**1. Introduction**

Optimization challenges arise in a wide range of fields and sectors of human activity, where we must discover optimal or near-optimal solutions to specific problems while staying within certain constraints. Optimization issues are essential in both scientific and industrial fields. Timetable scheduling, traveling salesman problems, nurse time supply planning, railway programming, space planning, vehicle routing problems, Group-shop organizing problems, portfolio improvement, and so on are a number of real-world illustrations of optimization opportunities. For this reason, many optimization algorithms are created [1].

Optimization focuses on establishing efficient and reliable computational infrastructures that will be used, among other things, to improve the performance of meta-heuristic techniques dramatically. As a result, numerous heuristic algorithms for identifying speedier near-optimal solutions have been created. Moreover, heuristic algorithms can solve with acceptable quality in a short amount of time [2].

Scientists have devoted a great deal of work to understand the complex social habits of ants, and computer scientists are now learning that these patterns can be exploited to tackle complex combinatorial improvement challenges. Ant colony optimization (ACO), the most successful and generally recognized algorithmic technique based on ant behavior, results from an effort to design algorithms motivated by one element of ant behavior, the capability to locate what computer scientists would term shortest pathways. ACO is a population-based metaheuristic for resolving complex optimization challenges. This method is a probabilistic optimization procedure used to solve computational issues and discover the best path using graphs. Artificial ants in ACO seek software agents for possible answers to a particular improvement issue. The optimization challenge is the challenge of discovering the optimum path on a weighted diagram to use the ACO. The artificial ants (hence referred to as ants) then incrementally create solutions by traveling along the graph. Using the pheromone model, a set of parameters associated with graph components (nodes or edges) whose values are updated at runtime by the ants, the solution construction process is skewed in one direction [3].

ACO is a well-known bio-inspired combinatorial optimization approach. Marco Dorigo proposed ACO in his Ph.D. thesis in the early 1990s to solve the optimal path issue in a graph [4]. It was first used to resolve the well-known dilemma of the traveling salesman, and it has since become widely used. After that, it's used to solve various complex optimization problems of several types. A great deal of time has been spent studying the complex social habits of ants, and computer scientists are now discovering that similar patterns can be exploited to solve complex combinatorial optimization problems, which represents a significant advance in the field. Each cycle begins with a departure from the nest, searching for a food source, and

ends with a return to the nest. Each ant leaves a chemical known as pheromone on the path they walk during the journey. The pheromone concentration on each path is determined by the path's length and the quality of the accessible food supply. Because the concentration of pheromones present on a path affects ant selection, the higher the pheromone concentration, the more likely it is that ants will select the path. Using pheromone concentration and some heuristic value, such as the objective function value, each ant chooses a path in a probabilistic manner based on their environment [5].

Consider the following illustration. Let us consider the following scenario: there are two options for obtaining food from the colony. At first, there is no pheromone to be found on the ground. Consequently, the probability of choosing either of these two paths is equal, or 50 percent. For example, consider two ants who decide two alternative routes to obtain food, each with a fifty-fifty chance of success (see **Figure 1(a)**).

A significant amount of distance separates these two routes. Therefore, the ant who takes the shortest path to the food will be the first to reach it (see **Figure 1(b)**).

It returns to the colony after locating food and carrying some food with it. It leaves pheromone on the ground as it follows the returning path. The ant that takes the shortest route will arrive at the colony first (see **Figure 1(c)**).

As soon as the third ant decides to go out in search of food, it will choose the path that will take it the shortest distance, determined by the level of pheromones on the ground. A shorter road contains more pheromones than a longer path (see **Figure 1(d)**). The third ant will choose the shorter path because it is more convenient.

Upon returning to the colony, it was discovered that more ants had already traveled the path with higher pheromone levels than the ant who had taken the longer route. Therefore, when another ant tries to reach the colony's goal (food), it will discover that each trail has the same level of pheromones as the previous one. As a result, it selects one at random from the list. **Figure 1(e)** depicts an example of the option described above.

After several repetitions of this process, the shorter path has a higher pheromone level than the others and is more likely to be followed by the animal. As a result, all ants will take the shorter route the next time (see **Figure 1(f )**).

**Figure 1.** *Ant Colony optimization – A simple schematic view (a to f) [6].*

An ACO is based on the technique known as Swarm Intelligence, which is a component of Artificial Intelligence (AI) methodologies for solving technical problems in the industrial sector [7].
