• 제목/요약/키워드: Branch-and-Bound Algorithm

검색결과 194건 처리시간 0.024초

A Heuristic for Dual Mode Routing with Vehicle and Drone

  • Min, Yun-Hong;Chung, Yerim
    • 한국컴퓨터정보학회논문지
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    • 제21권9호
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    • pp.79-84
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    • 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.

동적 공정계획에서의 기계선정을 위한 다목적 유전자 알고리즘 (Multi-Objective Genetic Algorithm for Machine Selection in Dynamic Process Planning)

  • 최회련;김재관;이홍철;노형민
    • 한국정밀공학회지
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    • 제24권4호
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    • pp.84-92
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    • 2007
  • Dynamic process planning requires not only more flexible capabilities of a CAPP system but also higher utility of the generated process plans. In order to meet the requirements, this paper develops an algorithm that can select machines for the machining operations by calculating the machine loads. The developed algorithm is based on the multi-objective genetic algorithm that gives rise to a set of optimal solutions (in general, known as the Pareto-optimal solutions). The objective is to satisfy both the minimization number of part movements and the maximization of machine utilization. The algorithm is characterized by a new and efficient method for nondominated sorting through K-means algorithm, which can speed up the running time, as well as a method of two stages for genetic operations, which can maintain a diverse set of solutions. The performance of the algorithm is evaluated by comparing with another multiple objective genetic algorithm, called NSGA-II and branch and bound algorithm.

An Optimal Algorithm for the Sensor Location Problem to Cover Sensor Networks

  • 김희선;박성수
    • 한국경영과학회:학술대회논문집
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    • 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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    • pp.17-24
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    • 2006
  • We consider the sensor location problem (SLP) on a given sensor field. We present the sensor field as grid of points. There are several types of sensors which have different detection ranges and costs. If a sensor is placed in some point, the points inside of its detection range can be covered. The coverage ratio decreases with distance. The problem we consider in this thesis is called multiple-type differential coverage sensor location problem (MDSLP). MDSLP is more realistic than SLP. The coverage quantities of points are different with their distance form sensor location in MDSLP. The objective of MDSLP is to minimize total sensor costs while covering every sensor field. This problem is known as NP-hard. We propose a new integer programming formulation of the problem. In comparison with the previous models, the new model has a smaller number of constraints and variables. This problem has symmetric structure in its solutions. This group is used for pruning in the branch-and-bound tree. We solved this problem by branch-and-cut(B&C) approach. We tested our algorithm on about 60 instances with varying sizes.

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다차원 색인을 이용한 하향식 계층 클러스터링 (Top-down Hierarchical Clustering using Multidimensional Indexes)

