Parallel techniques for solving large scale travelling salesperson problems

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 shortest route finding problem is a significant topic in graph theory and combinatorial optimization, with wide applications in logistics, transportation, and scheduling. This research aims to improve the quality of the solution and time efficiency in solving the Traveling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algorithm using the application of the Tabu Search algorithm. The CIH algorithm constructs an initial solution by inserting points based on minimum weight. At the same time, the Tabu Search algorithm is applied to enhance the solution by avoiding local optima using a tabu list mechanism. The research data, consisting of the distances between parking retribution collection points by the Malang City Transportation Agency in Sukun Sub-district, were obtained from Google Maps. The algorithm performance evaluation is done by comparing the total mileage before and after optimization, and statistically analyzed using the Wilcoxon signed-rank test because the data does not follow a normal distribution. The results showed that optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted in routes with shorter travel distances than using the CIH algorithm alone. This finding proves that optimizing the CIH algorithm with Tabu Search increases the effectiveness of finding the shortest route.The shortest route finding problem is a significant topic in graph theory and combinato-rial optimization, with wide applications in logistics, transportation, and scheduling. Thisresearch aims to improve the quality of the solution and time efficiency in solving the Trav-eling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algo-rithm using the application of the Tabu Search algorithm. The CIH algorithm constructs aninitial solution by inserting points based on minimum weight. At the same time, the TabuSearch algorithm is applied to enhance the solution by avoiding local optima using a tabulist mechanism. The research data, consisting of the distances between parking retributioncollection points by the Malang City Transportation Agency in Sukun Sub-district, were ob-tained from Google Maps. The algorithm performance evaluation is done by comparing thetotal mileage before and after optimization, and statistically analyzed using the Wilcoxonsigned-rank test because the data does not follow a normal distribution. The results showedthat optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted inroutes with shorter travel distances than using the CIH algorithm alone. This finding provesthat optimizing the CIH algorithm with Tabu Search increases the effectiveness of findingthe shortest route.

Traveling Salesman Problem (TSP) is one of the distribution issues which is long discussed in the optimization review, where the review problem is how a salesman visits the entire travel route within the coverage area and returns to the starting point of departure with the rule that no destination should be visited more than once. PT. Panjunan is a company engaged in the products distribution of various principles. Currently the managing process of customer location data at the company is still not maximal due to the absence of calculations in every daily visit routes so it impact on the effectiveness of time. In addition, the absence of visualization of real customer data on the field leads to the error distribution and marketing of goods which is uneven, not on target and impact on the decline in sales value. One of the techniques used to accelerate the search solutions of TSP problems is to use an insertion algorithm, or also called the Cheapest Insertion Heuristic (CIH) algorithm. The discussion of this research is to study and apply CIH algorithm in determining the optimization of daily sales traffic route with the aim of this research is to make daily trip route optimization program by applying Cheapest Insertion Heuristics algorithm and provide real customer data visualization on original map in the field as analysis material for operational team and management by utilizing Google Maps API service. System development method used in this research using waterfall model with implementation tools is laravel framework and mySQL as DBMS.

The Traveling Salesman Problem (TSP) is a combinatorial optimization problem which has a plethora of real-world applications in various domains. Since large scale TSP problems are difficult to be solved by deterministic algorithms in a reasonable amount of time, heuristic and meta-heuristic algorithms such as swarm intelligence algorithms are usually used for solving TSP. These algorithms provide near-optimal solutions in a feasible amount of time. The Dragonfly Algorithm (DA) is a recent swarm intelligence algorithm and it has shown to have a higher performance as compared to other swarm intelligence algorithms in various applications. Since the original DA algorithm is proposed for solving continuous optimization problems, it cannot be used for solving TSP and although a binary version of the algorithm, called BDA, is also proposed, it is not suitable for solving TSP. Hence, in this paper, a variant of the DA algorithm is proposed. DA is adapted for solving TSP by adapting its equations and making use of the method of swap sequences to update the position of the artificial dragonflies in the search space. The algorithm is employed to solve a TSP problem which consists of four cities and the results show that the proposed algorithm is able to provide the optimal TSP path.

In this paper, we present some new results obtained for the traveling salesman problem (TSP) by using the iterated tabu search (ITS) meta-heuristic. ITS is a promising extension to the ordinary tabu search scheme. It seeks near-optimal solutions by combining intensification (standard tabu search) and diversification (perturbation of solutions) in a proper way. For the TSP, the main effect is achieved due to decomposition of the solution neighbourhood structure and considerably speeding-up the tabu search process, which is used, namely, in the role of intensification. This fast-iterated tabu search (FITS) technique resulted in quite encouraging solutions for the TSP instances from the TSP instance library TSPLIB. FITS obviously outperformed the other heuristic algorithms used in the experimentation, especially, on the smaller TSP instances.

