그래프 최적화 문제를 위한 점진적 유전 알고리즘

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 8. 문병로.A combinatorial optimization problem is an optimization problem having a discrete solution space. Lots of the graph problems belong to this category as graphs are discrete objects. Graphs are widely used in the various field and there are lots of real world combinatorial optimization problems which take the graphs as their input. For some of these problems, the magnitude of the solution space is exponential to the size of the problem, and thereby efficient space search algorithms are required to deal with them. Genetic algorithms are widely used to solve combinatorial optimization problems, and incremental genetic algorithms could be used to efficiently solve graph optimization problems.We define subproblems and solve them step by step instead of tackling the problems directly. A subproblem solved by an incremental genetic algorithm deals with a restriction of the original graph structure. The subproblems are solved in the intermediate steps and the size of the subproblem is gradually increased. We apply the same genetic algorithm to each subproblem, and it is initialized with the evolved population of the previous step. We propose incremental genetic algorithms for two different combinatorial optimization problemsthe subgraph isomorphism problem and graph cut optimization problem. We devise an optimal substructure on the subproblem sequence and explain how it is related to the optimality of the process, along with other related factors. We present graph expansion methodologies and vertex reordering schemes to define an appropriate sequence of subproblems. We combine the proposed incremental approach with a hybrid genetic algorithm for the subgraph isomorphism problem, and the algorithm was further developed for nearly perfect results. Based on our analysis, we also propose an incremental genetic algorithm to solve graph cut optimization problems. We tested the implementation of the algorithm on benchmark graph instances for the graph partitioning problem and the maximum cut problem. Through experiments, we investigate and analyze how the sequence of subproblems affects the search space landscape. The performance of a genetic algorithm makes an improvement when the incremental approach is applied with respect to an appropriate sequence of subproblems.Chapter I. Introduction 1 Chapter II. Incremental Genetic Algorithm 6 2.1 Overview and Traditional Applications 6 2.2 Application on Graph Optimization Problems 9 2.2.1 Formalization of the Incremental Process 9 2.2.2 Theoretical Background 12 2.2.3 Sequence of Subproblems 15 Chapter III. Subgraph Isomorphism Problem 19 3.1 Introduction 19 3.2 The Proposed Algorithm 21 3.2.1 The Structure of the Incremental Genetic Algorithm 21 3.2.2 Design Issues 25 3.2.3 Genetic Framework 28 3.3 Experimental Results 31 3.3.1 Dataset and Evaluation 31 3.3.2 Results and Discussions 33 3.3.3 Overall Results 39 3.4 Further Improvement 42 3.4.1 New Operators 43 3.4.2 Improvements by New Operators 45 3.4.3 Overall Result 46 Chapter IV. Graph Cut Optimization Problems 50 4.1 Introduction 50 4.2 The Proposed Algorithm 51 4.2.1 Subproblem Structure 51 4.2.2 Reordering Schemes 54 4.2.3 Genetic Framework 55 4.3 Experimental Results 57 4.3.1 Dataset and Evaluation 57 4.3.2 Results on Graph Partitioning Problem 58 4.3.3 Results on Maximum Cut Problem 66 4.3.4 Results on Problem Variants 70 Chapter V. Related Applications 75 5.1 Measuring Source Code Similarity with an Incremental Genetic Algorithm 75 5.1.1 Introduction 75 5.1.2 The Proposed System 76 5.1.3 Experimental Results 80 5.1.4 Discussion 88 5.2 Linear Ordering Problem and an Approximate Fitness Evaluation 88 5.2.1 Introduction 88 5.2.2 The Proposed Method 89 5.2.3 Experimental Results 91 Chapter VI. Conclusions 94 Bibliography 96 국문 초록 106Docto

Combining Multiple Clusterings via Crowd Agreement Estimation and Multi-Granularity Link Analysis

The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability to weight the base clusterings without access to the original data and can be affected significantly by the low-quality, or even ill clusterings. Secondly, they generally focus on the instance level or cluster level in the ensemble system and fail to integrate multi-granularity cues into a unified model. To address these two limitations, this paper proposes to solve the clustering ensemble problem via crowd agreement estimation and multi-granularity link analysis. We present the normalized crowd agreement index (NCAI) to evaluate the quality of base clusterings in an unsupervised manner and thus weight the base clusterings in accordance with their clustering validity. To explore the relationship between clusters, the source aware connected triple (SACT) similarity is introduced with regard to their common neighbors and the source reliability. Based on NCAI and multi-granularity information collected among base clusterings, clusters, and data instances, we further propose two novel consensus functions, termed weighted evidence accumulation clustering (WEAC) and graph partitioning with multi-granularity link analysis (GP-MGLA) respectively. The experiments are conducted on eight real-world datasets. The experimental results demonstrate the effectiveness and robustness of the proposed methods.Comment: The MATLAB source code of this work is available at: https://www.researchgate.net/publication/28197031

Optimal Placement of Valves in a Water Distribution Network with CLP(FD)

This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design. We take the formulation of the problem by Giustolisi and Savic (2008) and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network. We believe that the area of the so-called hydroinformatics can benefit from the techniques developed in Constraint Logic Programming and possibly from other areas of logic programming, such as Answer Set Programming.Comment: Best paper award at the 27th International Conference on Logic Programming - ICLP 2011; Theory and Practice of Logic Programming, (ICLP'11) Special Issue, volume 11, issue 4-5, 201

A Framework for Developing Real-Time OLAP algorithm using Multi-core processing and GPU: Heterogeneous Computing

The overwhelmingly increasing amount of stored data has spurred researchers seeking different methods in order to optimally take advantage of it which mostly have faced a response time problem as a result of this enormous size of data. Most of solutions have suggested materialization as a favourite solution. However, such a solution cannot attain Real- Time answers anyhow. In this paper we propose a framework illustrating the barriers and suggested solutions in the way of achieving Real-Time OLAP answers that are significantly used in decision support systems and data warehouses

Finding Near-Optimal Independent Sets at Scale

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.Comment: 17 pages, 1 figure, 8 tables. arXiv admin note: text overlap with arXiv:1502.0168