# Swarm intelligence/Algorithms

## List of Algorithms

### Altruism algorithm

Researchers in Switzerland have developed an algorithm based on Hamilton's rule of kin selection. This algorithm shows how altruism in a swarm of entities can, over time, evolve and result in more effective swarm behaviour.[2][3]

### Ant colony optimization

Ant colony optimization (ACO), introduced by Dorigo in his doctoral dissertation, is a class of optimization algorithms modeled on the actions of an ant colony. ACO is a probabilistic technique useful in problems that deal with finding better paths through graphs. Artificial 'ants'—simulation agents—locate optimal solutions by moving through a parameter space representing all possible solutions. Natural ants lay down pheromones directing each other to resources while exploring their environment. The simulated 'ants' similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions.[4]

### Artificial bee colony algorithm

Artificial bee colony algorithm (ABC) is a meta-heuristic algorithm introduced by Karaboga in 2005,[5] and simulates the foraging behaviour of honey bees. The ABC algorithm has three phases: employed bee, onlooker bee and scout bee. In the employed bee and the onlooker bee phases, bees exploit the sources by local searches in the neighbourhood of the solutions selected based on deterministic selection in the employed bee phase and the probabilistic selection in the onlooker bee phase. In the scout bee phase which is an analogy of abandoning exhausted food sources in the foraging process, solutions that are not beneficial anymore for search progress are abandoned, and new solutions are inserted instead of them to explore new regions in the search space. The algorithm has a well-balanced exploration and exploitation ability.

### Artificial immune systems

Artificial immune systems (AIS) concerns the usage of abstract structure and function of the immune system to computational systems, and investigating the application of these systems towards solving computational problems from mathematics, engineering, and information technology. AIS is a sub-field of Biologically inspired computing, and natural computation, with interests in Machine Learning and belonging to the broader field of Artificial Intelligence.

### Bat algorithm

Bat algorithm (BA) is a swarm-intelligence-based algorithm, inspired by the echolocation behavior of microbats. BA uses a frequency-tuning and automatic balance of exploration and exploitation by controlling loudness and pulse emission rates.[6]

### Gravitational search algorithm

Gravitational search algorithm (GSA) based on the law of gravity and the notion of mass interactions. The GSA algorithm uses the theory of Newtonian physics and its searcher agents are the collection of masses. In GSA, there is an isolated system of masses. Using the gravitational force, every mass in the system can see the situation of other masses. The gravitational force is therefore a way of transferring information between different masses (Rashedi, Nezamabadi-pour and Saryazdi 2009).[7] In GSA, agents are considered as objects and their performance is measured by their masses. All these objects attract each other by a gravity force, and this force causes a movement of all objects globally towards the objects with heavier masses. The heavy masses correspond to good solutions of the problem. The position of the agent corresponds to a solution of the problem, and its mass is determined using a fitness function. By lapse of time, masses are attracted by the heaviest mass. We hope that this mass would present an optimum solution in the search space. The GSA could be considered as an isolated system of masses. It is like a small artificial world of masses obeying the Newtonian laws of gravitation and motion (Rashedi, Nezamabadi-pour and Saryazdi 2009). A multi-objective variant of GSA, called Non-dominated Sorting Gravitational Search Algorithm (NSGSA), was proposed by Nobahari and Nikusokhan in 2011.[8]

### Glowworm swarm optimization

Glowworm swarm optimization (GSO), introduced by Krishnanand and Ghose in 2005 for simultaneous computation of multiple optima of multimodal functions.[9][10][11][12] The algorithm shares a few features with some better known algorithms, such as ant colony optimization and particle swarm optimization, but with several significant differences. The agents in GSO are thought of as glowworms that carry a luminescence quantity called luciferin along with them. The glowworms encode the fitness of their current locations, evaluated using the objective function, into a luciferin value that they broadcast to their neighbors. The glowworm identifies its neighbors and computes its movements by exploiting an adaptive neighborhood, which is bounded above by its sensor range. Each glowworm selects, using a probabilistic mechanism, a neighbor that has a luciferin value higher than its own and moves toward it. These movements—based only on local information and selective neighbor interactions—enable the swarm of glowworms to partition into disjoint subgroups that converge on multiple optima of a given multimodal function.

