Ant Colony Optimization Algorithms: Fundamentals and Applications

By Fouad Sabry

What Is Ant Colony Optimization Algorithms

The Ant Colony Optimization Algorithm, also known as ACO, is a probabilistic technique for addressing computational problems in the fields of computer science and operations research. These problems can be boiled down to the task of finding good paths through graphs. The behavior of natural ants served as inspiration for the development of multi-agent systems, which are represented by artificial ants. The communication of biological ants through the use of pheromones is frequently the major paradigm that is adopted. Combinations of artificial ants and local search algorithms have become the technique of choice for several optimization tasks involving some kind of graph, such as internet routing and vehicle routing. This is because these combinations are able to find optimal solutions more quickly than traditional methods.

How You Will Benefit

(I) Insights, and validations about the following topics:

Chapter 1: Ant colony optimization algorithms

Chapter 2: Job-shop scheduling

Chapter 3: Open-shop scheduling

Chapter 4: Quadratic assignment problem

Chapter 5: Generalized assignment problem

Chapter 6: Set cover problem

Chapter 7: Partition problem

Chapter 8: Bankruptcy prediction

Chapter 9: Protein-protein interaction

Chapter 10: Protein folding

(II) Answering the public top questions about ant colony optimization algorithms.

(III) Real world examples for the usage of ant colony optimization algorithms in many fields.

Who This Book Is For

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of ant colony optimization algorithms.

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• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Jul 1, 2023

Book preview

Chapter 1: Ant colony optimization algorithms

The Ant Colony Optimization Algorithm, often known as ACO, is a probabilistic approach for addressing computational problems in the fields of computer science and operations research. These issues may be boiled down to the task of finding optimal pathways across graphs. The behavior of natural ants served as inspiration for the development of multi-agent systems, which are represented by artificial ants. The communication of biological ants via the use of pheromones is often the major paradigm that is adopted. Combinations of artificial ants and local search algorithms have emerged as the technique of choice for a wide variety of optimization problems that include some kind of graph, such as the routing of vehicles and the routing of data over the internet.

Take, for instance, the optimization of ant colonies. One strategy that is similar to this one is called the bees algorithm, and it is modeled after the behavior of another social insect called the honey bee when it comes to foraging.

This algorithm, which is used in swarm intelligence approaches and contributes to several metaheuristic optimizations, is a part of the family of algorithms known as ant colony algorithms. First first up by Marco Dorigo in 1992 in the doctoral thesis he was working on, it has some parallels with methods for the estimate of distributions.

In the wild, several kinds of ants will (at first) forage aimlessly and, after they have located a source of sustenance, will return to their colony while leaving pheromone trails behind them. If more ants discover this track, it is quite probable that they will not continue to wander aimlessly but will instead continue to follow it, and if they are successful in finding food, they will return to the road and strengthen it (see Ant communication).

When one ant discovers a good (that is, short) way from the colony to a food supply, additional ants are more likely to follow that road, and ultimately positive feedback leads to many ants following a single path. This is the overall outcome. The goal of the method known as the ant colony is to reproduce this behavior by having simulated ants move around a network that represents the issue that needs to be resolved.

New concepts are required since intelligence is no longer centralized but can be found throughout all minuscule objects.

It is well known that anthropocentric principles may lead to the construction of information technology systems in which data processing, The control units and the computing of the forces are centralized.

These centralized units' performance has been steadily improving over time, and they are comparable to the human brain in many respects.

The representation of the brain has developed into the pinnacle goal of computer science.

Ambient networks of intelligent objects and, sooner or later, a new generation of information systems that are built on nanotechnology and are even more dispersed than the previous one, will significantly alter our understanding of this idea.

Devices that are so little that they may be likened to insects do not, on their own, possess a high level of intelligence.

Indeed, Their level of intellect may be described as being on the lower end.

