OFNAnt Method Based on TSP Ant Colony Optimization

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

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 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

This chapter mainly aims to introduce some widely used ACO algorithms and their origins, such as the AS, EAS, MMAS, and so on. It is found that all concerns are focused on the pheromone update strategy. Some uses the best-so-far-ant or the iteration-best ant independently/interactively to update the trail that ants travelled. Meanwhile, the update law may differ a bit for different ACO algorithms. Among the four ACO algorithms, two versions have received great popularities in various applications, i.e. AS and MMAS. Another contribution in this chapter is the extension of the general ACO algorithm to the system of ants of different tasks, and its behaviour is modelled and implemented in the track initiation problems. Simulation results are also presented to show the effectiveness of the novel ACO algorithm. According to the example presented in this chapter, we believe that the general framework of AS can be modified to solve various optimal or non-optimal problems.

Capacitated Vehicle Routing Problem (CVRP) is a real life constrain satisfaction problem in which customers are optimally assign to individual vehicles (considering their capacity) to keep total travel distance of the vehicles as minimum as possible while serving customers. Various methods are investigated to solve CVRP in last few decades, the most popular way of solving CVRP is splitting the task into two different phases: firstly, assigning customers under different vehicles and secondly, finding optimal route of each vehicle. Sweep clustering algorithm is well studied for clustering nodes. On the other hand, route optimization is simply a traveling salesman problem (TSP) and a number of TSP optimization methods are investigated for this purpose. This study investigates a variant of Sweep algorithm for clustering nodes and different SI based methods for route generation to get optimal CVRP solution. In conventional Sweep algorithm, cluster formation starts from 0° and consequently advance toward 360° to consider all the nodes. In this study, Sweep cluster are considered from different starting angle. On the other hand, two well-known Swarm Intelligence (SI) methods (i.e., Ant Colony Optimization and Particle Swarm Optimization (PSO)) and two recent SI based algorithms (i.e., Producer-Scrounger Method and Velocity Tentative PSO) are considered for route optimization. We have compared the performance of these methods to solve CVRP. The experimental results on a large number of benchmark CVRP reveal that different starting angle has positive effect on Sweep clustering and finally, VTPSO is able to produce better solution than other methods.

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.

Since introduced bio-inspired algorithms have proven be the superior algorithm in many optimization problems. Near optimum performance of these algorithms along with their very simple calculation rules has resulted in widespread utilization of biological computing in many fields of science like communications, robotics, software engineering, networks, etc. Swarm intelligence observed in social insects such as ants, resulting in a behavior beyond the scope of individual members of society, has been an important source of inspiration for these algorithms. Ant Colony Optimization, a particularly successful research direction in swarm intelligence based algorithms dedicated to discrete optimization problems, has been effectively used in a variety of combinatorial problems such as quadratic assignments, traveling salesman problems, and routing in telecommunication networks. In this paper we propose a new algorithm named Multi Resolution Ant Colony, which uses swarm intelligence in a continuous (non-discrete) environment, for finding extremes, i. e. minimums and maximums, of a function. Genetic Algorithm (GA), up to now, has been a candidate for solving these kinds of problems when analytical methods failed. The dependency of analytical methods on initial condition is one of the most important reasons to utilize Genetic Algorithms instead. The method we present has advances over GA in that it can either, find the extremes itself (simulation results show the out-performance of our algorithm to GA in this area), or be fed to analytical methods (in low resolutions steps, not possible in GA).

Interferometric Synthetic Aperture Radar (InSAR) is a microwave imaging system with all-weather earth observation. Because of its wide observation area, high precision, day and night operational capabilities, it has a significant advantage in monitoring large-scale surface deformation. Phase unwrapping is a key step in InSAR data processing. The core of Goldstein traditional branch unwrapping method is the establishment of branch-cutting lines. The shorter the overall length of the branch line, the solution is more accurate. Based on the idea of solving the shortest path of Travelling Salesman Problem (TSP), a new algorithm combining ant colony algorithm and genetic algorithm is proposed. Based on the advantages of these two algorithms, we avoid the disadvantages of excessive parameters, slow calculation speed and low efficiency in ant colony algorithm, reduce the time consumed by ant colony algorithm in solving local optimal solution, improve the local search ability of ant colony algorithm, establish shorter branch line than traditional branch method, prevent islanding effect and improve the precision of phase unwrapping. The tests performed on real and simulated interferometric SAR data confirm the validity of the proposed method.

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.

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.

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.

Improved ant colony optimization algorithm for the traveling salesman problems

Objectives: A well-known NP-complete problem is the travelling salesman problem (TSP). It has numerous engineering and scientific applications. In this article, we have proposed a multi-conveyance TSP where different conveyances are present to travel from one city to another city. This is an extension to classical TSP. In this TSP, the salesman visits all the cities only once during his/her tour, using different conveyances to travel from one city to another. The cost of travelling between cities using various modes of conveyance varies. The objective of this research is to find the minimum cost tour using an ant colony optimization (ACO) based approach by satisfying the constraints of the proposed multi-conveyance TSP. Method: The considered TSP has been solved using a novel ACO technique. The proposed ACO is adopted with the Roulette-wheel selection and “tuning solution” techniques. We have used a few benchmark datasets from TSPLIB to check the effectiveness of the proposed algorithm. The experimental findings for a few benchmarks TSP instances show that almost always, the proposed ACO is able to find a better result. Then, we used some redefined and randomly generated datasets for experiments. The experimental outcomes for various input datasets are also very encouraging. Findings: The goal of the proposed TSP is to find a complete tour with a minimum cost without exceeding the total travel cost and total travel time. Thus, there are two novel constraints in the classical TSP. Novelty: A unique aspect of the proposed research is the use of several conveyance facilities and a fixed total travel time and cost. This is new, as these three factors are integrated into a single TSP model. Keywords: Travelling Salesman Problem; Travel Cost; Travel Time; MultiConveyance TSP; Ant Colony Optimization

Collective data mining in the ant colony decision tree approach