• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.2
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• pp.129-138
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• 2003

The traveling salesman problem (TSP) is an NP-hard problem. As the number of nodes increases, it takes a lot of time to find an optimal solution. Instead of considering all arcs, if we select and consider only some arcs more likely to be included in an optimal solution, we can find efficiently an optimal solution. Arc candidate set is a group of some good arcs. For the Lack of study in the asymmetric TSP. it needs to research arc candidate set for the asymmetric TSP systematically. In this paper, we suggest a regression function determining arc candidate set for the asymmetric TSP. We established the function based on 2100 experiments, and we proved the goodness of fit for the model through various 787problems. The result showed that the optimal solutions obtained from our arc candidate set are equal to the ones of original problems. We expect that this function would be very useful to reduce the complexity of TSP.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.2
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• pp.157-167
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• 2005

This paper presents a new perturbation technique for developing efficient iterated local search procedures for the asymmetric traveling salesman problem(ATSP). This perturbation technique uses global information on ATSP instances to speed-up computation and to improve the quality of the tours found by heuristic method. The main idea is to escape from a local optima by introducing perturbations on the out-of-kilter arcs in the problem instance. For a local search heuristic, we use the Kwon which finds optimum or near-optimum solutions by applying the out-of-kilter algorithm to the ATSP. The performance of our algorithm has been tested and compared with known method perturbing on randomly chosen arcs. A number of experiments has been executed both on the well-known TSPLIB instances for which the optimal tour length is known, and on randomly generated Instances. for 27 TSPLIB instances, the presented algorithm has found optimal tours on all instances. And it has effectively found tours near AP lower bound on randomly generated instances.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.52
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• pp.97-107
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• 1999

The asymmetric traveling salesman problem is a representative NP-Complete problem. Polynomial algorithm for this problem has not been yet found. So, many heuristic methods have been researched in this problem. We need heuristic methods that produce good answers for some larger problems in reasonable times. 3-opt is well known for the effective local-search heuristic method. It has been used in many applications of the asymmetric traveling salesman problem. This paper discusses 3-opt's properties and ineffective aspects and presents a highly effective heuristic method. 3-opt does not consider good arcs(shorter distance or little cost). This paper presents a fast heuritic algorithm compared with 3-opt by inserting good arcs and deleting related arcs later.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.2
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• pp.17-26
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• 2008

The traveling salesman problem is to find tours through all cities at minimum cost ; simply visiting the cities only once that a salesman wants to visit. As such, the traveling salesman problem is a NP-complete problem ; an heuristic algorithm is preferred to an exact algorithm. In this paper, we suggest an effective cost relaxation using a candidate arc set which is obtained from a regression function for the traveling salesman problem. The proposed method sufficiently consider the characteristics of cost of arcs compared to existing methods that randomly choose the arcs for relaxation. For test beds, we used 31 instances over 100 cities existing from TSPLIB and randomly generated 100 instances from well-known instance generators. For almost every instances, the proposed method has found efficiently better solutions than the existing method.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.33
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• pp.111-118
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• 1995

This paper suggests a hybrid genetic algorithm for asymmetric traveling salesman problem(TSP). The TSP was proved to be NP-complete, so it is difficult to find optimal solution in reasonable time. Therefore it is important to develope an algorithm satisfying robustness. The algorithm applies dynamic programming to find initial solution. The genetic operator is uniform order crossover and scramble sublist mutation. And experiment of parameterization has been performed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.518-518
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• 1996

• International Journal of Computer Science & Network Security
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• v.23 no.6
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• pp.193-201
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• 2023

In this paper, we consider the maximum scatter traveling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the minimum length edge in a salesman's tour that travels each city only once in a network. It is a very complicated NP-hard problem, and hence, exact solutions can be found for small sized problems only. For large-sized problems, heuristic algorithms must be applied, and genetic algorithms (GAs) are found to be very successfully to deal with such problems. So, this paper develops a hybrid GA (HGA) for solving the problem. Our proposed HGA uses sequential sampling algorithm along with 2-opt search for initial population generation, sequential constructive crossover, adaptive mutation, randomly selected one of three local search approaches, and the partially mapped crossover along with swap mutation for perturbation procedure to find better quality solution to the MSTSP. Finally, the suggested HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that the suggested HGA is better. Further, we provide solutions to some asymmetric TSPLIB instances of many sizes.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.59
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• pp.1-10
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• 2000

The traveling salesman problem is a representative NP-Complete problem. It needs lots of time to get a solution as the number of city increase. So, we need an efficient heuristic algorithm that gets good solution in a short time. Almost edges that participate in optimal path have somewhat low value cost. This paper discusses the property of nearest neighbor and 3-opt. This paper uses nearest neighbor's property to select candidate edge. Candidate edge is a set of edge that has high probability to improve cycle path. We insert edge that is one of candidate edge into intial cycle path. As two cities are connected. It does not satisfy hamiltonian cycle's rule that every city must be visited and departed only one time. This paper uses 3-opt's method to sustain hamiltonian cycle while inserting edge into cycle path. This paper presents a highly efficient heuristic algorithm verified by numerous experiments.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.9-18
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• 1996

Many algorithms have been developed for optimizing the asymmectric traveling salesman problem known as a representative NP-Complete problem. The most efficient ones of them are branch and bound algorithms based on the subtour elimination approach. To increase efficiency of the branch and bound algorithm. number of decision nodes should be decreased. For this the minimum bound that is more close at the optimal solution should be found or an effective bounding strategy should be used. If the optimal solution has been known, we may apply it usefully to branching. Because a good feasible solution should be found as soon as possible and have similar features of the optimal solution. By the way, the upper bound solution in branch and bound algorithm is most close at the optimal solution. Therefore, the upper bound solution can be used instead of the optimal solution and information of which can be applied to new branching criteria. As mentioned above, this paper will propose an effective branching rule using the information of the upper bound solution in the branch and bound algorithm. And superiority of the new branching rule will be shown by comparing with Bellmore-Malone's one and carpaneto-Toth's one that were already proposed.

• Management Science and Financial Engineering
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• v.7 no.2
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• pp.1-11
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• 2001

Gouveia and Pires (European Journal of Operations Research 112(1999) 134-146) have proposed four extended formulations having precedence variables as extra variables and characterized the projections of three of the four formulations into the natural variable space. In Gouveia and Pires (Discrete Applied Mathematics 112 (2001)), they also have introduced some other extended formulations with the same extra variables and conjectured that the projection of one of the proposed formulations is equivalent to the one proposed by Dantzig, Fulkerson, and Johnson (Operations Research 2(1954) 393-410). In this paper, we provide a unifying framework based on which we give alternative proofs on the projections of three extended formulations and new proofs on those of two formulations appeared in Gouveia and Pires(1999, 2001).