  • 황재준;문양세;황규영
    • 한국정보과학회논문지:데이타베이스
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    • 제29권5호
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    • pp.367-380
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    • 2002
  • 최근 공간 데이타 분석, 영상 분석 등과 같은 대용량 데이타를 관리하는 다양한 응용 업무들이 증가함에 따라, 대용량의 데이타베이스를 위한 클러스터링 기법이 많이 연구되고 있다. 그 중에서도 계층 클러스터링 기법은 데이타베이스의 계층 분할을 표현하는 계층 트리를 생성하고 이를 이용하여 효율적인 클러스터링을 수행하는 방법으로서, 지금까지는 주로 트리를 하위 계층으로부터 상위 계층으로 생성해 가는 상향식(bottom-up) 계층 클러스터링 기법들이 연구되었다. 이러한 상향식 클러스터링 방법은 트리를 생성하기 위하여 전체 데이타베이스를 한 번 이상 액세스하여야 할 뿐만 아니라, 하위 계층에서부터 검색을 시작하기 때문에 트리의 많은 부분을 검색하여야 하는 문제점이 있다. 본 논문에서는 대부분의 데이타베이스 응용에서 이미 유지하고 있는 다차원 색인을 이용하여 클러스터링을 수행하는 새로운 하향식(top-down) 계층 클러스터링 기법을 제안한다. 일반적으로 다차원 색인에서는 가까운 객체들이 동일한 (혹은 인접한) 페이지에 저장될 가능성이 큰 클러스터링 성질을 가진다. 이러한 다차원 색인의 클러스터링 성질을 사용하면 각 객체들간의 거리를 일일이 계산하지 않고도 이웃한 객체들을 식별할 수 있다. 우선 객체들의 밀도에 기반하여 클러스터를 정형적으로 정의한다. 이를 위하여, 객체를 포함하는 영역의 밀도를 이용한 영역 대조 분할(region contrast partition) 개념을 사용한다. 또, 클러스터링 알고리즘에서의 빠른 검색을 위하여 분기 한정(branch-and-bound) 알고리즘을 사용하며, 여기서의 한계값(bound)을 제안하고 이의 정확성을 이론적으로 증명한다. 실험 결과, 제안한 방법은 상향식 계층 클러스터링 방법인 BIRCH와 비교하여, 정확성 측면에서 우수하거나 유사한 것으로 나타났으며, 데이타 페이지 액세스 횟수를 데이타베이스 크기에 따라 최고 26~187배까지 감소시킨 것으로 나타났다. 이 같은 결과로 볼 때, 제안한 방법은 대용량 데이타베이스에서의 클러스터링 성능을 크게 향상시키는 기법으로서, 일반 데이타베이스 응용에 실용적으로 적용 가능하다고 판단된다.

Joint Antenna Selection and Multicast Precoding in Spatial Modulation Systems

  • Wei Liu;Xinxin Ma;Haoting Yan;Zhongnian Li;Shouyin Liu
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제17권11호
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    • pp.3204-3217
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    • 2023
  • In this paper, the downlink of the multicast based spatial modulation systems is investigated. Specifically, physical layer multicasting is introduced to increase the number of access users and to improve the communication rate of the spatial modulation system in which only single radio frequency chain is activated in each transmission. To minimize the bit error rate (BER) of the multicast based spatial modulation system, a joint optimizing algorithm of antenna selection and multicast precoding is proposed. Firstly, the joint optimization is transformed into a mixed-integer non-linear program based on single-stage reformulation. Then, a novel iterative algorithm based on the idea of branch and bound is proposed to obtain the quasioptimal solution. Furthermore, in order to balance the performance and time complexity, a low-complexity deflation algorithm based on the successive convex approximation is proposed which can obtain a sub-optimal solution. Finally, numerical results are showed that the convergence of our proposed iterative algorithm is between 10 and 15 iterations and the signal-to-noise-ratio (SNR) of the iterative algorithm is 1-2dB lower than the exhaustive search based algorithm under the same BER accuracy conditions.

일반거리산정방법을 이용한 다-물류센터의 최적 수송경로 계획 모델 (A Vehicle Routing Model for Multi-Supply Centers Based on Lp-Distance)

  • 황흥석
    • 산업공학
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    • 제11권1호
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    • pp.85-95
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    • 1998
  • This study is focussed on an optimal vehicle routing model for multi-supply centers in two-echelon logistic system. The aim of this study is to deliver goods for demand sites with optimal decision. This study investigated an integrated model using step-by-step approach based on relationship that exists between the inventory allocation and vehicle routing with restricted amount of inventory and transportations such as the capability of supply centers, vehicle capacity and transportation parameters. Three sub-models are developed: 1) sector-clustering model, 2) a vehicle-routing model based on clustering and a heuristic algorithm, and 3) a vehicle route scheduling model using TSP-solver based on genetic and branch-and-bound algorithm. Also, we have developed computer programs for each sub-models and user interface with visualization for major inputs and outputs. The application and superior performance of the proposed model are demonstrated by several sample runs for the inventory-allocation and vehicle routing problems.

