Hybrid Sweep Algorithm and Modified Ant System with Threshold 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.

Ant Colony Optimization (ACO) algorithm is a stochastic algorithm that is used for solving combinational optimization problem. It is inspired by the foraging behavior of ant colony. The ant colony walks along density of pheromone from ant's nest to feeding sources. It leads to create shortest path from ant's nest to feeding sources. ACO is normally troubled with the problems of trapping in local optimum. This paper proposed an improved ACO algorithm by mutation is applied with pheromone of ants when ant colony traps in local optimum. The proposed technique is tested on twenty-two maps from the Traveling Salesman Problem Library (TSPLIB) and gives more satisfied search results in comparison with ACOs.

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, Metaheuristic algorithms have proven significant efficacy in handling None- Deterministic polynomial hard (NP-hard) combinatorial optimization problems, mainly the Traveling Salesman Problem (TSP) which has been used to evaluate and test many metaheuristics algorithms such as Ant Colony optimizations. This paper contributes a new optimization algorithm to the famous-family of swarm and evolutionary techniques named Scuba Diver Optimization Algorithm (SDOA) which is a novel population-based metaheuristic optimization algorithm inspired by the behavioural and physiological dynamics of scuba divers in the open water environments. SDOA simulates main diving factors including (depth, tank pressure/oxygen, bottom time, and ascent strategies) for keeping a balance between explorations and exploitations during the search process. SDOA novelty appears in its adaptive control of solution diversity using pressure and oxygen level thresholds, enabling robust avoidance of local optima and faster convergence. The SDOA algorithm was evaluated on a range of TSP instances from the TSPLIB library, which were categorized into three groups: Group 1, comprising instances with 1–99 cities; Group 2, including instances with 100–999 cities; and Group 3, consisting of large-scale instances with 1000 or more cities. And the results of SDOA is compared with established metaheuristics algorithms such as Ant Colony Optimization, Artificial Bee Colony, and Genetic Algorithm. The study results showing that SDOA consistently produces shorter (near optimal) tour lengths with significantly minimum computational time in larger problem sizes (Group 3). The proposed algorithm also demonstrates better scalability and stability in different initialization and population sizes. Future directions include adapting SDOA for solving other optimization problems including multi-objective or dynamic optimization contexts.

In view of the disadvantages of the basic ant colony algorithm in solving non-deterministic polynomial problems, such as slow convergence rate and local optimal solution. In this paper, the updating rules of pheromone and the updating strategy of target city in ant colony algorithm are improved, and an improved ant colony algorithm (IACA) is proposed. In addition, it is applied to the shortest traversal path search of travel salesman problem. Taking 33 provincial capitals and berlin52 problems as test objects, this paper compares the search efficiency of the proposed algorithm with that of the basic ant colony algorithm. It can be seen from the simulation results that IACA has a faster convergence rate than the basic ant colony algorithm. IACA is obviously superior to the basic ant colony algorithm in terms of convergence and the quality of the optimal solution. It provides a new choice for solving similar optimization problems.

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.

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.

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

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.

Parameter adaptation-based ant colony optimization with dynamic hybrid mechanism

Ant colony optimization algorithm with mutation mechanism and its applications

The chapter discusses the application of Opposition-Based Optimization (OBO) to ant algorithms. Ant Colony Optimization (ACO) is a powerful optimization technique that has been used to solve many complex problems. Despite its successes, ACO is not a perfect algorithm: it can remain trapped in local optima, miss a portion of the solution space or, in some cases, it can be slow to converge. Thus, we were motivated to improve the accuracy and convergence of the current algorithm by extending it with the concept of OBO. In the case of ACO, the application of opposition can be challenging because ACO usually optimizes using a graph representation of problems, where the opposite of solutions and partial components of the solutions are not clearly defined. The chapter presents two types of opposition-based extensions to the ant algorithm. The first type, called Opposite Pheromone per Node (OPN), involves a modification to the construction phase of the algorithm which affects the decisions of the ants by altering the pheromone values used in the decision. Basically, there is an opposite rate that determines the frequency at which opposite pheromone will be used in the construction step. The second method, Opposite Pheromone Update (OPU), involves an extension to the update phase of the algorithm that performs additional updates to the pheromone content of opposite decisions. The opposition-based approaches were tested using the Travelling Salesman Problem (TSP) and the Grid World Problem (GWP). Overall, the application of some fundamental opposition concepts led to encouraging results in the TSP and the GWP. OPN led to some accuracy improvements and OPU demonstrated significant speed-ups. However, further work is necessary to fully evaluate the benefits of opposition. Theoretical work involving the application of opposition to graphs is necessary, specifically in establishing the ‘opposite graph’.

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

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.

In this paper, a hybrid algorithm is proposed for travelling salesman problem (TSP). TSP, one of the vehicle route planning problems, is to minimize the cost of travel of a salesman in visiting all the cities in a given set, and return to the starting city. Basically, the proposed algorithm combines ant colony optimization (ACO) with genetic algorithm (GA) and can explore and exploit search spaces. It has both the advantage of ACO, the ability to find feasible solutions and to avoid premature convergence, and that of GA, the ability to avoid being trapped in local optima. The test results show that proposed algorithm finds optimum solutions effectively.