Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks

The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to discover a competitive construction heuristic for graph colouring. Our proposed approach, ReLCol, uses deep Q-learning together with a graph neural network for feature extraction, and employs a novel way of parameterising the graph that results in improved performance. Using standard benchmark graphs with varied topologies, we empirically evaluate the benefits and limitations of the heuristic learned by ReLCol relative to existing construction algorithms, and demonstrate that reinforcement learning is a promising direction for further research on the graph colouring problem.Comment: 15 pages, 6 figures, to be published in LION17 conference proceeding

Learning-Based Approaches for Graph Problems: A Survey

Over the years, many graph problems specifically those in NP-complete are studied by a wide range of researchers. Some famous examples include graph colouring, travelling salesman problem and subgraph isomorphism. Most of these problems are typically addressed by exact algorithms, approximate algorithms and heuristics. There are however some drawback for each of these methods. Recent studies have employed learning-based frameworks such as machine learning techniques in solving these problems, given that they are useful in discovering new patterns in structured data that can be represented using graphs. This research direction has successfully attracted a considerable amount of attention. In this survey, we provide a systematic review mainly on classic graph problems in which learning-based approaches have been proposed in addressing the problems. We discuss the overview of each framework, and provide analyses based on the design and performance of the framework. Some potential research questions are also suggested. Ultimately, this survey gives a clearer insight and can be used as a stepping stone to the research community in studying problems in this field.Comment: v1: 41 pages; v2: 40 page

Operations research: from computational biology to sensor network

In this dissertation we discuss the deployment of combinatorial optimization methods for modeling and solve real life problemS, with a particular emphasis to two biological problems arising from a common scenario: the reconstruction of the three-dimensional shape of a biological molecule from Nuclear Magnetic Resonance (NMR) data. The fi rst topic is the 3D assignment pathway problem (APP) for a RNA molecule. We prove that APP is NP-hard, and show a formulation of it based on edge-colored graphs. Taking into account that interactions between consecutive nuclei in the NMR spectrum are diff erent according to the type of residue along the RNA chain, each color in the graph represents a type of interaction. Thus, we can represent the sequence of interactions as the problem of fi nding a longest (hamiltonian) path whose edges follow a given order of colors (i.e., the orderly colored longest path). We introduce three alternative IP formulations of APP obtained with a max flow problem on a directed graph with packing constraints over the partitions, which have been compared among themselves. Since the last two models work on cyclic graphs, for them we proposed an algorithm based on the solution of their relaxation combined with the separation of cycle inequalities in a Branch & Cut scheme. The second topic is the discretizable distance geometry problem (DDGP), which is a formulation on discrete search space of the well-known distance geometry problem (DGP). The DGP consists in seeking the embedding in the space of a undirected graph, given a set of Euclidean distances between certain pairs of vertices. DGP has two important applications: (i) fi nding the three dimensional conformation of a molecule from a subset of interatomic distances, called Molecular Distance Geometry Problem, and (ii) the Sensor Network Localization Problem. We describe a Branch & Prune (BP) algorithm tailored for this problem, and two versions of it solving the DDGP both in protein modeling and in sensor networks localization frameworks. BP is an exact and exhaustive combinatorial algorithm that examines all the valid embeddings of a given weighted graph G=(V,E,d), under the hypothesis of existence of a given order on V. By comparing the two version of BP to well-known algorithms we are able to prove the e fficiency of BP in both contexts, provided that the order imposed on V is maintained

Accelerating ant colony optimization by using local search

This thesis report is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Computer Science and Engineering, 2015.Cataloged from PDF version of thesis report.Includes bibliographical references (page 42-45).Optimization is very important fact in terms of taking decision in mathematics, statistics, computer science and real life problem solving or decision making application. Many different optimization techniques have been developed for solving such functional problem. In order to solving various problem computer Science introduce evolutionary optimization algorithm and their hybrid. In recent years, test functions are using to validate new optimization algorithms and to compare the performance with other existing algorithm. There are many Single Object Optimization algorithm proposed earlier. For example: ACO, PSO, ABC. ACO is a popular optimization technique for solving hard combination mathematical optimization problem. In this paper, we run ACO upon five benchmark function and modified the parameter of ACO in order to perform SBX crossover and polynomial mutation. The proposed algorithm SBXACO is tested upon some benchmark function under both static and dynamic to evaluate performances. We choose wide range of benchmark function and compare results with existing DE and its hybrid DEahcSPX from other literature are also presented here.Nabila TabassumMaruful HaqueB. Computer Science and Engineerin