Efficient GPU Implementation of Genetic Algorithm to Solve the Traveling Salesman Problem

Traveling salesman problem (TSP) is a problem of determining the shortest path for a salesman to take to visit all cities. Although a small number of cities is easy to solve, as the number of cities increases, it’s not possible to solve in polynomial time as it was a combinatorial nondeterministic polynomial (NP-hard) problem. Hence, this project is implementing a genetic algorithm (GA) to solve TSP using Python programming. The focus of this paper is to analyze the GA using order crossover (OX) and random crossover (RX) and propose a combination mechanism, direct combination (OX-RX) and Dynamic Linear combination (OXRX-Linear) to optimize TSP. We test GA for OX and RX in a random set of cities, up to 75 total cities. Then compare the result of the proposed combination OX-RX and OX-RXLinear. The result shows that both proposed combined mechanisms OX-RX and OX-RX-Linear improve the performance of GA in solving TSP.

Optimization problem like Travelling Salesman Problem (TSP) can be solved by applying Genetic Algorithm (GA) to obtain perfect approximation in time. In addition, TSP is considered as a NP-hard problem as well as an optimal minimization problem. Selection, crossover and mutation are the three main operators of GA. The algorithm is usually employed to find the optimal minimum total distance to visit all the nodes in a TSP. Therefore, the research presents a new crossover operator for TSP, allowing the further minimization of the total distance. The proposed crossover operator consists of two crossover point selection and new offspring creation by performing cost comparison. The computational results as well as the comparison with available well-developed crossover operators are also presented. It has been found that the new crossover operator produces better results than that of other cross-over operators.

Traveling salesman problem in which all the vertices are assumed to be on a spherical surface is a special case of the conventional travelling salesman problem. There are exact and approximate algorithms for the travelling salesman problem. As the solution time is a performance parameter in most real-time applications, approximate algorithms always have an important area of research for both researchers and engineers. In this chapter, approximate algorithms based on heuristic methods are considered for the travelling salesman problem on the sphere. Firstly, 28 test instances were newly generated on the unit sphere. Then, using various heuristic methods such as genetic algorithms, ant colony optimization, and fluid genetic algorithms, the initial solutions for solving test instances of the traveling salesman problem are obtained in Matlab®. Then, the initial heuristic solutions are used as input for the 2-opt algorithm. The performances and time complexities of the applied methods are analyzed as a conclusion.

In the first part we are going to discuss about the Travelling Salesman Problem. As we are aware of that the Travelling Salesman Problem is an NP-hard problem thus it is impossible to solve it through the normal algorithm or say deterministic algorithm. If the number of cities in Travelling Salesman Problem is very small say 4-5 then we can think of solving it through brute force approach but the number of cities become 100-200 then it is impossible to comprehend as the number of possible solution or routes increases exponentially relative to the number of cities. Then we discuss about the benefits of Genetic Algorithm and how we can apply the study or use the benefit of Genetic Algorithm to solve Travelling Salesman Problem. Also we are going to go through every step of Genetic Algorithm and see very closely how all the work is done on every step. Then we are going to discuss about the background we have gone through like what kind of work or development has been done ever since in every other research papers. Then we are going to discuss about our methodology in a very detailed manner i.e. the actual method or process we have used or proposed in our paper. As we were going through it we realize as why we take some values of crossover or mutation rating as optimal for some problem not optimal for other, how do we decide it and why we do it, what difference does it make to our implementation. We have tried to answer this kind of question through our paper. And finally we go through the conclusive part of our work and talk about possibilities in future or possible work that can be done in the near future.

In this work a detailed study about the implementation of genetic algorithms (GAs) using parallelism and field programmable gate arrays (FPGAs) is presented. Concretely, we use the traveling salesman problem (TSP) as case study. First at all, the TSP is described as well as the GA used for solving it. Afterwards, we present the hardware implementation of this algorithm. We detail 13 different hardware versions, searching that each new version improves the previous one. Many of these improvements are based on the use of parallelism techniques. Finally, the found results are shown and analysed: hardware/software comparisons, resource use, operation frequency, etc. We conclude indicating the parallelism techniques that obtain better results and stating FPGA implementation is better when the problem size increases or when better solutions (nearer to the optimum) must be found.

