uniform distribution for multi-objective problems. The set of designs obtained for the submarine propeller design problem demonstrate the merits of MODA in solving challenging real problems with unknown true Pareto optimal front as well. Note that the source codes of the DA, BDA, and MODA algorithms are publicly available at http://www.alimirjalili.com/DA.html.
Nature is full of social behaviours for performing different tasks. Although the ultimate goal of all individuals and collective behaviours is survival, creatures cooperate and interact in groups, herds, schools, colonies, and flocks for several reasons: hunting, defending, navigating, and foraging. For instance, Wolf packs own one of the most well-organized social interactions for hunting. Wolves tend to follow a social leadership to hunt preys in different steps: chasing preys, circling preys, harassing preys, and attacking preys [1, 2]. An example of collective defence is schools of fishes in oceans. Thousands of fishes create a school and avoid predators by warning each other, making the predation very difficult for predators . The majority of predators have evolved to divide such schools to sub-schools by attacking them and eventually hunting the separated individuals.
Navigation is another reason for some of the creature to swarm. Birds are the best examples of such behaviours, in which they migrate between continents in flocks conveniently. It has been proven that the v-shaped configuration of flight highly saves the energy and equally distribute drag among the individuals in the flock . Last but not least,foraging is another main reason of social interactions of many species in nature. Ants and bees are the best examples of collective behaviours with the purpose of foraging. It has been proven that ants and bees are able to find and mark the shortest path from the nest/hive to the source of food . They intelligently search for foods and mark the path utilizing pheromone to inform and guide others.
It is very interesting that creatures find the optimal situations and perform tasks efficiently in groups. It is obvious that they have been evolved over centuries to figure out such optimal and efficient behaviours. Therefore, it is quite reasonable that we inspire from them to solve our problems. This is then main purpose of a field of study called swarm intelligence (SI), which was first proposed by Beni and Wang in 1989 . SI refers to the artificial implementation/ simulation of the collective and social intelligence of a group of living creatures in nature . Researchers in this field try to figure out the local rules for interactions between the individuals that yield to the social intelligence. Since there is no centralized control unit to guide the individuals, finding the simple rules between some of them can simulate the social behaviour of the whole population.
The ant colony optimization (ACO) algorithm is one of the first SI techniques mimicking the social intelligence of ants when foraging in an ant colony [8, 9]. This algorithm has been inspired from the simple fact that each ant marks its own path towards to food sources outside of the nest by pheromone. Once an ant finds a food source, it goes back to the nest and marks the path by pheromone to show the path to others. When other ants realize such pheromone marks, they also try to follow the path and leave their own pheromones. The key point here is that they might be different paths to the food source. Since a longer path takes longer time to travel for ants, however, the pheromone vaporizes with higher rate before it is re-marked by other ants. Therefore, the shortest path is achieved by simply following the path with stronger level of pheromone and abandoning the paths with weaker pheromone levels. Doringo first inspired from these simple rules and proposed the well-known ACO algorithm .
The particle swarm optimization (PSO) algorithm is also another well-regarded SI paradigm. This algorithm mimics the foraging and navigation behaviour of bird flocks and has been proposed by Eberhart and Kennedy . The main inspiration originates from the simple rules of interactions between birds: birds tend to maintain their fly direction towards their current directions, the best location of food source obtained so far, and the best location of the food that the swarm found so far . The PSO algorithm simply mimics these three rules and guides the particles towards the best optimal solutions by each of the individuals and the swarm simultaneously.
The artificial bee colony (ABC) is another recent and popular SI-based algorithm. This algorithm again simulates the social behaviour of honey bees when foraging nectar and has been proposed by Karaboga . The difference of this algorithm compared to ACO and PSO is the division of the honey bees to scout, onlooker, and employed bees . The employed bees are responsible for finding food sources and informing others by a special dance. In addition, onlookers watch the dances, select one of them, and follow the path towards the selected food sources. Scouters discover abandoned food sources and substitute them by new sources.
Since the proposal of these algorithms, a significant number of researchers attempted to improve or apply them in to different problems in diverse fields [15–20]. The successful application of these algorithms in science and industry evidences the merits of SI-based techniques in practice. The reasons are due to the advantages of SI-based algorithms. Firstly, SI-based techniques save information about the search space over the course of iteration, whereas such information is discarded by evolutionary algorithms (EA) generation by generation. Secondly, there are fewer controlling parameters in SI-based algorithm. Thirdly, SIbased algorithm is equipped with less operators compared to EA algorithms. Finally, SI-based techniques benefit from flexibility, which make them readily applicable to problems in different fields.