A new heuristic algorithm is proposed by this paper, on multi-objective optimization using metaheuristics and TSP (travelling salesman problems). Basic thinking behind this algorithm is minimizing the TSP path or tour by dividing the entire tour into blocks that are overlapped to each other and then improve each individual block separately. Although it is unproven that a good solution have small improvement chances if a node moved far way to a position compared to its original solution. By intensively searching each block, further improvement is possible in TSP path or tour that never be supported in various search methods and genetic algorithm. Proposed algorithm and computational experiment performance was tested, and these tests are carried out with support of already present instances of problem. According to the results represented by paper, the computation verifies that proposed algorithm can solve TSPs efficiently. Proposed algorithm is then used for selecting optimal test cases, thousands of those test cases which are selected after confirming that they identify bugs and they itself selected from a repository of test cases; these thousand test cases are those test cases which are selected from several thousand test cases because they detect bugs. Few test cases from repository act as milestones (nodes) and having certain weight associated with each, proposed algorithm based on TSP implemented over selected result and select the optimal result or path or solution. These selected optimal test cases or selected path are further used to perform the regression testing, by applying those test cases selected by proposed algorithm in order to remove most of the faults or bugs effectively, i.e. take less time and identify almost all the bugs with few test cases. Hence this proposed algorithm assures most effective solution for regression testing test case selection.

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.

This work shows the application of Wang’s Recurrent Neural Network with the Winner Takes All (WTA) principle to solve the classic Operational Research problem called the Traveling Salesman Problem. The upgrade version proposed in this work for the ‘Winner Takes All’ principle is called soft, because the winning neuron is updated with only part of the activation values of the other competing neurons. The problems in the TSPLIB (Traveling Salesman Problem Library Reinelt, 1991) were used to compare the soft version with the ‘Winner Takes All’ hard version and they show improvement in the results using the 'Winner Takes All' soft version in most of the problems tested. The implementation of the technique proposed in this paper uses the parameters of Wang‘s Neural Network for the Assignment problem (Wang, 1992; Hung & Wang, 2003) using the ’Winner Takes All' principle to form Hamiltonian circuits (Siqueira et al. 2007) and can be used for both symmetric and asymmetric Traveling Salesman Problems. The 2-opt technique is used to improve the routes found with the proposed Neural Network, thus becoming a technique that is competitive to other Neural Networks. Other heuristic techniques have been developed recently to solve the Traveling Salesman Problem, and the work of Misevicius et al. (2005) shows the use of the ITS (Iterated Tabu Search) technique with a combination of intensification and diversification of solutions for the TSP. This technique is combined with the 5-opt and errors are almost zero in almost all of the TSPLIB problems tested. The work of Wang et al. (2007) shows the use of Particle Swarm to solve the TSP with the use of the fraction (quantum) principle to better guide the search for solutions. The authors make comparisons with Hill Climbing, Simulated Annealing and Tabu Search, and show in a 14-cities case that the results are better than those of the other techniques. In the area of Artificial Neural Networks, an interesting technique can be found in the work of Massutti & Castro (2009), who use a mechanism to stabilize winning neurons and the centroids of the groups of cities for the growing and pruning the network. The authors show modifications in the Rabnet’s (real-valued antibody network) parameters for the Traveling Salesman Problem and comparisons made with TSPLIB problems solved by other techniques show that the Rabnet has better results.

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.

Nurse Rostering Problem (NRP) is one of NP - hard combinatorial optimization problems about the distribution of medical resources. In the past, there have been several proposed methods like heuristic algorithms and algorithms based on establishing rigorous mathematical models. Especially, the hybrid algorithm combined integer programming and evolutionary algorithm (IP+EA) have been proved to be effective for NRP. However, these methods are not efficient in dealing with large-scale NPR instances, like Chinese NRP. In order to overcome the premature convergence of IP+EA, we propose a hybrid evolutionary algorithm based on scout bee global search strategy. Inspired by the behavior of scouts in artificial bee colony algorithms, the global search is integrated into EA, which can lead the algorithm to escape from local optima. The experimental results indicate that, our proposed approach is more effective than several existing algorithms to solve the Chinese NRP.

Summary form only given, as follows. A stochastic neural model is proposed for the solution of hard combinatorial optimization problems, inspired by the Hopfield-Tank model and the stochastic search ability of simulated annealing. The authors start with a discrete-time algorithm for the simulation of a Hopfield-Tank network and modify it through the incorporation of probabilistic decisions which allow energy increases at each time step. The algorithm has been tested on the traveling salesman problem (TSP), and the results are encouraging. For these tests the authors used a formulation of TSP which ensures that every stable state of the network corresponds to a feasible TSP tour. From the simulation algorithm they then extract some possible foundations for the formalization of their model. >

A heuristic algorithm is developed for the classical scheduling problem in which independent jobs are nonpreemptively scheduled on identical parallel machines with the objective of minimizing the makespan with load balancing. The algorithm uses iteratively the LPT procedure to be successful computational tools in many hard Combinatorial Optimization problems. We present an approximation algorithm based on balance the Hopfild with binary decision variables which are a kind of assignment variables for the classical deterministic scheduling problem of minimizing the makespan on identical machines. These problems are characterized by their complexity, known as NP-hard in most cases. Computational results indicate that the proposed algorithm is very competitive with respect to well-known constructive algorithms for a large number of benchmark.

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.

We eliminate the useless edges for traveling salesman problem (TSP) based on frequency \(K_5\)s. A frequency \(K_5\) is computed with ten optimal five-vertex paths with given endpoints in a corresponding \(K_5\) in \(K_n\). A binomial distribution model is built based on frequency \(K_5\)s. As the frequency of each edge is computed with N frequency \(K_5\)s, the binomial distribution demonstrates that the frequency of an optimal Hamiltonian cycle edge is bigger than 4N on average. Thus, one can eliminate the edges with frequency below 4N to reduce the number of concerned edges for resolving TSP. A heuristic algorithm is given to eliminate the useless edges. After many useless edges are cut, the computation time of algorithms for TSP will be considerably reduced.

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.