Modified Ant Colony Optimization with pheromone mutation for travelling salesman problem

Ant colony optimization (ACO) algorithm is a metaheuristic inspired by the behavior of real ants in their search for the shortest path to food sources. The ACO algorithm takes on these characteristics of robust, positive feedback distributed computing, easy fusing with other algorithms. But the basic ACO algorithm has some deficiencies of premature and stagnation phenomenon in the evolution process, and is easily trapped into local optimal solution. And it is difficult to explore other solutions in the neighbor space. So a improved ACO(DPSEMACO) algorithm based on dual population strategy, bi-directional dynamic adjust evaporation factor strategy of the pheromone and parallel strategy is proposed to solve the traveling salesman problem(TSP). In the DPSEMACO algorithm, the ants are divided into the two subpopulations by borrowing the mutual cooperation mechanism of biological community, which evolve separately and exchange information timely. The bi-directional dynamic adjusting evaporation factor strategy of the pheromone is used to change the corresponding path pheromone of different subpopulations in order to avoid to trap into a local optimum. The parallel strategy can avoid falling into a local optimum. And the DPSEMACO algorithm can expand the search space and improve the overall searching performance by repeated changing the pheromone of the each subpopulation and adaptive adjusting evaporation factor. Finally, in order to prove the optimization performance of the proposed DPSEMACO algorithm, some classic TSP instances are selected from the TSPLIB in this paper. And some existing methods are selected to compare the optimization performance with the proposed DPSEMACO algorithm. The experimental results demonstrate that the proposed DPSEMACO algorithm is feasible and effective in solving TSP, and takes on a good global searching ability and high convergence speed.

Using the new method and roulette wheel, the traditional Ant Colony Algorithm is improved in the aspect of searching process and pheromone modification. The defects of low searching efficiency and easy to fall into local minimum in traditional Ant Colony Algorithm are remedied. the validity of the improved algorithm has been verified using a testing function.Moreover,a satisfactory optimum solution for a Power Distribution Network Planning has been obtained. And the effective design method for permanent-magnet synchronous Ant colony algorithm is a simulation based on the species evolution to solve complex optimization problem for heuristic. The idea of ant colony algorithm are simulated ants foraging behavior,That is, the use of a large number of ants in the search space in the random search,And use of information has always been to strengthen the search route, and guide other artificial ants search,At the same time, the introduction of the volatile pheromone mechanism(1). Ant colony algorithm proposed by the Italian scholars Dorigo in the twentieth century nineties. The algorithm in the traveling salesman problem (TSP), quadratic assignment problem (QAP) and shop scheduling problem (JSP) solution to achieve good results. Now ant colony algorithm has been optimized in the motor design, network distribution, function optimization and integrated circuit wiring in areas such as applied. Forestry waste from electricity distribution network from the power station involved in each location, size to meet future demand for electricity in rural areas since, at the same time for each subject since the power station capacity, radial network structure, as well as reliability requirements, such as binding. Because of lot of variables and constraints involved, spontaneous power distribution network planning is a very complex combinatorial optimization problem. In this paper, these issues of improved ant colony algorithm and proposes a multi-modal adaptive ant colony pheromone search mechanisms, and their use for the electricity distribution network optimization, and achieved good results. I. THE MATHEMATICAL MODEL OF ACA The ant optimization algorithm is mainly composed of the switching rules and the renewaling information element rule. As an example,We present the ACO algorithm applied to the TSP(Traveling Salesman Problem) for illustrating the principle of ant colony algorithm. there is the assumption N cities, traveling salesman problem are looking for an optimal travel path of the shortest route. The TSP models the situation of a travelling sales man who is required to pass through a number of cities(2). The goal of the travelling sales man is to traverse these cities(visiting each city exactly once)so that the total travelling distance is minimal. Feasible solution of the traveling salesman problem is a non-repeat sequences of all the citis. Assumeing that only m ants Add to the given n cities: dij(i,j=1,2,…,n) where dij is distance between city i with city j. bi(t) where bi(t) is the number of ants is located in city i when it's t. m= ∑ = n

The traveling salesman problem (TSP) is an NP-hard problem. Thus far, a large number of researchers have proposed different ant colony optimization (ACO) algorithms to solve the TSP. These algorithms inevitably encounter problems such as long convergence time and the tendency to easily fall into local optima. On the basis of the ACO algorithm, this study proposes a dynamic adaptive ACO algorithm (DAACO). DAACO realizes the diversity of initialization of the ACO algorithm by dynamically determining the number of ants to be prevented from falling into local optimization. DAACO also adopts a hybrid local selection strategy to increase the quality of ant optimization and reduce the optimization time. Among the 20 instances of the TSPLIB dataset, the DAACO algorithm obtains 19 optimal values, and the solutions of 10 instances are better than those of other algorithms. The experimental results on the TSPLIB dataset show that the DAACO algorithm has obvious advantages in terms of convergence time, solution quality, and average value relative to existing state-of-the-art ACO algorithms.

