In this research, the application of the **ant** **colony** **optimization** **algorithm** for **robot** **path** **planning** is investigated. The goal is to find the shortest and collision-free route (if exists) between a starting point and a destination point in a grid network. To simulate a dynamic environment, obstacles with different shapes and sizes are added after the optimal **path** is founded in the original (obstacle free) network. Two different pheromone re-initialization schemes (Le., the local initialization and the global initialization) are discussed and compared. Computer simulation results are presented to demonstrate the effectiveness of the ACO **algorithm**.

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robotics. Indeed, a significant amount of research has been devoted to this problem in recent years. The **ant** **colony** **optimization** **algorithm** is another approach to solve this problem. Each **ant** drops a quantity of artificial pheromone on every point that the **ant** passes through. This pheromone simply changes the probability that the next **ant** becomes attracted to a particular grid point. The techniques described in the paper adapt a global attraction term which guides ants to head toward the destination point. The paper describes the various techniques for the **robot** **path** **planning** using the **Ant** **colony** **Algorithm**. The paper also provides the brief comparison of the three techniques described in the paper.

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The initial state of particle swarm **optimization** **algorithm** is a group of particles randomly distributed in the solution interval, constantly updating the position and velocity of the particles, constantly comparing to obtain the optimal or suboptimal solution and achieve **path** **planning** [6]. Particle swarm formula is as follows:

the generation of cluster heads and the number of cluster heads in the protocol. The nodes in the network are randomly elected as cluster heads, and the energy consumption of the nodes is not considered. The cluster heads which are far away from the base station will die early because of the premature depletion of energy. In view of the above shortcomings, Ma et al. (2013) proposed LEACH-C, and LEACH- C made some improvements to LEACH. The cluster structure of the LEACH-C protocol was generated by the base station through simulated annealing **algorithm** [4]. Since the cluster heads selected by the LEACH-C protocol send information in the form of one or more hops to the base station, this will result in the problem that the cluster heads near the base station will receive and forward the data too much, which will consume more energy and shorten the lifetime. The hybrid, energy-efficient distributed clustering protocol determines the radius of each cluster. The basis for the protocol to select the cluster head set is the residual energy of nodes and followed by the density of nodes. For the main basis, the node with more remaining energy is more likely to be elected as the cluster head of this round; for the secondary basis, that is the degree of proximity between the nodes or the density of the nodes in the network. For cluster heads in the same cluster coverage area, they have the same rights to run as the final cluster heads through the average reachable parameter (AMRP). For cluster members that exist in a number of cluster coverage areas, different strategies are applied. They refer to sub parameter AMRP to add the final cluster. The LEACH protocol has another disadvantage that the protocol neither calculate nor refer to the residual energy of each sensor node when the cluster head set is elected. If the nodes with little remaining energy are selected as cluster heads, the energy consumption will be greatly increased, the energy will be exhausted too early, and the operation of the whole network will be greatly affected. In view of this defect, Sun and Jian-Zhong (2013) took the remaining energy of the node into consideration when selecting the cluster head, and solved the defect of the LEACH protocol [5].

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As discussed, the neighboring nodes are included in the priority queue. Consequently, the search **algorithm** resumes its search until it reaches a node with the lowest value in the queue less than f. The value of the shortest **path** is the value of f considering h at a zero value for the building entrance within an acceptable empirical test. Furthermore, ACO optimizes the resulting **path** to generate the ideal **path** from the gate as a starting point to the entrance as a final destination. At the early time, ants randomly search for food to return with them to their **colony**. Using pheromone, ants mark their **path** to food leading other ants to follow this **path**. The **path** that has the highest value of pheromone is the one leads to food. Thus, the value is determined by the pheromone-based on the usage of such by ants. In this proposed model, food is given the value of (0, 1). In the case of an empty parking bay, the status of the parking is zero (0) which refers to food for ants. In the case of a full parking bays, the status of the parking is one (1) which refers to no food for ants. On another perspective, ants use pheromone for the **path** they followed for food. However, this pheromone fades over time when the **path** is not used. This case suggests that ants follow another **path** of food. This process updates ants with the latest ideal **path** for food. Therefore, in this model, ants are referred to as a number and pheromone are referred to as a value that changes based on ants’ usage of paths. Finally, when ants find an empty parking bay within the parking suggested by A* **algorithm**, it begins its **path** **optimization** according to certain measures. In the beginning, the ACO will initialize its parameters which are the nodes and ants’ number, the initial **path** is generated by A* **algorithm** and the pheromone. Then ACO will set the distances of the nods and the matrices. Once all the parameters are ready, the ACO will start by the first **ant** which is K assigned as 1 and locate it on the initial node which is the gate used by the car. Then the **ant** will start from the first node and will define a random number from zero to one. The random number is defined as 0.5. If this random number is smaller than the initial **path** which is q0, that means there is a **path** and **ANT** should follow this **path** which means perform (1). Otherwise **ANT** will explore new paths then perform (2).

