• 한국경영과학회지
• /
• 제14권2호
• /
• pp.53-66
• /
• 1989

The Public Vehicle Routing Problem (PVRP) is to find the minimum total cost routes of M or less Public-Vehicles to traverse the required arcs(streets) at least once, and return to their starting depot on a directed network. In this paper, first, a mathematical model is formulated as minimal cost flow model with illegal subtour elimination constraints, and with the fixed cost and routing cost as an objective function. Second, an efficient branch and bound algorithm is developed to obtain an exact solution. A subproblem in this method is a minimal cost flow problem relaxing illegal subtour elimination constraints. The branching strategy is a variable dichotomy method according to the entering nonrequired arcs which are candidates to eneter into an illegal subtour. To accelerate the fathoming process, a tighter lower bound of a candidate subproblem is calculated by using a minimum reduced coast of the entering nonrequired arcs. Computational results based on randomly generated networks report that the developed algorithm is efficient.

• 한국지형학회지
• /
• 제24권4호
• /
• pp.103-115
• /
• 2017

This paper shows the types of deteriorated hiking trails and degrading factors at three Great Walks such as Tongariro Alpine Crossing, Routeburn Track and Kepler Track in New Zealand. The deteriorated trails could be classified into gullying, widening, narrowing, branching and sidewall erosion. Department of Conservation carefully manages overland flows on trails for preventing surface erosion, thus the Great Walks show only a minor problem of gully on trails which is usually active in a mountainous area. Widening and branching of trails caused by tread erosion are not also developed due to the restriction of visitors as well as the management of rainwash. However, despite the detailed maintenance and prevention of an overuse of trails, some trails traversing steep slopes in a alpine zone under a periglacial environment are severely degraded along their sidewalls. It suggests that a unvegetated sidewall of trails has to be strictly managed in an early stage of occurrence and a slope-traversing section should be selected with more consideration when establishing a route of hiking trails.

• 한국경영과학회지
• /
• 제16권2호
• /
• pp.86-102
• /
• 1991

The purpose of this paper is to present a branch and bound algorithm for the hierarchical transportation network design problem in 2-level directed networks. This problem is to find the least cost of hierarchical transportation networks which consist of a primary path and a secondary path. The primary path is a simple path from a prespecified orgin node to a prespecified terminal node. All nodes must be either a transsipment node on the primary path or connected to that path via secondary arcs. This problem is formulated to a 0-1 inter programming problem with assignment and illegal subtour elimination equations as constaints. We show that the subproblem relaxing subtour elimination constraints is transformed to a linear programming problem by means of the totally unimodularity. Optimal solutions of this subproblem are polynoially obtained by the assignment algorithm and complementary slackness conditions. Therefore, the optimal value of this subproblme is used as a lower bound. When an optimal solution of the subproblem has an illegal subtour, a better disjoint rule is adopted as the branching strategy for reducing the number of branched problems. The computational comparison between the least bound rule and the depth first rule for the search strategy is given.

• 한국융합학회논문지
• /
• 제7권5호
• /
• pp.213-219
• /
• 2016

본 논문에서는 한 개의 선형 제약식 하에서 의사결정변수가 상한 값을 갖는 오목 함수 최소화 문제를 다룬다. 제시된 분지 한계 해법은 단체를 분할 단위로 사용하였다. 오목함수를 가장 단단하게 하한추정하는 볼록덮개함수를 단체 상에서 유일하게 구할 수 있기 때문이다. 분지가 일어날 때마다 후보 단체로부터 1 차원 낮은 2 개의 하위 단체들이 생성된다. 이 때 후보 단체에 포함되어 있던 가능해 집합은 각각의 하위 단체로 분할된다. 한계 연산 절차는 선형인 볼록 덮개 함수를 목적 함수로 하는 선형계획법을 부문제로 정의하고 해를 구한다. 부문제의 최적 목적함수 값으로부터 최적 오목목적함수의 하한과 상한을 갱신하고, 원문제의 최적해를 포함하지 않는 단체들을 고려 대상에서 제외시킨다. 본 해법의 최대 장점은 하위 단체로 분할될수록 부문제들의 크기가 점점 작아진다는데 있다. 이것은 한계 연산의 계산량이 줄어든다는 것을 의미한다. 본 연구의 결과는 배낭 제약식 유형의 제약식 하에서의 오목 함수 최소화 문제의 해법을 개발하는데 응용될 수 있을 것이다.

