Solving Traveling Salesman Problem Research Articles

Improvement to application of PSO algorithm on TSP problems

In the field of swarm intelligence algorithms, particle swarm optimization algorithms have the ability of fast search and are widely used in lots of application scenarios because they are easy to implement. Therefore, different improvements have been made for their various properties. In this paper, aiming to accelerate its convergence speed, we further improve the existing hybrid particle swarm algorithm by using the idea of self adaptive and simulated annealing, examining its performance by solving Travelling salesman problem. It demonstrate that the relevant improvements can optimize the algorithm performance and have better convergence speed when iteration value was set 30, 50, or 70 by making comparions between the experiment results of both algorithm. The code used in this article is available on github. The experimental results show that the optimization proposed in this paper can optimize the algorithm to a certain extent at 30, 50, and 70 iterations, mainly because the improved algorithm can keep the convergence speed stable in more iterations.

A Novel Crossover based Discrete Artificial Algae Algorithm for Solving Traveling Salesman Problem

The Artificial Algae Algorithm (AAA) is a newly proposed metaheuristic algorithm that is inspired by microalgae behaviors. This algorithm has been proposed for solving continuous optimization problems and achieved good results for the continuous problems. In addition, binary versions of AAA are proposed in the literature. This paper presents a discrete version of AAA, which is named Discrete Artificial Algae Algorithm (DAAA). For discretization of AAA, Crossover operators (one-point and uniform) are used in the processes (helical movement, evolutionary process, and adaptation). In this study, in addition to crossover operators, transformation operators such as swapping, insertion, symmetry, and reversion are also used. DAAA’s performance was analyzed on a well-known discrete optimization problem called the Traveling Salesman Problem (TSP). DAAA was tested on thirty-two Benchmark instances of the TSP. These instances were small-sized, medium-sized, and large-sized. Firstly, the AAA processes (evolutionary process, adaptation, and helical movement) with the combination of nearest neighbor and transformation operators were tested for selected benchmark instances and this testing was called Process Analysis. After this process Analysis the best processes with which to continue were selected, and after this decision comparisons with other algorithms were started. The main comparison is between discrete Social Spider Algorithm (DSSA) and DAAA, and DAAA outperformed DSSA on most of the problems. Further, DAAA’s performance on some of the benchmark instances was compared with some of the well-known algorithms for TSP. In this comparison, DAAA has achieved better results than many other algorithms. Experimental results show that DAAA has the capability of solving discrete optimization problems and outperforming other algorithms.

Quantitatively Evaluating the Effect of Read Noise in Memristive Hopfield Network on Solving Traveling Salesman Problem

Hopfield neural network, as a recurrent neural network, has been widely used to solve non-deterministic polynomial time-hard problems. However, the network tends to get trapped into local minima and thus converge to sub-optimal solutions. In this work, the intrinsic read noise in the memristive Hopfield network was harnessed as the random perturbation source to mitigate this problem. Firstly, the read noise in devices (TiN/TaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /TiN) at different resistance levels from a 1 Kb array was statistically measured, and the distribution of it was extracted. Then the effect of reading noise levels on the performance of a 64 × 64 network solver is quantitatively evaluated through confining all devices with the identical distribution. Based on such a strategy, the success probability, the distribution of distance, the energy consumption, and time to solution, at different noise levels and iteration cycles were investigated. The simulated results demonstrate that the intrinsic read noise in the resistive weight matrix is indeed helpful for the network to escape from local minima, serving as a useful computing resource.

Hybrid Lion Swarm Optimization Algorithm for Solving Traveling Salesman Problem

In view of Traveling Salesman Problem (TSP) is a NP hard problem, Lion Swarm Optimization (LSO) Algorithm is a new swarm intelligence optimization algorithm. Therefore, in this paper, it uses improved hybrid LSO algorithm to solve TSP. Because the basic LSO algorithm is mainly used to solve the continuous problem, and the TSP is a discrete combinatorial optimization problem, this paper improves the LSO algorithm, introduces the greedy strategy, and combines with the Population Competitive Search (PCS) algorithm in the later stage of the search. As a result, the convergence speed is accelerated and the search efficiency is improved. The classic TSP example is tested, and the simulation results show that the algorithm proposed in this paper has strong stability and is an effective method for solving TSP.

«МУРАВЬИНЫЙ» АЛГОРИТМ В РЕШЕНИИ ЗАДАЧИ КОММИВОЯЖЕРА

The paper provides a brief theoretical overview of existing approaches to solving travelling salesman problem. The software implementation of the problem solution using the ant algorithm is performed. The analysis of the time efficiency of the algorithm on different volumes of input data is carried out. Dependency graph is plotted. Further directions of studying this algorithm are determined.

The Quantum Approximate Algorithm for Solving Traveling Salesman Problem

The Quantum Approximate Algorithm for Solving Traveling Salesman Problem

DIFFERENT METHODOLOGY FOR SOLVING TRAVELLING SALESMAN PROBLEM

DIFFERENT METHODOLOGY FOR SOLVING TRAVELLING SALESMAN PROBLEM

Can the Agent with Limited Information Solve Travelling Salesman Problem?