Finding optimal solutions to NP-Hard problems requires exponential time with respect to the size of the problem. Consequently, heuristic methods are usually utilized to obtain approximate solutions to problems of such difficulty. In this paper, a novel swarm-based nature-inspired metaheuristic algorithm for optimization is proposed. Inspired by human collective intelligence, Wisdom of Artificial Crowds (WoAC) algorithm relies on a group of simulated intelligent agents to arrive at independent solutions aggregated to produce a solution which in many cases is superior to individual solutions of all participating agents. We illustrate superior performance of WoAC by comparing it against another bio-inspired approach, the Genetic Algorithm, on one of the classical NP-Hard problems, the Travelling Salesperson Problem. On average a 3% - 10% improvement in quality of solutions is observed with little computational overhead.

Travelling Salesman Problem(TSP) is an NP hard problem, which has been addressed via several heuristic algorithms like genetic algorithms (GA) etc. The paper presents TSP solution using Teaching Learning Based optimization(TLBO) which includes many similarities like the other nature-inspired algorithms. In addition, the strategy adds an auxiliary operator to regulate the sequence of array elements in mutation process with partial-mapped crossover used over the selected candidates of the population. Experimental study shows that introduced strategy can provide better convergence. The prominent feature of the strategy is in its stability and superior ways to handle computational complexity while dealing with TSP optimization as compared to GA.

The Traveling Salesman Problem (TSP) is a well-known problem in computer science that requires finding the shortest possible route that visits every city exactly once. TSP has broad applications in logistics, routing, and supply chain management, where finding optimal or near-optimal solutions efficiently can lead to substantial cost and time reductions. However, traditional solvers rely on iterative processes that can be computationally expensive and time-consuming for large-scale instances. This research proposes a novel deep learning architecture designed to predict optimal or near-optimal TSP tours directly from the problem’s distance matrix, eliminating the need for extensive iterations to save total solving time. The proposed model leverages the attention mechanism to effectively focus on the most relevant parts of the network, ensuring accurate and efficient tour predictions. It has been tested on the TSPLIB benchmark dataset and observed significant improvements in both solution quality and computational speed compared to traditional solvers such as Gurobi and Genetic Algorithm. This method presents a scalable and efficient solution for large-scale TSP instances, making it a promising approach for real-world traveling salesman applications.

The generalized traveling salesman problem (GTSP) is a generalization of the classical traveling salesman problem. The GTSP is known to be an NP-hard problem and has many interesting applications. In this paper we present a local-global approach for the generalized traveling salesman problem and as well an efficient algorithm for solving the problem based on genetic algorithms. Computational results are reported for Euclidean TSPlib instances and compared with the existing ones. The obtained results point out that our GA is an appropriate method to explore the search space of this complex problem and leads to good solutions in a short amount of time.

Implementation of a parallel Genetic Algorithm on a cluster of workstations: Traveling Salesman Problem, a case study