The traveling salesman problem (TSP) is a classic problem in optimization, frequently used for measuring the performance of optimization algorithms. The goal in solving the TSP is to determine the lowest-cost circuit through a set of cities on a graph. Ant colony optimization (ACO) algorithms, inspired by nature, use simulated ants that modify their environment through laying and removing pheromone, represented by weights on the edges of the graph connecting each city. In this study, a novel algorithm is developed, Multi-Colony System (MCS), which uses multiple colonies of simulated ants in combination to produce superior solutions to the TSP. In comparison with Ant Colony System (ACS), a standard well-performing ACO algorithm, MCS has displayed improved performance, producing tours up to 19.4% shorter than those of ACS in the same amount of time. The performance of MCS in this study presents potential advantages in applications beyond the TSP, including the ability of multiple colonies to both develop a greater number of solutions simultaneously and to more efficiently avoid local maxima in the search space.

Inverse transient radiation analysis in one-dimensional participating slab using improved Ant Colony Optimization algorithms

A modified ant colony optimization algorithm for dynamic topology optimization

Over the years, ant colony optimisation (ACO) algorithms have been proposed particularly for solving the hard combinatorial optimisation problems, such as the travelling salesman problem (TSP) and the job-shop scheduling problem (JSSP). Also, most real-world applications are concerned with the multi-objective optimisation problems. In this paper a new ant colony optimisation (ACO) algorithm is proposed for solving two or more objective functions, simultaneously. It is based on the ant colony system (ACS) algorithm and uses the random weight-based method. It is applied on several benchmark instances of the TSP and the JSSP from the literature and compared with more recent multi-objective ant colony optimisation algorithms (MOACO). The experimental results have shown that the proposed algorithm achieves better performance for solving the travelling salesman problem and the job-shop scheduling problem with multiple objectives. It also obtained well distribution all over the Pareto-optimal front.

Ant Colony Optimization (ACO) is a metaheuristic inspired by the foraging behavior of ant colonies that has been successful in the resolution of hard combinatorial optimization problems like the Traveling Salesman Problem (TSP). This paper proposes the Omicron ACO (OA), a novel population-based ACO alternative originally designed as an analytical tool. To experimentally prove OA advantages, this work compares the behavior between the OA and the MMAS as a function of time in two well-known TSP problems. A simple study of the behavior of OA as a function of its parameters shows its robustness.

Travelling salesman problem is a special case of the vehicle routing problem. The objective of the travelling salesman problem is to find the shortest path for visiting every city without repeating city. Among metaheuristic algorithms, Ant System has been the most popular algorithm for solving the travelling salesman problem. However, Ant System has a disadvantage of often falling into local optimal solutions. This research proposed a modified Ant System with a modified pheromone density updating to reduce the rate of convergence. A threshold is also used to create a greater variety of routes. Moreover, the proposed algorithm used a Sweep Algorithm to generate initial population so that the next city to visit is close to each other. To prevent the ants from getting trapped at a local optimum, three types of local search, swap, insert, and reverse, are used to veer away the paths towards the higher pheromone density at a local optimum. The tested results of the proposed algorithm were compared to those of other three algorithms: GA-PSO-ACO, Hybrid VNS, and HAACO. On 13 out of 15 small- and medium-sized datasets, the proposed method outperformed or performed as well as the others.KeywordsTravelling salesman problemAnt systemSweep algorithmCombinatorial optimization

In order to improve the search result and low evolution speed, and avoid the tendency towards stagnation and falling into the local optimum of ant colony optimization(ACO) in solving the complex function, the traditional ant colony optimization algorithm is analyzed in detail, an improved ant colony optimization(IWSMACO) algorithm based on information weight factor and supervisory mechanism is proposed in this paper. In the proposed IWSMACO algorithm, the information weight factor is added to the path selection and pheromone adjustment mechanisms in order to dynamically adjust path selection probability and randomly select the behavior rules for further intelligentializing the ant colony. The supervisory mechanism added the dynamic convergence criterion of supervisory distance and used the optimal pheromone update strategy to self-adaptively select the excellent ants for updating the pheromone trails, and improve the solution qualities of each iteration, better guide the later ants for learning. Finally, the proposed IWSMACO algorithm is carried out by 12 TSP instances. The simulation experiment results show that the proposed IWSMACO algorithm can not only avoid falling into the local optimum, but also enhance the convergence speed. And it takes on remarkable optimized ability and higher search accuracy.