Here, we develop new heuristic algorithm for solving TSP (Travelling Salesman Problem). In our proposed algorithm, the agent cannot estimate tour lengths but detect only a few neighbor sites. Under the circumstances, the agent occasionally ignores the NN method (choosing the nearest site from current site) and chooses the other site far from current site. It is dependent on relative distances between the nearest site and the other site. Our algorithm performs well in symmetric TSP and asymmetric TSP (time-dependent TSP) conditions compared with the NN algorithm using some TSP benchmark datasets from the TSPLIB. Here, symmetric TSP means common TSP, where costs between sites are symmetric and time-homogeneous. On the other hand, asymmetric TSP means TSP where costs between sites are time-inhomogeneous. Furthermore, the agent exhibits critical properties in some benchmark data. These results suggest that the agent performs adaptive travel using limited information. Our results might be applicable to nonclairvoyant optimization problems.

IMPLEMENTATION HYBRID GENETIC ALGORITHM WITH ADAPTIVE LOCAL SEARCH SCHEME FOR SOLVING TRAVELING SALESMAN PROBLEM ON ANDROID

Ponte Academic JournalDec 2016, Volume 72, Issue 12 IMPLEMENTATION HYBRID GENETIC ALGORITHM WITH ADAPTIVE LOCAL SEARCH SCHEME FOR SOLVING TRAVELING SALESMAN PROBLEM ON ANDROIDAuthor(s): Teguh Narwadi ,d Subiyanto, Arief ArfriandiJ. Ponte - Dec 2016 - Volume 72 - Issue 12 doi: 10.21506/j.ponte.2016.12.8 Abstract:A weaknesses of the genetic algorithm (GA) is when GA traps to a local optimum and unable\r\nto escape, so its performance continues to deteriorate. One of the methods to overcome these weaknesses\r\nis hybrid genetic algorithm with adaptive local search scheme (HGA). This paper present application of\r\nHGA to effectively solve the traveling salesman problem. This application was developed on android\r\nbecause android is now widely used around the world and it is mobile system. The use of local search\r\ntechnique to search for a better solution in the neighborhood. If it finds a better solution, it changes the\r\ncurrent solution GA with this new one. For local search scheme that can automatically control the use of\r\nlocal search technique into GA so that local search is adaptive to the GA. The best solution is generated\r\nby the algorithm shown in google maps on android. In the experiment, to test the effectiveness of the\r\nHGA is compare with GA in 5 sample from the cities in Central Java, Indonesia with different numbers of\r\ncities. According to the experiment results obtained that in 3 tests out of 5 (60%), HGA found the optimal\r\nsolutions and in 2 test (40%), found the same with the best solution of GA. The worst solution and the\r\naverage solution HGA shows in 5 tests out of 5 (100%) is better than GA. The results have shown that the\r\nhybrid genetic algorithm outperforms the genetic algorithm especially in the case with the problem higher\r\ncomplexity. Download full text:Check if you have access through your login credentials or your institution Username Password

An efficient General Variable Neighborhood Search for large Travelling Salesman Problem with Time Windows

General Variable Neighborhood Search (GVNS) is shown to be a powerful and robust methodology for solving travelling salesman and vehicle routing problems. However, its efficient implementation may play a significant role in solving large size instances. In this paper we suggest new GVNS heuristic for solving Travelling salesman problem with time windows. It uses different set of neighborhoods, new feasibility checking procedure and a more efficient data structure than the recent GVNS method that can be considered as a state-of-the-art heuristic. As a result, our GVNS is much faster and more effective than the previous GVNS. It is able to improve 14 out of 25 best known solutions for large test instances from the literature.

Fuzzy Particle Swarm Optimization with Simulated Annealing and Neighborhood Information Communication for Solving TSP

In this paper, an effective hybrid algorithm based on Particle Swarm Optimization (PSO) is proposed for solving the Traveling Salesman Problem (TSP), which is a well-known NP-complete problem. The hybrid algorithm combines the high global search efficiency of fuzzy PSO with the powerful ability to avoid being trapped in local minimum. In the fuzzy PSO system, fuzzy matrices were used to represent the position and velocity of the particles in PSO and the operators in the original PSO position and velocity formulas were redefined. Two strategies were employed in the hybrid algorithm to strengthen the diversity of the particles and to speed up the convergence process. The first strategy is based on Neighborhood Information Communication (NIC) among the particles where a particle absorbs better historical experience of the neighboring particles. This strategy does not depend on the individual experience of the particles only, but also the neighbor sharing information of the current state. The second strategy is the use of Simulated Annealing (SA) which randomizes the search algorithm in a way that allows occasional alterations that worsen the solution in an attempt to increase the probability of escaping local optima. SA is used to slow down the degeneration of the PSO swarm and increase the swarm’s diversity. In SA, a new solution in the neighborhood of the original one is generated by using a designed ? search method. A new solution with fitness worse than the original solution is accepted with a probability that gradually decreases at the late stages of the search process. The hybrid algorithm is examined using a set of benchmark problems from the TSPLIB with various sizes and levels of hardness. Comparative experiments were made between the proposed algorithm and regular fuzzy PSO, SA, and basic ACO. The computational results demonstrate the effectiveness of the proposed algorithm for TSP in terms of the obtained solution quality and convergence speed.