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In [1] authors have proposed a distributed optimal Community-aware Opportunistic Routing (CAOR) **algorithm** to show an MSN into a network that handiest includes network houses. That they had shown that in the community of community houses can nevertheless calculate the least expected transport delays of nodes through a reverse Dijkstra set of rules and achieved the surest opportunistic routing overall performance. In the meantime, the range of communities became some distance much less than the variety of nodes in significance, the computational cost and preservation fee of contact data had impressively reduced. They validated how the set of rules expressively accomplishes the earlier ones through massive simulations, based on an actual MSN trace and an artificial MSN hint. [2] In this paper authors have discussed the existing routing protocols for VANETs and categorized them into a taxonomy based totally on key attributes inclusive of community structure, applications supported, routing strategies, forwarding techniques, mobility models and pleasant of carrier metrics. Protocols belonging to unicast, multicast, geo-cast and broadcast classes are mentioned. Strengths and weaknesses of numerous protocols using topology-based totally, role based and cluster-based approaches are analyzed.[3] In this paper, authors have defined routing of facts in distinctly cell network and technique of metaheuristic referred to as **ant** **colony** **optimization** (ACO). ACO has been found to be appropriate for routing and many investigators located it right for VANET. Its feature of pheromone trail makes it extra powerful in terms of routing.In [4] authors have proposed a new hybrid area-primarily based routing protocol that is predominantly designed to address hyperlink failures. This protocol united functions of reactive routing with place-based terrestrial routing in a manner that thoroughly used all of the region facts

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-----------------------------------------------------------------------------------***--------------------------------------------------------------------------- Abstract - Flight Plan depicts shortest course between two points either in identified/ unidentified route. The project emphasizes on identifying shortest possible traversal **path** having minimal distance along with minimum effort on the propulsion between identified points of reference. The minima of cumulative effort of distance traversed and motoring power consumption metrics are the identifiable characteristics, registering Flight Plan. Modified **Ant** **Colony** **Optimization** (mACO), is the design **algorithm** which envisages the route **planning**. Local maxima-minima are mapped to global values within constrained environment for route determination. The environment (constrained/ unconstrained) classified by the mission requirements keep abreast with objectives like territorial penetration, radar netting, no-fly zones etc. The pheromone level is directly proportional to the flight distance and evaporation level is proportional to battery discharge/ power consumption metric. The former metric provides multiple options for routes of which minima of later metric is considered as identified route **path**. Cooperative Maneuvering (Leader – follower) employing rigid geometric cohesion contour **algorithm** is being implemented for swarm **optimization** in traversal between source – destination.

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We tested the ACO-RRT* **algorithm** performance with a holonomic **robot** in three simulated scenarios (see Figure 5). We chose a holonomic **robot**, since it enables us to abstract the **algorithm** capabilities from the robot’s kinodynamic constraints. We assume that the **robot** corresponds to a single point. However, more complex **robot** shapes could easily be introduced within this framework. The three sce- narios correspond to realistic scenarios that could be encountered while navigating an indoor facility. Moreover, similar scenarios have been considered to evaluate some of the most recent state-of-the art methods. 7,24 Analysis in more complex scenarios and the consideration of kinody- namic constraints is left for future research. All scenarios measure 100 m 100 m and the goal is to find the optimal **path** that goes from x A to x B . Since Scenario 3 is more structured, the placement of the initial position plays a crucial role. Therefore, in Scenario 3 we consider different possible starting positions x A , which are randomly selected in each simulation run. For the evaluation we consider a goal region centred around the goal position, not just a single state. Scenario 1 is composed of 10 rectangles of different sizes and the optimal **path** measures 88 m. Sce- nario 2 contains a narrow passage, which is often consid- ered one of the most challenging **path**-**planning** problems.

