• Journal of the Korea Society of Computer and Information
• /
• v.21 no.9
• /
• pp.79-84
• /
• 2016

In this paper we consider the problem of finding the triplet (S,${\pi}$,f), where $S{\subseteq}V$, ${\pi}$ is a sequence of nodes in S and $f:V{\backslash}S{\rightarrow}S$ for a given complete graph G=(V,E). In particular, there exist two costs, $c^V_{uv}$ and $c^D_{uv}$ for $(u,v){\in}E$, and the cost of triplet (S,${\pi}$,f) is defined as $\sum_{i=1}^{{\mid}S{\mid}}c^V_{{\pi}(i){\pi}(i+1)}+2$ ${\sum_{u{\in}V{\backslash}S}c^D_{uf(u)}$. This problem is motivated by the integrated routing of the vehicle and drone for urban delivery services. Since a well-known NP-complete TSP (Traveling Salesman Problem) is a special case of our problem, we cannot expect to have any polynomial-time algorithm unless P=NP. Furthermore, for practical purposes, we may not rely on time-exhaustive enumeration method such as branch-and-bound and branch-and-cut. This paper suggests the simple heuristic which is motivated by the MST (minimum spanning tree)-based approximation algorithm and neighborhood search heuristic for TSP.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.13 no.3
• /
• pp.431-437
• /
• 2010

It's strongly needed to minimize the logistics response time for supporting military operations in wartime. In this paper, we suggest the ILP formulation for minimizing logistics response time in wartime. Main structure of this formulation is based on the traveling purchaser problem(TPP) which is a generalized form of the well-known traveling salesman problem(TSP). In the case of general TPP, objective function is to minimize the sum of traveling cost and purchase cost. But, in this study, objective function is to minimize traveling cost only. That's why it's more important to minimize traveling cost(time or distance) than purchase cost in wartime. We find out optimal solution of this problem by using ILOG OPL STUDIO(CPLEX v.11.1) and do the sensitive analysis about computing time according to number of operated vehicles.

• The KIPS Transactions:PartB
• /
• v.10B no.3
• /
• pp.237-242
• /
• 2003

Ant Colony System (ACS) Algorithm is new meta heuristic for hard combinatorial optimization problem. It is a population based approach that uses exploitation of positive feedback as well as greedy search. It was first proposed for tackling the well known Traveling Salesman Problem (TSP). In this paper, we introduce ACS of new method that adds reinforcement value for each edge that visit to Local/Global updating rule. and the performance results under various conditions are conducted, and the comparision between the original ACS and the proposed method is shown. It turns out that our proposed method can compete with tile original ACS in terms of solution quality and computation speed to these problem.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.35 no.1
• /
• pp.111-124
• /
• 2010

In the last decade, traveling purchaser problem (TPP) has received some attention of the researchers in the operational research area. TPP is a generalization of the well-known traveling salesman problem (TSP), which has many real-world applications such as purchasing the required raw materials for the manufacturing factories and the scheduling of a set of jobs over some machines, and many others. In this paper we suggest heterogeneous multiple traveling purchaser problem with budget constraint (HMTPP-B) which looks for several cycles starting at and ending to the depot and visiting a subset at a minimum traveling cost and such that the demand for each product is satisfied and the cost spent for purchasing the products does not exceed a given budget threshold. All the past studies of TPP are restricted on a single purchaser. Therefore we randomly generated some instances. CPLEX is used for getting optimal solutions in these experiments.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.4
• /
• pp.217-222
• /
• 2011

Genetic algorithms are one of the most important methods used to solve the Traveling Salesman Problem. Therefore, many researchers have tried to improve the Genetic Algorithm by using different methods and operations in order to find the optimal solution within reasonable time. This paper intends to find a new approach that adopts an improved genetic algorithm to solve the Traveling Salesman Problem, and compare with the well known heuristic method, namely, Kohonen Self-Organizing Map by using different data sets of symmetric TSP from TSPLIB. In order to improve the search process for the optimal solution, the proposed approach consists of three strategies: two separate tour segments sets, the improved crossover operator, and the improved mutation operator. The two separate tour segments sets are construction heuristic which produces tour of the first generation with low cost. The improved crossover operator finds the candidate fine tour segments in parents and preserves them for descendants. The mutation operator is an operator which can optimize a chromosome with mutation successfully by altering the mutation probability dynamically. The two improved operators can be used to avoid the premature convergence. Simulation experiments are executed to investigate the quality of the solution and convergence speed by using a representative set of test problems taken from TSPLIB. The results of a comparison between the new approach using the improved genetic algorithm and the Kohonen Self-Organizing Map show that the new approach yields better results for problems up to 200 cities.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.46 no.1
• /
• pp.15-22
• /
• 2023