• 한국통신학회논문지
• /
• 제19권12호
• /
• pp.2386-2396
• /
• 1994

본 논문에서는 최적의 유한 정밀도 계수를 갖는 1차원 및 2차원 필터 설계 알고리듬을 제안하였다. 제안된 알고리듬은 선형 계획(LP-linear programming)을 반복적으로 사용하는 BaB(branch and bound) 알고리듬에 인접해 있는 SP(sub-problem)들의 최적해가 서로 매우 밀접한 관계가 있다는 사실에 기초를 두고 있다. 기존의 설계 알고리듬은 각 SP를 풀기 위하여 LP를 새로 수행한 반면에, 제안된 알고리듬은 인접한 SP들 사이의 관계를 이용하여 LP의 입력이 되는 주파수 제한조건의 수를 크게 줄인다. 따라서 기존의 방법에 비하여 전체적인 이산계수 FIR 필터 설계의 계산량이 줄어든다. 또한, 본 논문에서는 계수가 특히 2의 멱승의 합으로 주어지는 경우 기존의 방법보다 더욱 효율적인 가지치기 방법을 제안하였다. 이러한 가지치기 방법을 제안된 LP 해결 방법과 함께 이용함으로써 2의 멱승의 합으로 계수가 주어지는 필터의 설계 시간을 더욱 크게 줄일 수 있음을 보였다.

• Bulletin of the Korean Chemical Society
• /
• 제26권11호
• /
• pp.1735-1737
• /
• 2005

We obtain probabilities at a crossing of two linearly time-dependent potentials that are constantly coupled to the other by solving a time-dependent Schrödinger equation. We find that the system which was initially localized at one state evolves to split into both states at the crossing. The probability splitting depends on the coupling strength $V_0$ such that the system stays at the initial state in its entirety when $V_0$ = 0 while it is divided equally in both states when $V_0 \rightarrow {\infty}$ . For a finite coupling the probability branching at the crossing is not even and thus a complete probability transfer at $t \rightarrow {\infty}$ is not achieved in the linear potential crossing problem. The Landau-Zener formula for transition probability at $t \rightarrow {\infty}$ is expressed in terms of the probabilities at the crossing.

• 한국경영과학회지
• /
• 제19권1호
• /
• pp.153-168
• /
• 1994

This paper is concerned with the development of tree-search algorithm for the exact solution to the vehicle problem (VRP), where set of vehicles of known capacity based at depot, have to be routed in order to supply customers with known requirements. When is required is to design routes, so that the total cost (i. e. total route length or time duration, ect.) is minimized. For obtianing the exact solution, the most important factors are the value of bound and branching strategy. Using the bound based on with bound ascent procedures from subgradient and state-space ascents, the incorporation of bounds into tree search algorithm to solve the problem is shown. Computational results of the corresponding algorithm show that VRPs with up to 40 customers can be solved optimally with this algorithm.

• International Journal of Computer Science & Network Security
• /
• 제24권1호
• /
• pp.45-51
• /
• 2024

The subject of navigation has drawn a large interest in the last few years. The navigation within a city is to find the path between two points, source location and destination location. In many cities, solving the routing problem is very essential as to find the route between different locations (starting location (source) and an ending location (destination)) in a fast and efficient way. This paper considers streets with diagonal streets. Such streets pose a problem in determining the directions of the route to be followed. The paper presents a solution for the path planning using the reconfigurable mesh (R-Mesh). R-Mesh is a parallel platform that has very fast solutions to many problems and can be deployed in moving vehicles and moving robots. This paper presents a solution that is very fast in computing the routes.

• 한국경영과학회:학술대회논문집
• /
• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
• /
• pp.137-144
• /
• 2003

We consider Two-echelon Single source Capacitated Facility Location Problem (TSCFLP). TSCFLP is a variant or Capacitated Facility Location Problem (CFLP). which has been an important issue in boa academic and industrial aspects. Given a set or possible facility locations in two echelons (warehouse / plant), a set or customers, TSCFLP is a decision problem to find a set or facility locations to open and to determine an allocation schedule that satisfies the demands or the customers and the capacity constraints or the facilities, while minimizing the overall cost. It ran be shown that TSCFLP Is strongly NP-hard For TSCFLf, few algorithms are known. which are heuristics. We propose a disaggregated version or the standard mixed integer programming formulation or TSCFLP We also provide a class or valid Inequalities Branch-and-price algorithm with rutting plane method Is used to find an optimal solution Efficient branching strategy compatible with subproblem optimization problems Is also provided. We report computational results or tests on 15 randomly generated instances.

• International Journal of Computer Science & Network Security
• /
• 제21권4호
• /
• pp.1-8
• /
• 2021

The subject of navigation has drawn a large interest in the last few years. Navigation problem (or path planning) finds the path between two points, source location and destination location. In smart cities, solving navigation problem is essential to all residents and visitors of such cities to guide them to move easily between locations. Also, the navigation problem is very important in case of moving robots that move around the city or part of it to get some certain tasks done such as delivering packages, delivering food, etc. In either case, solution to the navigation is essential. The core to navigation systems is the navigation algorithms they employ. Navigation algorithms can be classified into navigation algorithms that depend on maps and navigation without the use of maps. The map contains all available routes and its directions. In this proposal, we consider the first class. In this paper, we are interested in getting path planning solutions very fast. In doing so, we employ a parallel platform, Reconfigurable mesh (R-Mesh), to compute the path from source location to destination location. R-Mesh is a parallel platform that has very fast solutions to many problems and can be deployed in moving vehicles and moving robots. This paper presents two algorithms for path planning. The first assumes maps with linear streets. The second considers maps with branching streets. In both algorithms, the quality of the path is evaluated in terms of the length of the path and the number of turns in the path.