Earticle

This paper covers algorithms to determine a machine assignment strategy to locations on a single straight track by minimizing the total backtrack distance. Three different algorithms ar presented: an efficient heuristic procedure, the branch-and-bound algorithm, and the nerual network approach. Simulation results show that the proposed algorithms have potential power to design an on-line optimizer.

이진트리의 최소 선형 배열(MinLA) 문제의 해는 선형 복잡도 의 근사 알고리즘으로 구하고 있으며, 에 대해 다양한 근사 알고리즘 수행 결과가 제시되어 있고, 단지 2개 알고리즘만이 최적 해 3,696을 얻었다. 본 논문은 이진트리의 정확한 해를 복잡도로 구하는 알고리즘을 제안하였다. 제안된 알고리즘은 먼저, 개 노드들에 중위 탐색(in-order search) 방법으로 번호를 부여하고, 와 레벨에 존재하는 노드들에 대해 단 노드 자식들까지의 범위를 대상으로 번호를 재배열하는 방법을 적용하였다. 제안된 알고리즘을 에 적용한 결과 Chung[14]의 이론을 증명하였으며, 에 대해서는 Chung[14]의 60보다 좋은 58을 얻었다. 또한, 기존의 근사 알고리즘들은 배열 결과를 제시하지 않고 있는데 비해 제안된 알고리즘은 정확한 배열 방법도 제시하는 장점을 갖고 있다. 따라서 제안된 알고리즘은 인 이진트리에 대해서도 항상 빠르게 최적의 해를 얻을 수 있기 때문에 기존의 근사 알고리즘을 적용하지 않아도 된다.

In the deficiency of an exact solution yielding algorithm, approximate algorithms remain as a solely viable option to the Minimum Linear Arrangement(MinLA) problem of Binary tree. Despite repeated attempts by a number of algorithm on , only two of them have been successful in yielding the optimal solution of 3,696. This paper therefore proposes an algorithm of complexity that delivers the exact solution to the binary tree. The proposed algorithm firstly employs an In-order search method by which number of nodes are assigned with a distinct number. Then it reassigns the number of all nodes that occur on level and , including that of child of leaf node. When applied to , the proposed algorithm has proven Chung[14]’s conjecture and obtained a superior result. Moreover, on the contrary to existing algorithms, the proposed algorithm illustrates a detailed assignment method. Capable of expeditiously obtaining the optimal solution for the binary tree of , the proposed algorithm could replace the existing approximate algorithms.

격자 그래프의 최소 선형 배열(MinLA)은 선형 복잡도 O(n) 의 근사 알고리즘이 적용되고 있으며, 33×33격자의 최적 MinLA는 31,680으로 알려져 있다. 본 논문은 격자의 정확한 해 MinLA를 복잡도 O(1)으로 구하는 분할배열 알고리즘을 제안하였다. 분할배열 알고리즘은 컨테이너에 박스를 넣는 방법으로 m행을 r1, r2, r3로, n열을 c1, c2, c3로 분할하여 7개 컨테이너를 얻고 규칙을 가지도록 분할한다. 분할된 박스들에 있는 정점들 위치 순서로 번호를 부여하여 MinLA를 구한다. m,n ≥ 11에 대해 C2, C4, C6박스 크기를 2씩 증가시키면서 MinLA가 증가할 때까지 반복 수행한다. 이 과정은 에 대해 최대 4회 반복 수행하는 특징이 있다. 제안된 알고리즘은 m=n과 m≠n인 모든 격자에 적용할 수 있다. 분할배열 알고리즘을 2≤n≤100 격자에 적용하였으며, 33×33과 100×100격자에 대해 기존 알고리즘들보다 월등히 좋은 최적의 결과를 얻었다. 제안된 알고리즘은 간단하면서도 보다 정확한 해를 얻을 수 있어 m,n이 무한히 크더라도 쉽게 해를 얻을 수 있어 VLSI 회로 설계 분야에 응용이 될 수 있을 것이다.