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This paper assesses the problem of designing multiple gravity assist (MGA) trajectories, including the sequence of planetary encounters. The problem is treated as **planning** and scheduling of events, such that the original mixed combinatorial-continuous problem is discretised and converted into a purely discrete problem with a finite number of states. We propose the use of a two-dimensional trajectory model in which pairs of celestial bodies are connected by transfer arcs containing one deep-space manoeuvre. A modified **Ant** **Colony** Optimisation (ACO) **algorithm** is then used to look for the optimal solutions. This approach was applied to the design of optimal transfers to Saturn and to Mercury, and a comparison against standard genetic **algorithm** based optimisers shows its effectiveness.

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In the global static environment, aiming at the shortcomings of traditional **ant** **colony** **algorithm** in obstacle avoidance and **path** **planning** in concave area, an improved Bayesian **ant** **colony** **algorithm** based on posterior probability is proposed. The **algorithm** takes grid map as environment map, and integrates the Heuristic information of target nodes and repulsive information of obstacles into conditional probability in the search process of **ant** **colony** **algorithm**. Then the posterior probability is calculated as the Bayesian **path** selection probability, which increases the obstacle avoidance ability of UAV and alleviates the shortage of easily trapping in concave area. The simulation results show that the improved **algorithm** can find the optimal **path** more effectively.

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When searching for food, initially each **ant** moves at random manner. While moving, each **ant** deposited a chemical pheromone trail on the ground. All Ants can smell pheromone. When ants choosing their way, they choose the paths marked by strong pheromone concentrations because more the pheromone trails better the **path**. As soon as ants find a food source, it evaluates the quality and the quantity of the food and carries some of it when ants back to their nest. During the return trip, the quantity of pheromone that an **ant** leaves on the ground may depend on the quality and quantity of the food. The pheromone trails must guide other ants to the food source (Agrawal, R et al 1993).

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where represent the Euclidian distance between the start and target points, is the number of breakpoints (trajectory change occurred).While the most important property of heuristic algorithms, including the ABC **algorithm** is that they are designed for the unconstrained **optimization** problems, they can also be adapted to the constrained **optimization** problems by using penalty. If a solution doesn’t satisfy the constraints, this solution is not acceptable, even if the value of the objective function is minimized [15]. The total function is called as fitness function. Namely, if constraints are in the feasible region, then the penalty function is equal to zero. Otherwise, the fitness function is penalized by a penalty function. Many researchers introduced different methods for representing a proper fitness function for finding an optimal **path**. In this work, a proposal of new expression for fitness function is introduced to enhance the smoothness of the robot's **path**. Mobile **robot** needs a portable power source; this maximizes the need for power saving by preventing the **robot** from making unnecessary turning and redundant movements. Consequently, minimizing the angles between the straight lines that connecting the breakpoints would be a second objective function (Eq. (8) and Eq. (9)) that the **algorithm** should be satisfied in addition to the first objective which is minimizing the distance (Eq.(7)).

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The above sketch shows how real ants find a shortest **path**. (A) Ants arrive at a decision point. (B) Some ants choose the upper **path** and some the other **path**. The choice is random. (C) Since ants move at approximately constant speed, the ants which choose the lower shorter **path** reach the opposite decision point faster than which chose the upper, longer **path**. (D) Pheromone accumulates at higher rate on shorter **path**.

is traced from the same and rest of power is drawn from further sources. The generation of electric power may be planned and the future power needs can be predicted by using Artificial Neural Network (ANN) [3] method. Exact scheduling reduces the cost and provides efficient operation. Economic, time, weather and random disturbance are some important categories of factors that affect the system load. The economic trends have a significant impact on the system load demand. The seasonal effect, weekly-daily cycles and holidays are influencing the load structure. Temperature and humidity are the major weather factors that affect the system load. Neural Networks are capable to handle the non-linearity between the load and the factors affecting the load [4]. It is trained and tested using Backpropagation Neural Network (BPNN) **algorithm**. This is the most powerful error reducing **algorithm**. It has the characteristics of fast approach on the local optima and at the same time, it gets stuck in local minima. Sometimes BPNN fails to find the global optimum. Therefore global **optimization** **algorithm** **Ant** **Colony** **Optimization** (ACO) [5] is used to predict the better **path**.