An Ant Colony Optimization Algorithm(ACO) is one of the frequently used algorithms to solve the Traveling Salesman Problem(TSP). Since the ACO searches for the optimal value by updating the pheromone, it is difficult to consider the distance between the nodes and other variables other than the amount of the pheromone. In this study, fuzzy logic is added to ACO, which can help in making decision with multiple variables. The improved algorithm improves computation complexity and increases computation time when other variables besides distance and pheromone are added. Therefore, using the algorithm improved by the fuzzy logic, it is possible to solve TSP with many variables accurately and quickly. Existing ACO have been applied only to pheromone as a criterion for decision making, and other variables are excluded. However, when applying the fuzzy logic, it is possible to apply the algorithm to various situations because it is easy to judge which way is safe and fast by not only searching for the road but also adding other variables such as accident risk and road congestion. Adding a variable to an existing algorithm, it takes a long time to calculate each corresponding variable. However, when the improved algorithm is used, the result of calculating the fuzzy logic reduces the computation time to obtain the optimum value.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.3
• /
• pp.37-49
• /
• 1993

In this paper, the TSP(traveling salesman problem) which its costs(distance) between nodes are defined with Max($\bar{x}$, $\bar{y}$) has been dealt. In order to find a satisfactory solution for this kind of problem, we generate weighted matrix, and then develope a new heuristic problem solving method using the weighted matrix. Also we analyze the effectiveness of the newly developed heuristic method comparing it with other heuristic algorithm already exists for Euclidean TSP. Finally, we apply a new developed algorithm to real Max($\bar{x}$,$\bar{y}$) TSP such as PCB inserting.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.40 no.6
• /
• pp.87-94
• /
• 2003

One of the important fields for heuristic algorithm is how to balance between Intensification and Diversification. Ant Colony Optimization(ACO) is a new meta heuristic algorithm to solve hard combinatorial optimization problem. It is a population based approach that uses exploitation of positive feedback as well as Breedy search It was first Proposed for tackling the well known Traveling Salesman Problem(TSP). In this paper, we deal with the performance improvement techniques through balance the Intensification and Diversification in Ant Colony System(ACS). First State Transition considering the number of times that agents visit about each edge makes agents search more variously and widen search area. After setting up criteria which divide elite tour that receive Positive Intensification about each tour, we propose a method to do addition Intensification by the criteria. Implemetation of the algorithm to solve TSP and the performance results under various conditions are conducted, and the comparision between the original An and the proposed method is shown. It turns out that our proposed method can compete with the original ACS in terms of solution quality and computation speed to these problem.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.169.5-169
• /
• 2001

This study proposes a neural network for solving optimization problems such as the TSP (Travelling Salesman Problem), scheduling, and line balancing. The Hopfield network has been used for solving such problems, but it frequently gives abnormal solutions or non-optimal ones. Moreover, the Hopfield network takes much time especially in solving large size problems. To overcome such disadvantages, this study adopts nodes whose outputs changes with a fixed value at every evolution. The proposed network is applied to solving a TSP, finding the shortest path for visiting all the cities, each of which is visted only once. Here, the travelling path is reflected to the energy function of the network. The proposed network evolves to globally minimize the energy function, and a ...

• IE interfaces
• /
• v.24 no.1
• /
• pp.51-57
• /
• 2011

The traveling purchaser problem (TPP) is a generalization of the well-known traveling salesman problem (TSP), which has many real-world applications such as purchasing the required raw materials for the manufacturing factories and the scheduling of a set of jobs over some machines, and many others. In the last decade, TPP has received some attention of the researchers in the operational research area. However, all of the past researches for TPP are restricted on a single purchaser (vehicle). It could be the limitation to solve the real world problem. The purpose of this paper is to suggest the capacitated multiple TPP (CMTPP). It could be used in inbound logistics optimization in supply chain management area and many others. Since TPP is known as NP-hard, we also developed the heuristic algorithm to solve the CMTPP.