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저축 CNC 환경에서의 황삭가공 (Rough Cut Tool Path Planning in Fewer-axis CNC Machinig)

  • 강지훈;서석환;이정재
    • 한국CDE학회논문집
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    • 제2권1호
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    • pp.19-27
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    • 1997
  • This paper presents rough cut tool path planning for the fewer-axis machine consisting of a three-axis CNC machine and a rotary indexing table. In the problem dealt with in this paper, the tool orientation is "intermediately" changed, distinguished from the conventional problem where the tool orientation is assumed to be fixed. The developed rough cut path planning algorithm tries to minimize the number of tool orientation (setup) changes together with tool changes and the machining time for the rough cut by the four procedures: a) decomposition of the machining area based on the possibility of tool interference (via convex hull operation), b) determination of the optimal tool size and orientation (via network graph theory and branch-and bound algorithm), c) generation of tool path for the tool and orientation (based on zig-zag pattern), and d) feedrate adjustment to maintain the cutting force at an operation level (based on average cutting force). The developed algorithms are validated via computer simulations, and can be also used in pure fiveaxis machining environment without modification.

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최적 모듈 선택 아키텍쳐 합성을 위한 저전력 Force-Directed 스케쥴링에 관한 연구 (A Study on Low Power Force-Directed scheduling for Optimal module selection Architecture Synthesis)

  • 최지영;김희석
    • 대한전자공학회:학술대회논문집
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    • 대한전자공학회 2004년도 하계종합학술대회 논문집(2)
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    • pp.459-462
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    • 2004
  • In this paper, we present a reducing power consumption of a scheduling for module selection under the time constraint. A a reducing power consumption of a scheduling for module selection under the time constraint execute scheduling and allocation for considering the switching activity. The focus scheduling of this phase adopt Force-Directed Scheduling for low power to existed Force-Directed Scheduling. and it constructs the module selection RT library by in account consideration the mutual correlation of parameters in which the power and the area and delay. when it is, in this paper we formulate the module selection method as a multi-objective optimization and propose a branch and bound approach to explore the large design space of module selection. Therefore, the optimal module selection method proposed to consider power, area, delay parameter at the same time. The comparison experiment analyzed a point of difference between the existed FDS algorithm and a new FDS_RPC algorithm.

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작업장 특성을 고려한 가공경로선정 문제의 유전알고리즘 접근 (-Machining Route Selection with the Shop Flow Information Using Genetic Algorithm-)

  • 이규용;문치웅;김재균
    • 산업경영시스템학회지
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    • 제23권54호
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    • pp.13-26
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    • 2000
  • Machining route selection to produce parts should be based on shop flow information because of input data at scheduling tasks and is one of the main problem in process planning. This paper addresses the problem of machining route selection in multi-stage process with machine group included a similar function. The model proposed is formulated as 0-1 integer programing considering the relation of parts and machine table size, avaliable time of each machine for planning period, and delivery date. The objective of the model is to minimize the sum of processing, transportation, and setup time for all parts. Genetic algorithm approach is developed to solve this model. The efficiency of the approach is examined in comparison with the method of branch and bound technique for the same problem. Also, this paper is to solve large problem scale and provide it if the multiple machining routes are existed an optimal solution.

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와주를 고려한 가공경로 선정에서의 유전알고르즘 접근 (Machining Route Selection with Subcontracting Using Genetic Algorithm)

  • 이규용;문치웅;김재균
    • 경영과학
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    • 제17권2호
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    • pp.55-65
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    • 2000
  • This paper addresses a problem of machining route selection in multi-stage process with machine group. This problem is considered the subcontracting and the production in-house such as regular and overtime work. the proposed model is formulated as a 0-1 integer programming constraining the avaliable time of each machine for planning period and total overtimes. The objective of the model is to minimize the sum of processing cost, overtime cost, and subcontracting cost. To solve this model, a genetic algorithm(GA) approach is developed. The effectiveness of the proposed GA approach is evaluated through comparisons with the optimal solution obtained from the branch and bound. In results, the same optimal solution is obtained from two methods at small size problem, and the consistent solution is provided by the GA approach at large size problem. The advantage of the GA approach is the flexibility into decision-making process because of providing multiple machining routes.

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