### Intelligent water drops

Intelligent water drops algorithm or the IWD algorithm is a nature-inspired swarm-based optimization algorithm which was first introduced in 2007. The algorithm attempts to mimic the behavior of natural water drops in rivers. Here, the soil is the quantity that is carried by each artificial water drop in the algorithm. Several versions of the algorithm have been suggested for different applications.[13]

### Particle swarm optimization

Particle swarm optimization (PSO) is a global optimization algorithm for dealing with problems in which a best solution can be represented as a point or surface in an n-dimensional space. Hypotheses are plotted in this space and seeded with an initial velocity, as well as a communication channel between the particles.[14][15] Particles then move through the solution space, and are evaluated according to some fitness criterion after each timestep. Over time, particles are accelerated towards those particles within their communication grouping which have better fitness values. The main advantage of such an approach over other global minimization strategies such as simulated annealing is that the large number of members that make up the particle swarm make the technique impressively resilient to the problem of local minima.

### River Formation Dynamics

River Formation Dynamics (RFD) is based on imitating how water forms rivers by eroding the ground and depositing sediments. After drops transform the landscape by increasing/decreasing the altitude of places, solutions are given in the form of paths of decreasing altitudes. Decreasing gradients are constructed, and these gradients are followed by subsequent drops to compose new gradients and reinforce the best ones. This heuristic optimization method was first presented in 2007 by Rabanal et al.[16] The applicability of RFD to other NP-complete problems was studied in.[17][18][19]

### Self-propelled particles

Self-propelled particles (SPP), also referred to as the Vicsek model, was introduced in 1995 by Vicsek et al.[20] as a special case of the boids model introduced in 1986 by Reynolds.[21] A swarm is modelled in SPP by a collection of particles that move with a constant speed but respond to a random perturbation by adopting at each time increment the average direction of motion of the other particles in their local neighbourhood.[22] SPP models predict that swarming animals share certain properties at the group level, regardless of the type of animals in the swarm.[23] Swarming systems give rise to emergent behaviours which occur at many different scales, some of which are turning out to be both universal and robust. It has become a challenge in theoretical physics to find minimal statistical models that capture these behaviours.[24][25][26]

### Stochastic diffusion search

Stochastic diffusion search (SDS)[27][28] is an agent-based probabilistic global search and optimization technique best suited to problems where the objective function can be decomposed into multiple independent partial-functions. Each agent maintains a hypothesis which is iteratively tested by evaluating a randomly selected partial objective function parameterised by the agent's current hypothesis. In the standard version of SDS such partial function evaluations are binary, resulting in each agent becoming active or inactive. Information on hypotheses is diffused across the population via inter-agent communication. Unlike the stigmergic communication used in ACO, in SDS agents communicate hypotheses via a one-to-one communication strategy analogous to the tandem running procedure observed in Leptothorax acervorum.[29] A positive feedback mechanism ensures that, over time, a population of agents stabilise around the global-best solution. SDS is both an efficient and robust global search and optimisation algorithm, which has been extensively mathematically described.[30][31][32] Recent work has involved merging the global search properties of SDS with other swarm intelligence algorithms.[33][34]

### Multi-swarm optimization

Multi-swarm optimization is a variant of particle swarm optimization (PSO) based on the use of multiple sub-swarms instead of one (standard) swarm. The general approach in multi-swarm optimization is that each sub-swarm focuses on a specific region while a specific diversification method decides where and when to launch the sub-swarms. The multi-swarm framework is especially fitted for the optimization on multi-modal problems, where multiple (local) optima exist.

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