Wisdom of Artificial Crowds—A Metaheuristic Algorithm for Optimization

Traveling salesman problem (TSP) is a well-known NP-hard combinatorial optimization problem. It has been solved by a number of exact and approximate algorithms and serves as a testbed for new heuristic and metaheuristic optimization algorithms. However, it is often not easy to evaluate the hardness (complexity) of a TSP instance. Simple measures such as the number of cities or the minimum (maximum) route length do not capture the internal structure of a TSP instance sufficiently. In this work, we propose a new method for the assessment of TSP instance complexity based on clustering. The new approach is evaluated on a set of randomized TSP instances with different structure and its relation to the performance of a selected metaheuristic TSP solver is studied.

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 Traveling Salesman Problem (TSP) is one of the most well-known NP-hard combinatorial optimization problems, widely studied due to its numerous industrial applications in logistics, supply chain management, and resource planning. Over the years, various metaheuristic algorithms have been developed to provide near-optimal solutions within a reasonable computational time. While traditional methods such as Genetic Algorithms (GA) and Simulated Annealing (SA) have been applied widely to the TSP, recent developments in metaheuristics have introduced new methods that can ensure improved performance. In this study, we compare three new metaheuristics: Arctic Puffin Optimization (APO), Human Evolutionary Optimization (HEO), and Ship Rescue Optimization (SRO). These methods, inspired by puffin's behavior, human evolutions, and naval rescue, respectively, have demonstrated high optimization capability in various areas. However, these have not been extensively tried on solving the TSP yet. This research seeks to establish the performance of these algorithms by comparing their convergence rate, solution quality, and computational efficiency with well-established metaheuristics. The results of the experiment expose the strengths and weaknesses of such innovative approaches, showing their potential as competitive alternatives to solve complex combinatorial optimization problems

The traveling salesman problem is a popular problem in computer science due to its ease of explanation but difficulty in solving. As it is an NP-hard problem, heuristic methods such as genetic algorithms are often utilized to solve it. Genetic algorithms have many similar, repetitive steps in their evaluation, leading them to benefit from parallelization. This paper presents optimizations applied to a public genetic algorithm designed to solve the traveling salesman problem implemented in CUDA for GPU parallelization. Our optimizations were able to reduce the runtime by 87% with no reduction in the result quality and to further reduce the runtime by 98% with an 18% reduction in the quality of the results when compared to the initial CUDA implementation.

The Travelling Salesman Problem (TSP) is a well-known combinatorial optimization problem that belongs to a class of problems known as NP-hard, which is an exceptional case of travelling salesman problem (TSP), which determines a set of routes enabling multiple salesmen to start at and return to home cities (depots). The penguins search optimization algorithm (PeSOA) is a new metaheuristic optimization algorithm. In this paper, we present a discrete penguins search optimization algorithm (PeSOA) for solving the multiple travelling salesman problem (MTSP). The PeSOA evaluated by a set of benchmarks of TSP instance from TSPLIB library. The experimental results show that PeSOA is very efficient in finding the right solutions in a reasonable time

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.

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.

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.

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.

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.

The traveling salesman problem (TSP) is one of the classic combinatorial optimization problem NP-complete that requires much time to find the good solution. Indeed, the genetic algorithm is a stochastic optimization algorithm; it is to find an approximate solution of a hard problem. However, genetic algorithm has a great tendency to converge to a local minimum and stay stuck in adverse solutions. To solve this problem, we study in this paper the impact of the integration of a new local optimization heuristic Best 2-opt with the genetic operators on the quality of solution and the runtime of the GA. The hybridization proposed was tested on instances from 29 to 246 cities. The obtained results are very satisfied regarding to the solution qualities and the execution time.KeywordsGenetic AlgorithmLocal SearchMutation OperatorTravel Salesman ProblemTravel Salesman ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

With the increasing complexity of industrial manufacturing tasks, optimizing Multi-Point Manufacturing (MPF) operations, such as drilling and spot welding, has become essential for improving energy efficiency and execution speed. These tasks can be formulated as multi-dimensional Traveling Salesman Problems (TSPs), where robotic manipulators must traverse multiple points optimally while minimizing energy consumption. However, traditional heuristic algorithms, such as Genetic Algorithm (GA) and Ant Colony Optimization (ACO), face significant limitations. Their iterative nature leads to long computation times, and their performance heavily relies on precise parameter tuning to achieve high-quality solutions. To address these challenges, this study proposes a novel minimum energy consumption scheduling strategy for MPF problems, utilizing a Graph Neural Network (GNN)-based approach enhanced by Transfer Learning. The method employs Self-Adjusting Multi-modal Artificial Neural Networks (SAMANN) to reduce the 6D task nodes into a 2D representation, enabling the reuse of pre-trained 2D TSP models. Fine-tuning is then applied to further optimize performance. Compared with traditional heuristic algorithms, the proposed method significantly reduces computation time while maintaining solution quality. It is also found that the new approach surpasses the performance of the current state-of-the-art (SOTA) neural model in terms of both solution quality and training time across multi-dimensional TSPs and MPF problem domains, offering a robust and efficient solution for real-world MPF applications.

The Traveling Salesman Problem (TSP) is an NP-hard graph search problem. Despite having numerous modifications of the original abstract problem, Time Dependent Traveling Salesman Problem (TD TSP) was one of the most realistic extensions under real traffic conditions. In TD TSP the edges between nodes are assigned higher costs (weights), if they were traveled during the rush hour periods, or crossed the traffic jam regions, such as the city center(s). In this paper we introduce an even more real-life motivated approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem (IFTD TSP), which is a further extension of the TSP, and also of the classic TD TSP, with the additional notion of using intuitionistic fuzzy sets for the definition of uncertain costs, time, and space of the rush hour—traffic jam region affecting graph sections. In IFTD TSP we use fuzzy memberships and non-memberships sets for estimating the vague costs between nodes in order to quantify the behavior of traffic jam regions, and the rush hour periods. Since intuitionistic fuzzy sets are generalizations of classic fuzzy sets, our approach may be considered an extension and substitution of the original abstract TD TSP problem, even, of the (classic) Fuzzy TD TSP. Lastly, DBMEA (Discrete Bacterial Memetic Evolutionary Algorithm) was applied on the IFTD TSP model, the results of the simulation runs based on some extensions of the benchmarks generated from the original TD TSP data set showed quite good and promising preliminary results.