This paper deals with the minimum linear arrangement(MinLA) of a lattice graph, to which an approximate algorithm of linear complexity O(n) remains as a viable solution, deriving the optimal MinLA of 31,680 for 33×33 lattice. This paper proposes a partitioning arrangement algorithm of complexity O(1) that delivers exact solution to the minimum linear arrangement. The proposed partitioning arrangement algorithm could be seen as loading boxes into a container. It firstly partitions m rows into r1, r2, r3 and n columns into c1, c2, c3 , only to obtain 7 containers. Containers are partitioning with a rule. It finally assigns numbers to vertices in each of the partitioned boxes location-wise so as to obtain the MinLA. Given m,n ≥ 11, the size of boxes C2, C4, C6 is increased by 2 until an increase in the MinLA is detected. This process repeats itself 4 times at maximum given m,n ≤ 100. When tested to lattice in the range of 2 ≤ n ≤ 100, the proposed algorithm has proved its universal applicability to lattices of both m=n and m≠n. It has also obtained optimal results for 33×33 and 100×100 lattices superior to those obtained by existing algorithms. The minimum linear arrangement algorithm proposed in this paper, with its simplicity and outstanding performance, could therefore be also applied to the field of Very Large Scale Integration circuit where m,n are infinitely large.

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

We consider facility layout problems, where mn facility units are assigned into mn cells. These cells are arranged into a rectangular pattern with m rows and n columns. In order to solve this cell type facility layout problem, many approximation algorithms with improved local search methods were studied because it was quite difficult to find exact optimum of such problem in case of large size problem. In this paper, new algorithms based on Simulated Annealing (SA) method with two neighborhood generation methods are proposed. The new neighborhood generation method adopts the exchanging operation of facility units in accordance with adjacent preference. For evaluating the performance of the neighborhood generation method, three algorithms, previous SA algorithm with random 2-opt neighborhood generation method, the SA-based algorithm with the new neighborhood generation method (SA1) and the SA-based algorithm with probabilistic selection of random 2-opt and the new neighborhood generation method (SA2), are developed and compared by experiment of solving same example problem. In case of numeric examples with problem type 1 (the optimum layout is given), SA1 algorithm could find excellent layout than other algorithms. However, in case of problem type 2 (random-prepared and optimum-unknown problem), SA2 was excellent more than other algorithms.

Given the flow matrix, plant size (rectangle shape) and department sizes, the algorithm in this paper provides the plant layout with rectilinear distance measure. To construct automated facility design, eigenvector approach is employed. A branch and bound computer code developed by Tillinghast is modified to find the feasible fits of departments without shape distortion (see [1])in the plant rectangle. The computational results compared with CRAFT are shown.

This paper is motivated by the problem of fitting a group of cuboids into a simplified rotating vessel of the artificial satellite. Here we introduce a combinatorial optimization model which reduces the three-dimensional layout problem with behavioral constraints to a finite enumeration scheme. Moreover, a global combinatorial optimization algorithm is described in detail, which is an improved graph-theoretic heuristic.

We present a new integer programming formulation and a class of valid inequalities for solving the one-dimensional facility layout problem, which leads to a very efficient solution method for the problem.

This paper proposes a two-phase genetic algorithm (GA) to solve the problem of obtaining an optimum configuration of a paired single row assembly line. We pair two single-row assembly lines due to the shared usage of several workstations, thus obtaining an optimum configuration by considering the material flow of the two rows simultaneously. The problem deals with assigning workstations to a sequence and selecting the best arrangement by looking at the length and width for each workstation. This can be considered as an enhancement of the single row facility layout problem (SRFLP), or the so-called paired SRFLP (PSRFLP). The objective of this PSRFLP is to find an optimal configuration that seeks to minimize the distance traveled by the material handler and even the use of the material handler itself if this is possible. Real-world applications of such a problem can be found for apparel, shoe, and other manual assembly lines. This research produces the schematic representation solution using the heuristic approach. The crossover and mutation will be utilized using the schematic representation solution to obtain the neighborhood solutions. The first phase of the GA result is recorded to get the best pair. Based on these best matched pairs, the second-phase GA can commence.