Swarm intelligence is a relatively new approach to problem solving that takes inspiration from the social behaviors of insects and other animals. Ants, in particular, have inspired a number of methods and techniques among which the most studied and successful is the general-purpose optimization technique, also known as ant colony optimization, In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Ant Colony Optimization (ACO) algorithm is used to arrive at the best solution for TSP. In this article, the researcher has introduced ways to use a great deluge algorithm with the ACO algorithm to increase the ability of the ACO in finding the best tour (optimal tour). Results are given for different TSP problems by using ACO with great deluge and other local search algorithms.

Ant colony optimization (ACO) algorithm is a recent meta-heuristic method inspired by the behavior of real ant colonies. The algorithm uses parallel computation mechanism and performs strong robustness, but it faces the limitations of stagnation and premature convergence. In this paper, a hybrid PS-ACO algorithm, ACO algorithm modified by particle swarm optimization (PSO) algorithm, is presented. The pheromone updating rules of ACO are combined with the local and global search mechanisms of PSO. On one hand, the search space is expanded by the local exploration; on the other hand, the search process is directed by the global experience. The local and global search mechanisms are combined stochastically to balance the exploration and the exploitation, so that the search efficiency can be improved. The convergence analysis and parameters selection are given through simulations on traveling salesman problems (TSP). The results show that the hybrid PS-ACO algorithm has better convergence performance than genetic algorithm (GA), ACO and MMAS under the condition of limited evolution iterations.

Ant Colony Optimization (ACO) algorithm has a wide array of applications to solve combinatorial optimization problems, especially Traveling Salesman Problems (TSPs). The major limitations of ACO algorithm are premature convergence, the possibility that trapped in the local optima. In this paper, an improved Ant Colony Optimization algorithm is proposed which uses fractional order difference for pheromone updating and a weighted combined transition probability. The fractional order difference with the characteristic of long-term memory helps the algorithm make full use of the historical information, and the combined transition probability enhances the exploration ability of the algorithm by using the information of a few steps forward. The performance of the proposed algorithm is tested on various data sets from the standard TSP Library compared with the corresponding integer order algorithm and some evolutionary algorithms. According to the empirical results, our algorithm based on fractional order difference overcomes the classic integer order. Furthermore, the results on a number of TSP instances demonstrate that compared with other evolutionary algorithms, the proposed method can obtain the better solutions on most instances with stronger robustness.

The ant colony optimization (ACO) algorithm is improved and further integrated with the immune algorithm (IA) to address its problems, such as slow convergence, local optimum, and premature convergence in the path planning. An algorithm integrating IA and improved ant colony optimization (IACO) is, therefore, put forward to realize the optimal planning of global path for an unmanned surface vehicle (USV). First, the ACO algorithm was improved in three aspects, that is, generation of initial pheromones, transition probability, and update of pheromones. The proposed IA-IACO algorithm combined the advantages of IA and IACO, sped up the convergence, and enhanced the optimization capability and operational efficiency. Second, the IA-IACO algorithm was designed and applied in the global path planning of an unmanned surface vehicle, achieving great global optimization and convergence. Finally, a path smoothing algorithm was devised to achieve the implementable, economic, and stable path while guaranteeing the safe navigation of the USV. A simulation test was carried out to prove the effectiveness and superiority of the designed global path planning algorithm in the practical engineering.

Biomimicry means learning from nature. Well known examples include physical structures such as the Velcro fastener. But natural selection has also "engineered" mechanisms by which the components of adaptive biological systems are organized. For example, natural selection has caused the foragers in an ant colony to cooperate and communicate in order to increase the total foraging success of the colony. Ant colony optimization (ACO) is based on the pheromone trails by which many ant species communicate the locations of food in the environment around the nest. Computer algorithms based on ACO perform well in hard computational problems like the Traveling Salesman Problem. ACO algorithms normally use only a single attractive "pheromone". However, it seems that real ants use more. The Pharaoh's ant, Monomorium pharaonis , uses three different trail pheromones to provide short-term (volatile) and long-term attraction (non-volatile) and short-term (volatile) repellence so that foragers are directed to particular locations of the trail system where food can be collected. In addition, Pharaoh's ants also extract information from the geometry of the trail system and have division of labour among the forager workers, some of whom specialize in laying and detecting pheromone trails. ACO takes inspiration from ant colonies but does not need to faithfully model how ant colonies solve problems. For example, in ACO "pheromone" is applied retroactively once an "ant" has returned to the nest, which is something that can easily be implemented in a computer program but is obviously something that real ants cannot do. This raises the possibility that ACO might benefit from taking further inspiration from ant colonies. Presumably, real ants use multiple information sources and communication signals for a reason.