• Title, Summary, Keyword: binary linear programming

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Solving A Quadratic Fractional Integer Programming Problem Using Linearization

  • Gaur, Anuradha;Arora, S.R.
    • Management Science and Financial Engineering
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    • v.14 no.2
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    • pp.25-44
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    • 2008
  • This paper concentrates on reduction of a Quadratic Fractional Integer Programming Problem (QFIP) to a 0-1 Mixed Linear Programming Problem (0-1 MLP). The solution technique is based on converting the integer variables to binary variables and then the resulting Quadratic Fractional 0-1 Programming Problem is linearized to a 0-1 Mixed Linear Programming problem. It is illustrated with the help of a numerical example and is solved using the LINDO software.

Optimal Base Station Clustering for a Mobile Communication Network Design

  • Hong, Jung-Man;Lee, Jong-Hyup;Lee, Soong-Hee
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.5 no.5
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    • pp.1069-1084
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    • 2011
  • This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited. Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

Power-Delay Product Optimization of Heterogeneous Adder Using Integer Linear Programming (정수선형계획법을 이용한 이종가산기의 전력-지연시간곱 최적화)

  • Kwak, Sang-Hoon;Lee, Jeong-Gun;Lee, Jeong-A
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.10
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    • pp.1-9
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    • 2010
  • In this paper, we propose a methodology in which a power-delay product of a binary adder is optimized based on the heterogeneous adder architecture. We formulate the power-delay product of the heterogeneous adder by using integer linear programming(ILP). For the use of ILP optimization, we adopt a transformation technique in which the initial non-linear expression for the power-delay product is converted into linear expression. The experimental result shows the superiority of the suggested method compared to the cases in which only conventional adder is used.

Developing Smart Grids Based on GPRS and ZigBee Technologies Using Queueing Modeling-Based Optimization Algorithm

  • de Castro Souza, Gustavo Batista;Vieira, Flavio Henrique Teles;Lima, Claudio Ribeiro;de Deus, Getulio Antero Junior;de Castro, Marcelo Stehling;de Araujo, Sergio Granato;Vasques, Thiago Lara
    • ETRI Journal
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    • v.38 no.1
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    • pp.41-51
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    • 2016
  • Smart metering systems have become widespread around the world. RF mesh communication systems have contributed to the creation of smarter and more reliable power systems. This paper presents an algorithm for positioning GPRS concentrators to attain delay constraints for a ZigBee-based mesh network. The proposed algorithm determines the number and placement of concentrators using integer linear programming and a queueing model for the given mesh network. The solutions given by the proposed algorithm are validated by verifying the communication network performance through simulations.

The Generalized Multiple-Choice Multi-Divisional Linear Programming Knapsack Problem (일반 다중선택 다분할 선형계획 배낭문제)

  • Won, Joong-Yeon
    • Journal of Korean Institute of Industrial Engineers
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    • v.40 no.4
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    • pp.396-403
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    • 2014
  • The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).

Secure Outsourced Computation of Multiple Matrix Multiplication Based on Fully Homomorphic Encryption

  • Wang, Shufang;Huang, Hai
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.13 no.11
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    • pp.5616-5630
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    • 2019
  • Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

A Development of Optimal Algorithms for N/M/D/F/Fmax Scheduling Problems (N/M/D/F/Fmax 일정계획 문제에서 최적 알고리듬의 개발)

  • 최성운
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.13 no.21
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    • pp.91-100
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    • 1990
  • This paper is concerned with the development of optimal algorithms for multi-stage flowshop scheduling problems with sequence dependent setup times. In the previous researches the setup time of a job is considered to be able to begin at the earliest opportunity given a particular sequence at the start of operations. In this paper the setup time of a job is considered to be able to begin only at the completion of that job on the previous machine to reflect the effects of the setup time to the performance measure of sequence dependent setup time flowshop scheduling. The results of the study consist of two areas; first, a general integer programming(IP) model is formulated and a nixed integer linear programming(MILP) model is also formulated by introducing a new binary variable. Second a depth-first branch and bound algorithm is developed. To reduce the computational burdens we use the best heuristic schedule developed by Choi(1989) as the first trial. The experiments for developed algorithm are designed for a 4$\times$3$\times$3 factorial design with 360 observations. The experimental factors are PS(ratio of processing time to setup time), M(number of machines), N(number of jobs).

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A Study on Developing An Experimental Model to Solve for Optimal Forest-Level Timber Harvesting Schedules Using Linear Programming (대단지(大團地) 산림(山林)의 목재생산계획(木材生産計劃) 분석(分析)을 위한 선형계획(線型計劃) 실험전산모델에 관한 연구(硏究))

  • Chung, Joo Sang;Park, Eun Sik
    • Journal of Korean Society of Forest Science
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    • v.82 no.3
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    • pp.292-304
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    • 1993
  • This research developed a forest-level harvest scheduling model using linear programming (LP). The formulations of the LP model include timber production schemes with constraints of nondecling yield forest conversion strategies, the minimum timber supply, levels and the maximum cut acrages. The model is able to generate both Model I and Model II types of input matrix in MPS format. In this paper, use of LP in building the framework of the strategic forest planning model was justified by comparing the algorithmic characteristics of LP with those of Gentan probability and binary search approaches through literature reviews. In order to demonstrate the field applicability of the model proposed. (1) the harvest scheduling problem for about 11,000-hectare case study area (Mt. Baekun area in Southern Experimental Forest of Seoul National University) was formulated and soloed and (2) the effects of the change in task regulatory timber production constraints or. optimal harvesting schedules here investigated.

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Efficient Ρ-median approach to GT cell formation (GT 셀 형성을 위한 효율적 Ρ-median 접근법)

  • Won, Youkyung
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.40-43
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    • 2000
  • This paper is concerned with development of an efficient Ρ-median approach applicable to large cell formation(CF) problems. A two-phase methodology that seeks to minimize the number of exceptional elements is proposed. In phase I, two efficient Ρ-median formulations which contain fewer binary variables than existing Ρ-median formulations are constructed. These make it possible to implement large CF problem within reasonable computer runtime with commercially available linear integer programming codes. Given the initial cell configuration found with the new p-median formulations, in phase II bottleneck machines and parts are reassigned to reduce the number of exceptional elements. This procedure has the flexibility to provide the cell designer with alternative solutions. Test results on large CF problems show a substantial efficiency of the new Ρ-median formulations.

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Adaptive Genetic Algorithm for the Manufacturing/Distribution Chain Planning

  • Kiyoung Shin;Chiung Moon;Kim, Yongchan;Kim, Jongsoo
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.170-174
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    • 2003
  • In this research, we consider an integrated manufacturing/distribution planning problem in supply chain (SC) which has non-integer time lags. We focus on a capacitated manufacturing planning and capacity allocation problem for the system. We develop a mixed binary integer linear programming (MBLP) model and propose an efficient heuristic procedure using an adaptive genetic algorithm, which is composed of a regeneration procedure for evaluating infeasible chromosomes and the reduced costs from the LP-relaxation of the original model. The proposed an adaptive genetic algorithm was tested in terms of the solution accuracy and algorithm speed during numerical experiments. We found that our algorithm can generate the optimal solution within a reasonable computational time.

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