Traveling salesman problem (TSP) means that a travelling salesman needs to promote products in n cities (including the city where he lives). After visiting each city (each city can be visited once), he returns to the departure city. Let’s suppose that there is one road to connect each two cities. What is the best route to follow in order to minimize the distance of the journey? TSP has been proven to be a NP-hard problem, i.e. failure of finding a polynomial time algorithm to get a optimal solution. TSP is easy to interpret, yet hard to solve. This problem has aroused many scholars’ interests since it was put forward in 1932. However, until now, no effective solution has been found. Though TSP only represents a problem of the shortest ring road, in actual life, many physical problems are found to be the TSP. Example 1, postal route. Postal route problem is a TSP. Suppose that a mail car needs to collect mails in n places. Under such circumstances, you can show the route through a drawing containing n+1 crunodes. One crunode means a post office which this mail car departures from and returns to. The remaining n crunodes mean the crunodes at which the mails need to be collected. The route that the mail car passes through is a travelling route. We hope to find a travelling route with the shortest length. Example 2, mechanical arm. When a mechanical arm is used to fasten the nuts for the ready-to-assembling parts on the assembly line, this mechanical arm will move from the initial position (position where the first nut needs to be fastened) to each nut in proper order and then return to the initial position. The route which the mechanical arm follows is a travelling route in the drawing which contains crunodes as nuts; the most economical travelling route will enable the mechanical arm to finish its work within the shortest time. Example 3, integrated circuit. In the course of manufacturing the integrated circuit, we often need to insert thousands of electrical elements. It will consume certain energy when moving from one electrical element to the other during manufacturing. How can we do to arrange the manufacturing order to minimum the energy consumption? This is obviously a solution for TSP. Except for the above examples, problems like route distribution of transportation network, choice of tourist route, laying of pipelines needed for city planning and engineering construction are interlinked with the problems of finding the shortest route. So, it is of significance to make a study on the problem of the shortest route. This renders us a use value. As finding a solution for TSP plays an important role in the real life, since the TSP appeared, it has attracted many scholars to make a study on it.

<p><span>Travelling salesman problem is a well researched problem in computer science and has many practical applications. It is classified as a NP-hard problem as its exact solution can only be obtained in exponential time unless P = NP. There are different variants of the travelling salesman problem (TSP) and in this paper, asymmetric travelling salesman problem is addressed since this variant is quite often observed in real world scenarios. There are a number of heuristic approaches to this problem which provides approximate solutions in polynomial time, however this paper proposes an exact optimal solution which is accelerated with the help of multi-threading-based parallelization. In order to find the exact optimal solution, we have used the held-karp algorithm involving dynamic programming and to reduce the time taken to find the optimal path, we have used a multi-threaded approach to parallelize the processing of sub-problems by leveraging the central processing unit cores (CPUs). This method is an extension of a well researched solution to the TSP; however, this method shows that solutions to computationally intensive problems involving sub-problems such as the asymmetic travelling salesman problem (ATSP) can be accelerated with the help of modern CPUs.</span></p>

Single machine scheduling problem with setup times is proved to be an NP-hard problems, and its complexity is equivalent to the traveling salesman problem (TSP) of n cites. Integrating the advantages of simulation and genetic algorithm (GA), this paper proposes a GA based on simulation to solve this NP-hard problem. Then, it introduces how to build the simulation model and how to design chromosome coding and selection, crossover and mutation operators of GA for this special scheduling problem in details. An experiment has been carried out and the result proves that the method is feasible and should be adopted.

Genetic algorithms (GAs) are search algorithms based on population genetics and natural selection concepts. Maintaining population variety in GAs is critical for ensuring global exploration and mitigating the risks of premature convergence. Rapid convergence to local optima is one such challenge in the application of genetic algorithms. To address this issue, we provide Cave-Surface GA (CSGA), an alternative method based on the Dual Population Genetic Algorithm and inspired by the genetic variety observed in Mexican cavefish. Through inter-population crossbreeding, CSGA increases diversity via a secondary population (Cave population) and facilitates the exchange of information between populations, effectively counteracting premature convergence. Several experiments are carried out utilizing benchmark instances of the Traveling Salesman Problem (TSP) obtained from TSPLIB, a well-known TSP problem library. Our experimental results over many TSP instances show that CSGA outperforms both classic GAs and other GAs that use diversity preservation techniques, such as Multipopulation GA (MPGA). CSGA has the potential to give promising solutions to challenging optimization issues like TSP.

This research report introduces two new hybrid genetic algorithms and compares them to solve the traveling salesman problem (TSP). The new algorithms are a combination of a genetic algorithm (GA) with a nearest neighbor algorithm (NNA). The NNA is used to influence the population of the GA and the selection of the parents in the GA. The results of the conducted experiments, performed in MATLAB environment, have shown that the new algorithms can be successfully used to solve the TSP. Depending on the size of the TSP, the new algorithms achieve better results than the initial GA, which is also used. However, in terms of selecting the best algorithm, no conclusive results were obtained and the best choice depends on the particular TSP.