A tree structure model has been proposed for representing the unequal-area facility layout. Each facility has a different rectangular shape specified by its area and aspect ratio. In this layout problem, based on the assumption that the shop floor has enough space for laying out the facilities, no constraint is considered for a shop floor. Objectives are minimizing total part movement between facilities and total rectangular layout area where all facilities and dead spaces are enclosed. Using the genetic code corresponding to two kinds of information, facility sequence and branching positions in the tree structure model, a genetic algorithm has been applied for finding non-dominated solutions in the two-objective layout problem. We use three kinds of crossover (PMX, OX, CX) for the former part of the chromosome and one-point crossover for the latter part. Two kinds of layout problems have been tested by the proposed method. The results demonstrate that the presented algorithm is able to find good solutions in enough short time.

자동생산화를 위한 공장설계에 있어서 설비배치에 관한 연구는 제조 유연성 요소의 통합과 이용을 적절하게 수행함으로써 가능하다. 특히 현실적인 설비배치의 특성은 그룹테크놀로지와 물자흐름의 전략을 파악하고 그들의 방법을 조사함으로써 기존의 연구에서 이론적으로 치우치는 경향을 몇 가지의 방법을 통합함으로 실질적인 응용에 그 목적을 두고 있다. 본 연구는 그래프이론과 수학적인 모형을 개발하여 통합적인 접근방법을 전개한다. 또한 설비배치 디자인에 대한 평가를 정량적인 방법으로 나타내고 있으며 경영전략에 있어 제조설비능력을 제고하는데 그 응용성을 보여주고 있다. 그것은 자동화 생산환경에 있어 각 시스템의 응용성과 목적과 관계 그리고 물자흐름관계 등을 정확하게 반영하는데 이바지한다. 현대 제조산업에 있어 고려할 수 있는 모든 각각의 제조요소가 제 특성을 수행하기 위해서는 우선적으로 설비배치 디자인의 중요함을 예를 들어 보여준다.

Cellular formation and layout problem has been known as a NP-hard problem. Because of the algorithm that can be solved exact solution within polynomial time has been unknown yet. This paper suggests a systematic method to be obtain of 2-degree partial directed path from the frequency of consecutive forward order. We apply the modified Kruskal algorithm of minimum spanning tree to be obtain the partial directed path. the proposed reverse constructive algorithm can be solved for this problem with O(mn) time complexity. This algorithm performs same as best known result of heuristic and metaheuristic methods for 4 experimental data.

건설공사 현장에서 공간활용을 위해 가장 보편적으로 쓰이는 방법이 site plans 이다. 이 방법은 건설 물자재를 적재하고 운반할시 공간이 부족한 도심지 부근에서 어떻게 건설 물자재를 옮기고 적재하는가? 크래인의 위치는 어디에 선정할것인가? 하는 문제를 해결하기 위한 것이다. 본고는 이러한 문제를 수평적으로 해결함과 동시에 수직적으로도 해결할 수 있는 방안을 도출했다. 이러한 해결 방안은 건설현장을 지도 또는 감독하는 메니져에게 가장 효과적으로 건설 물자재를 적재시켜 줄 수 입어 방법론을 제시함으로써 공기의 단축을 가져올 수 있는 효과를 누릴 수 있다. 방법론으로는 Genetic Algorithm을 이용하여 multiple-floor layout 문제점 해결하였다.

The most commonly used method for space management in the industry is development of site plans. These plans outline how to manage material deliveries, staging areas, and crane locations for construction sites in suburban area but not in congested urban areas. This study focuses on how to efficiently manage space for construction facilities on high-rise buildings in congested urban areas where normally space for facilities around a building footprint is not available. The limitations of available horizontal space create a need to explore vertical expansion of facilities. This raises new aspects of vertical facility handling and flow that need to be considered in the facility design problem. The construction facilities layout plan method provides layout planners with a valuable technique to develop efficient sequences of work that optimally defines how to efficiently utilize the construction facilities and minimize the travel of specific facilities effort on multiple-floor buildings. A genetic algorithm-based heuristic will be presented for generating block layouts for multiple-floor la)rout problems.

