A survey: Ant Colony Optimization based recent research and implementation on several engineering domain

Abstract

Ant Colony Optimization (ACO) is a Swarm Intelligence technique which inspired from the foraging behaviour of real ant colonies. The ants deposit pheromone on the ground in order to mark the route for identification of their routes from the nest to food that should be followed by other members of the colony. This ACO exploits an optimization mechanism for solving discrete optimization problems in various engineering domain. From the early nineties, when the first Ant Colony Optimization algorithm was proposed, ACO attracted the attention of increasing numbers of researchers and many successful applications are now available. Moreover, a substantial corpus of theoretical results is becoming available that provides useful guidelines to researchers and practitioners in further applications of ACO. This paper review varies recent research and implementation of ACO, and proposed a modified ACO model which is applied for network routing problem and compared with existing traditional routing algorithms.

Introduction

Swarm Intelligence (SI) is a growing discipline of field of study which contains relatively optimal approach than the traditional approach for problem solving of almost all engineering domain. SI is developed from the imitations which are learned from the social behaviours of insects and animals, for example: ACO, Artificial Honey Bee (ABC), Fire Flies (FF), and Honey Bot. In which the ACO, is the field of “Ant Algorithm” studies models which is learned from the behavioural observation of real ant colonies. The ACO models used for the design of novel algorithms for the solution of optimization and distributed control problems. Foraging behaviour, division of labour, brood sorting, and co-operative transport are the several different aspects of the behaviour of ant colonies have inspired from the real ants’ and based on these inspiration different kinds of Ant Algorithms are proposed in the recent years. In which, the ACO is inspired by the foraging behaviour of ant colonies, and targets the discrete optimization problems.

The French Entomologist named Pierre-Paul Grasse observed that some species of termites react, which termed as “significant stimuli”. The term stigmergy is used to describes the particular type of communication in which the “workers are stimulated by the performance they have achieved”. Now the term, stigmergy is used for indirect, non-symbolic form of communication mediated by the environment. This stigmergy is achieved in the ACO using a chemical substance called pheromone, this chemical substance is deposited on the ground when ants walking to and from a food source. Other ants perceive the presence of this pheromone and tend to follow the routes where pheromone concentration is higher. Through this mechanism, ants are able to identify and transport food to their nest in a remarkably effective and easy way.

Pasteels, Deneubourg, and Goss (1987) thoroughly investigated the pheromone laying behaviour of the real ants in the experiment called as “double bridge experiment’’. In this double bridge model, the nest was connected to a food source by two bridges of equal lengths. The author used the term argentine ants for the ants which identifies the route, simply says these ants are the predictor or scout of their colony. In such a setting, ants start to explore the surroundings of the nest and eventually reach the food source. Along their route between food source and nest, argentine ants deposit pheromone. Initially, each ant randomly chooses one of the two bridges. In the later stages due to random fluctuations, one of the two bridges presents a higher concentration of pheromone than the other bridge and therefore attracts more ants. This behaviour increases a further amount of pheromone on that bridge which makes more attractive. Therefore, after some time the whole colony converges toward for use the higher concentrated bridge for their transport.

Goss, Aron, Deneubourg, and Pasteels (1989) considered a variant of the above double bridge experiment in which one bridge is significantly longer than the other; refer the double bridge in the Fig. 1. In this case, the ants choosing by chance the short bridge are the first to reach the nest. Therefore, the short bridge receives more density of pheromones earlier than the long bridge and this fact will increases the probability of shorter bridge for choosing by the further ants to select it. Deneubourg, Aron, Goss, and Pasteels (1990) developed a probability model of the observed behaviour of real ant. In which, assuming that at a given moment of time, m₁ ants have used the first bridge and m₁ ants have used the second one, the probability ‘p₁’ for an ant to choose the first bridge is:

$$p_1=\frac{(m_1+k{)}^h}{(m_1+k{)}^h+(m_2+k{)}^h}\text{,}$$

where parameters k and h are constant and which is to be fitted to the experimental data. By changing these k and h the impact of shorter path and the impact of less congestion path can achieved. In the double bridge experiment, the probability of the other bridge is p₂, which is p₂ = 1 − p₁.

The real ant and artificial ants are differed in few assumptions, in the real ant behaviour the pheromone intensity is reduced over time as the pheromone is the chemical substance and so it evaporates over time. However, in the ACO, this can be set to a constant rate, this pheromone evaporation reduces the influence of the pheromones deposited in the early stages of the search, and this property is very useful for adaptive route search in such a situation that frequent path failures.

Ant System, Ant Colony System and Ant Net proposed by (Dorigo and Gambardella, 1997, Dorigo et al., 1996, Dorigo and Stutzle, 2004) are the significant implementation of ACO. Dorigo et al. (1996) applied the simple probability rule and Dorigo and Gambardella (1997) applied the state transition rule for the decision model. According to Dorigo et al. (1996), Neto and Filho (2011), the following characteristics of Ant Model is described,

• The Ants exists in an environment represented mathematically as a graph, the ant always occupies a node in a graph which represents a search space. This node is called nf.

• It has an initial state.

• Although it cannot sense the whole graph, it can collect two kinds of information about the neighbourhood, (1) the weight of each trail linked to nf; and (2) the characteristics of each pheromone deposited on this trail by other ants of the same colony.

• Moves toward a trail C_ij that connects nodes ‘i’ and ‘j’ of the graph.

• Also, it can alter the pheromones of the trail C_ij, in an operation called as “deposit of pheromone levels”.

• It can sense the pheromone levels of all C_ij trails that connects a node i.

• It can determine a set of “prohibited” trails.

• It presents a pseudo-random behavior enabling the choice among the various possible trails.

• This choice can be (and usually is) influenced by the level of pheromone.

• It can move from node i to node j.

Dorigo and Stutzle (2004) redefined the pheromone update policy of ACO, and the term argentine ant is replaced with forward ant. Furthermore, there are some ACO approaches that adopt the privileged pheromone lying in which ants only deposit pheromones during their return trips. Simple ACO (SACO) uses two working ant model called forward ant and backward ant, the probabilistic forward ant generated in the nest and flooded towards food source. The forward ant do not deposit pheromone while moving, this helps in avoiding the formation of loops. Once the forward ant reaches its destination, it switched to the backward ant and copies the route information from the forward ant. Then the backward ant moves to the nest using the information copied from the forward node. Further in this paper, the research and application of ACO is explained, the organization of this paper is presented in the Fig. 2. This paper is the extended version of our previous reviews (Chandra Mohan & Baskaran, 2011e) with some more recent advancement in the survey of ACO and the proposed ACO based routing for the wide spread coverage and for helping the researchers community.