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Aravind and Micheal [18] proposed a hybrid of ACO and GA to find the shortest **path** with help of distance-value in Wireless Mesh Network. WMN is a promising wireless technology for several emerging and commercially interesting applications like broadband home networking, community and neighborhood networks, coordinated network management, intelligent transportation systems which provide wireless broadband service access at a reasonable cost. The **algorithm** implemented ACO to maintain the routing table in a simple and understandable form and explored the solution space in multiple directions at once to find all possible paths. These set of paths obtained as output by ACO were given as input to the GA. GA works efficiently for solving problems where the solution space is huge and time taken to search exhaustively is very high. The genetic **algorithm** undergoes the selection, crossover and mutation process and generates the result. The result contains only one **path** which is optimal among the shortest **path**. The **algorithm** of the proposed hybrid of ACO-GA is given below.

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In a changing environment of wireless sensor network, finding an optimal **path** is a challenging issue. One of the primary goal in WSN environment would be to improve the lifetime of the network. Vitality will be wasted when all the nodes are live even when they are not participating in a communication. Redundant data transmission may also cause energy wastage in dense environment. **Ant** **colony** **optimization** approach can be used for finding the optimal **path**. In future work, cluster head selection mechanism can be applied along with ACO to get the optimal cluster head.

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Many **ant** species, even with limited visual capabilities or completely blind, are able to find the shortest **path** between a food source and the nest by using pheromone as a communication mechanism. Ants drop pheromone on the ground as they walk from a food source to the nest, thereby creating a pheromone trail on the used **path**. The pheromone concentration of a **path** influences the choices ants make, and the more pheromone the more attractive a **path** becomes. Given that shorter paths are traversed faster than longer ones, they have a stronger pheromone concentration after a period time, contributing to being selected and reinforced more often. Ultimately the majority of ants will be following the same **path**, most likely the shortest **path** between the food source and the nest. Inspired by this behaviour, Dorigo et al. [11, 12, 13] have defined an artificial **ant** **colony** metaheuristic that can be applied to solve **optimization** problems, called **Ant** **Colony** **Optimization** (ACO).

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The aim of minimization analysis of network attack graphs is to find a minimum critical set of exploits that must be prevented to guarantee no attack scenario is possible. Sheyner et al. [4] and Jha et al. [9, 10] show this problem is in fact NP-hard. They propose a greedy **algorithm** that can find an approximately-optimal set of exploits, which must be prevented to thwart an intruder. **Ant** **Colony** **Optimization** (ACO) [11, 12] is a metaheuristic method that is inspired by the behavior of real ants. The underlying idea is that by using very simple means of communications, a group of ants is able to find shortest paths between the nest and the food sources [13]. Along the way, ants leave a chemical substance called pheromone. If no pheromone trails are available, ants move essentially at random, but in the presence of pheromone, they have a tendency to follow the trail. In fact, ants probabilistically prefer paths that are marked by strong pheromone concentrations. Choices between different paths occur when several paths intersect. Then, ants choose the **path** to follow by a probabilistic decision biased by the amount of pheromone. Because ants in turn leave pheromone on the **path** they are following, this behavior results in a self-reinforcing process leading to the formation of paths marked by strong pheromone concentrations [14]. This behavior also enables ants to find shortest paths between the nest and the food sources.

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While walking from one point to another, ants deposit a substance called pheromone, forming a pheromone trail. It has been shown, experimentally [4], that this pheromone trail, once employed by a **colony** of ants, can give rise to the emergence of a shortest **path**. In general, the amount of pheromone deposited by an articial **ant** is made proportional to the goodness of the solution an **ant** may build. To apply ACO algorithms to the reservoir operation problem, one may view it as a combinatorial **optimization** problem. The problem may be approached by considering a time series of inow, classifying the reservoir volume to several intervals and deciding on the release at each period, with respect to an optimality criterion. Feasible paths for ants to follow may be constrained by the continuity equation, as well as constraints on the storage volume. Upon each tour completion, a nite number of feasible solutions will form, leaving a new value for the pheromone.

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Real ants are capable of finding the shortest **path** from their nest to a food source without visual sensing. They are also able to adapt to changes in the environment. “**Ant** **Colony** **Optimization**” is an **algorithm** which searches for the solution of the problem under consideration in the way similar to real ants. It tries to make use of real **ant** abilities to solve various **optimization** problems. In this report study of simple **ant** algorithms has been done. Also, as an example they are applied on famous Traveling Salesman Problem. Finally, some results are tabulated comparing these algorithms with other **optimization** heuristics.

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