• 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.

• IE interfaces
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• v.24 no.2
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• pp.112-118
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• 2011

This paper introduces one type of prize collecting travelling salesman problem with time windows (PCTSPTW), proposes a mixed integer programming model for the problem, and shows that the problem can be reduced to the elementary shortest path problem with time windows and capacity constraints (ESPPTC). Then, a new dynamic programming algorithm is proposed to solve ESPPTC quickly. Computational results show the effectiveness of the proposed algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.04a
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• pp.328-338
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• 1994

TSP(Traveling Salesman Problem) is a famous problem in Operations Research fields due to its applicability to various problems. It is also well-known that the problem is hard to solve in reasonable time, since it is in the NP-Complete class. Hence it is desired to develop heuristics which have polynominal complexity and also solve the problem to near-optimality. This paper presents a heuristic algorithm for TSP using the concept of dynamic programming. The proposed method has the complexity of O(N$\^$3/), and gives improved solutions than other well-known algorithms in our extensive computational experiments.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.135-138
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• 1996

In solving the Travel Salesman Problem(TSP), we easily reach local optimal solutions with the existing methods such as TWO-OPT, THREE-OPT, and Lin-Kernighen. Tabu search, as a meta heuristic, is a good mechanism to get an optimal or a near optimal solution escaping from the local optimal. By utilizing AI concepts, tabu search continues to search for improved solutions. In this study, we focus on developing a new neighborhood structure that maintains the feasibility of the tours created by exchange operations in TSP. Intelligent methods are discussed, which keeps feasible tour routes even after exchanging several edges continuously. An extended tabu search model, performing cycle detection and diversification with memory structure, is applied to TSP. The model uses effectively the information gathered during the search process. Finally, the results of tabu search and simulated annealing are compared based on the TSP problems in the prior literatures.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.2
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• pp.120-129
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• 2004

This paper provides a simple but effective method, cost relaxation to escape from a local optimum of the traveling salesman problem. We would find a better solution if we repeat a local search heuristic at a different initial solution. To find a different initial solution, we use the cost relaxation method relaxing the cost of arcs. We used the Lin-Kernighan algorithm as a local search heuristic. In experimental result, we tested large instances, 30 random instances and 34 real world instances. In real-world instances, we found average 0.17% better above the optimum solution than the Concorde known as the chained Lin-Kernighan. In clustered random instances, we found average 0.9% better above the optimum solution than the Concorde.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.18-24
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• 2001

This paper presents a model and a heuristic algorithm for the Traveling Salesman Problem with Time Windows(TSPTW). The main difference of our model compared with the previous ones lies in that the time windows we are concerned are more flexible and realistic than the previous ones. In the typical TSPTW, the service at a node must begin within the time grid called the time window that is defined by the earliest and the latest time to start the service at each node. But, in real business practice, a lateness cost is usually penalized rather than the service is prohibited at all when a vehicle arrives after the latest time. Considering this situation, we develop a model with a new time window that allows an arrival after the latest time and penalizes the late arrival by charging a lateness cost. A two-phased heuristic algorithm is proposed for the model and is extensively tested to verify the accuracy and efficiency of the algorithm.

• Journal of the Korean Society for Railway
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• v.9 no.2 s.33
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• pp.206-211
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• 2006

This thesis presents railroad crew restoring problem, which is to determine the railroad plan allocation. This problem is constructed that determine the sequence of duties that railroad crews have to perform. We analyze characteristic of this problem and railroad industry. It's hard to consider many constraint conditions. We propose Integer Programming model and easy methodology to be considered all given operation rules. This problem is known to be NP-hard. We develop a genetic algorithm, which is proved to be powerful in solving optimization problems. We proposed the effective mathematical model and algorithm about making crew restoring in real industry.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.127-135
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• 2000

This paper provides a new method of initializing neurons used in self-organizing neural networks and sequencing input nodes for applying to Euclidean traveling salesman problem. We use a general property that in any optimal solution for Euclidean traveling salesman problem, vertices located on the convex hull are visited in the order in which they appear on the convex hull boundary. We composite input nodes as number of convex hulls and initialize neurons as shape of the external convex hull. And then adapt input nodes as the convex hull unit and all convex hulls are adapted as same pattern, clockwise or counterclockwise. As a result of our experiments, we obtain l∼3 % improved solutions and these solutions can be used for initial solutions of any global search algorithms.

• 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 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.