It is, for example, It is not feasible to incorporate a high performance calculator that has the capability to answer any sort of mathematical issue into a biochip that is implanted into the human body or integrated in an intelligent tag that is meant to track commercial items.

However, Once such things are linked to one another, they have a type of intelligence that is comparable to a colony of ants or bees.

In the event of particular difficulties, This kind of intelligence may be more effective than the reasoning of a centralized system that is analogous to the brain.

The use of pheromones as a means of communication is one of the most efficient and extensively used forms of communication that can be found in nature. Pheromones are utilized for communication between individual social insects as well as between social insects and their swarms by social insects such as bees, ants, and termites. The use of synthetic pheromones in multi-robot and swarm robotic systems has become more common as a result of their practicability. The use of pheromones as a form of communication was accomplished via a variety of methods, including chemical ones. Those implementations were not, however, capable of recreating all of the characteristics of pheromones that are seen in nature.

An experimental setup that made use of projected light was reported by Garnier, Simon, and their co-authors in an IEEE article that was published in 2007 to examine pheromone-based communication with tiny autonomous robots.

An artificial ant is a basic computational agent that seeks for good solutions to a given optimization issue. Ant colony optimization techniques use artificial ants to help solve optimization problems. In order to use an ant colony method, the optimization issue must first be transformed into the problem of finding the shortest route on a weighted network. This is necessary before the algorithm can be used. The initial stage of each iteration consists of each ant randomly constructing a solution, which may be thought of as the recommended sequence for traversing the edges of the graph. In the second phase, the multiple routes discovered by the ants are analyzed and compared to one another. The very last thing that has to be done is an adjustment to the pheromone levels on each edge.

procedure ACO_MetaHeuristic is

while not terminated do

generateSolutions()

daemonActions()

pheromoneUpdate()

repeat

end procedure

In order to go along the graph, each ant has to devise a solution.

To determine which edge it will visit next on its trip, When selecting a path, an ant will take into account the length of each edge that is accessible from its present location, as well as the amount of the pheromone that corresponds to it.

During each each phase of the algorithm, each ant moves from a state x to state y , corresponding to a more comprehensive intermediate solution.

Thus, each ant k computes a set A_{k}(x) of feasible expansions to its current state in each iteration, and, given the probabilities, shifts to one of them.

For ant k , the probability p_{xy}^{k} of moving from state x to state y depends on the combination of two values, the attractiveness \eta _{xy} of the move, as computed by some heuristic indicating the a priori desirability of that move and the trail level \tau _{xy} of the move, demonstrating how easy or difficult it has been in the past to execute that specific maneuver.

The trail level is an indicator of the attractiveness of making that maneuver after the fact, or a posteriori.

In general, the k th ant moves from state x to state y with probability

p_{xy}^{k}={\frac {(\tau _{xy}^{\alpha })(\eta _{xy}^{\beta })}{\sum _{z\in \mathrm {allowed} _{x}}(\tau _{xz}^{\alpha })(\eta _{xz}^{\beta })}}

where \tau _{xy} is the amount of pheromone deposited for transition from state x to y , 0 ≤ \alpha is a parameter to control the influence of \tau _{xy} , \eta _{xy} is the desirability of state transition xy (a priori knowledge, typically 1/d_{{xy}} , where d is the distance) and \beta ≥ 1 is a parameter to control the influence of \eta _{xy} .

\tau _{xz} and \eta _{xz} represent the trail level and attractiveness for the other possible state transitions.

When all of the ants have finished their work, the trails are often updated. This might result in an increase or decrease in the level of trails, which corresponds to movements that were either part of excellent solutions or poor solutions, respectively. One example of a rule for updating global pheromones is as follows:

{\displaystyle \tau _{xy}\leftarrow (1-\rho )\tau _{xy}+\sum _{k}^{m}\Delta \tau _{xy}^{k}}

where \tau _{xy} is the amount of pheromone deposited for a state transition xy , \rho is the pheromone evaporation coefficient, m is