This paper deals with a Direct-Input-Output Manufacturing System (DIOMS) which has a number of machine centers placed along a built-in automated storage/retrieval system (AS/RS). During its operations, the storage/retrieval(S/R) machine picks up a pallet from the pickup/deposit port of a machine center and then moves it either to an empty rack opening of the AS/RS for temporary storage or to place it on the port of another machine center for subsequent operation. The machine layout problem in DIOMS is formulated as an integer mathematical programming whose objective is to minimize the total expected distance of the loaded S/R machine during a production period. Recognizing the limit of the exact solution procedure(the Branch and Bound method), two improvement-type heuristics are proposed. One is based on the simulated annealing method and the other the pairwise interchange method. The validity of the heuristics is examined with example problems.

작업능률향상을 위한 설비배치의 문제는 총자재 운반비용을 최소화하고 실비간의 자재흐름을 최소화하는 문제와 배치들간의 근접도를 최대화시키는 정적인 문제로 다루어져 왔다. 본 논문에서는 이 같은 문제가 계획기간을 확장하는 문제나, 그 이전에 빈번한 문제 (system nervousness)를 D.P.를 이용한 동적인 특성으로 해결하는 것을 제시하고자 한다.

Layout 문제는 매우 복잡한 의사결정과정이며, 이론적인 면보다는 논리를 바탕으로 한 경험적 결정이 많이 필요한 분야다. 이 논문에서는 프레스와 용접공정을 중심으로 하는 두 자동차 부품 생산업체가 한 업체로 통합되면서 새로운 공장으로 이전하는 과정에서 발생한 Layout 문제를 해결해 나가는 방법을 소개하였다. 추진하는 과정에서 기존의 개념모델을 일부 수정하여 적용하였으며, AutoCAD, FactoryFlow와 같은 소프트웨어를 이용하여 정량적 평가를 지원하였다.

A problem of relevant interest to some industries is that of the optimum two-dimensional layout. In this problem, one is given a number of rectangular sheets and an order for a specified number of each of certain types of two-dimensional regular and irregular shapes. The aim is to cut the shapes out of the sheets in such a way as to minimize the amount of waste produced. In this paper, we propose a genetic algorithms using rotation parameters by which the best pattern of layout is found.

The facility layout problem has the goal of locating the different facilities in a floor to achieve the greatest efficiency in producing a product or service. This problem is usually formulated as the quadratic assignment problem(QAP). However, the problem of finding optimal layout is hard and traditional approaches are not computationally feasible. In this paper, a genetic algorithm is presented for obtaining efficient layouts. To test the effectiveness of the algorithm, a set of examples is solved and the results are compared to those from other Known algorithms. The comparison indicates that the proposed method performs well for the classical test problems.

This paper addresses the facility layout problem in multi-bay environments, where the bays are connected at one or both ends by an inter-bay material handling system. In most previous studies, the main concern is to allocate facilities or departments to the bays whose widths are fixed. In this research, we suggest the efficient models that provide the optimal layout solution under flexible bay width environments. We also suggest a mathematical model that provides the optimal solution using two-way facility allocation approach instead of one-way allocation technique. This paper also shows the approach of TABU search to the assignment and layout design of the departments. The results generated from TABU search are compared to the result from the mathematical model. Models are developed using mixed integer programming for various test problems and solved by CPLEX.

Beam stiffeners have frequently been used for raising natural frequencies of base structures. In stiffener layout optimization problems, most of the previous researches considering the position and/or the length of the stiffener as design variables dealt with structures having just simple convex shapes such as a square or rectangle. The reason is concave shape structures have difficulties ill formulating geometry constraints. In this paper, a new geometry constraint handling technique, which can define both convex and concave feasible lesions and measure a degree of geometry constraint violation, is proposed. Evolution strategies (ESs) is utilized as an optimization tool. In addition, the constraint-handling technique of EVOSLINOC (EVOlution Strategy for scalar optimization with Lineal and Nonlinear Constraints) is utilized to solve constrained optimization problems. From a numerical example, the proposed geometry constraint handling technique is verified and proves that the technique can easily be applied to structures in net only convex but also concave shapes, even with a protrusion or interior holes.