Optimizing Cockpit Display Configurations with a Genetic Algorithm System. Phase 1.

We propose a heuristic for parallel partitioning of graphs into equi-sized components. In particular, we identify a relationship between the graph partitioning problem (GPP) and the traveling saleman problem (TSP), and use that to reduce partitioning to TSP. Given that better performing heuristics are known for TSP than are for GPP, this reduction also leads to improved GPP heuristics. What is more, a good GPP solution can also be used to speed up computation of TSP.We first derive a good bi-partition from a cut of the TSP cycle in time proportional to the number of edges in the graph. We then continue this bi-partitioning recursively until the required number of partitions are left. Further, in order to speed up the computation of TSP, which we use as a subroutine, we perform an initial rough partitioning of the graph into K parts, compute TSP tours in each of these smaller partitions and then merge these local tours to solve the full TSP.We then use this full TSP solution to obtain the final partitioning in parallel. Our empirical analysis shows that for partition count k ≥ 32, our parallel algorithm gives a cut better in size than that of algorithms known for low cut-size (e.g., KaBaPE), and when time is of concern, it finishes in significantly less time with comparable cuts. We also show that our algorithm gives much smaller cuts in comparable time than those known for fast computation (e.g., PT-Scotch).

Partitioning graphs into equally large groups of nodes, minimizing the number of edges between different groups, is an extremely important problem in parallel computing. This paper presents genetic algorithms for suboptimal graph partitioning, with new crossover operators (KNUX, DKNUX) that lead to orders of magnitude improvement over traditional genetic operators in solution quality and speed. Our method can improve on good solutions previously obtained by using other algorithms or graph theoretic heuristics in, minimizing the total communication cost or the worst case cost of communication for a single processor. We also extend our algorithm to incremental graph partitioning problems, in which the graph structure or system properties changes with time. >

The Graph Partitioning Problem (GPP) is one of the fundamental multimodal combinatorial problems that has many applications in computer science. Many algorithms have been devised to obtain a reasonable approximate solution for the GP problem. This paper applies different Genetic Algorithms in solving GP problem. In addition to using the Simple Genetic Algorithm (SGA), it introduces a new genetic algorithm named the Adaptive Population Genetic Algorithm (APGA) that overcomes the premature convergence of SGA. The paper also presents a new approach using niching methods for solving GPP as a multimodal optimization problem. The paper also presents a comparison between the four genetic algorithms; Simple Genetic Algorithm (SGA), Adaptive Population Genetic Algorithm (APGA) and the two niching methods; Sharing and Deterministic Crowding. when applied to the graph partitioning problem. Results proved the superiority of APGA over SGA and the ability of niching methods in obtaining a set of multiple good solutions.KeywordsGenetic AlgorithmPremature ConvergenceTournament SelectionSimple Genetic AlgorithmSimilar IndividualThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

An important application of graph partitioning is data clustering using a graph model - the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. In this paper, we propose a new algorithm for graph partitioning with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partitioning. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bounds are derived. The min-max cut algorithm is tested on newsgroup data sets and is found to out-perform other current popular partitioning/clustering methods. The linkage-based refinements to the algorithm further improve the quality of clustering substantially. We also demonstrate that a linearized search order based on linkage differential is better than that based on the Fiedler vector, providing another effective partitioning method.

We investigate the problem of partitioning finite difference meshes in two dimensions among the processors of a parallel computer. The objective is to achieve a perfect load balance while minimizing the communication cost. There are well-known graph, hypergraph, and geometry-based partitioning algorithms for this problem. The known geometric algorithms have linear running time and obtain the best results for very special mesh sizes and processor numbers. We propose another geometric algorithm. The proposed algorithm is linear, is applicable to much more cases than some well-known alternatives, obtains better results than the graph partitioning algorithms, obtains better results than the hypergraph partitioning algorithms almost always. Our algorithm also obtains better results than a known asymptotically-optimal algorithm for some small number of processors. We also catalog related theoretical results.

The efficient execution of scientific simulations on HPC systems requires a partitioning of the underlying mesh among the processors such that the load is balanced and the inter-processor communication is minimized. Graph partitioning algorithms have been applied with much success for this purpose. However, the parallelization of multi-phase and multi-physics computations poses new challenges that require fundamental advances in graph partitioning technology. In addition, most existing graph partitioning algorithms are not suited for the newer heterogeneous high-performance computing platforms. This talk will describe research efforts in our group that are focused on developing novel multi-constraint and multi-objective graph partitioning algorithms that can support the advancing state-of-the-art in numerical simulation technologies. In addition, we will present our preliminary work on new partitioning algorithms that are well suited for heterogeneous architectures.

Over the last few years, graph partitioning has been recognized as a suitable technique for optimizing cellular network structure. For example, in a recent paper, the authors proposed a classical graph partitioning algorithm to optimize the assignment of cells to Packet Control Units (PCUs) in GSM-EDGE Radio Access Network. Based on this approach, the quality of packet data services in a live environment was increased by reducing the number of cell re-selections between different PCUs. To learn more about the potential of graph partitioning in cellular networks, in this paper, a more sophisticated, yet computationally efficient, partitioning algorithm is proposed for the same problem. The new method combines multi-level refinement and adaptive multi-start techniques with algorithms to ensure the connectivity between cells under the same PCU. Performance assessment is based on an extensive set of graphs constructed with data taken from a live network. During the tests, the new method is compared with classical graph partitioning approaches. Results show that the proposed method outperforms classical approaches in terms of solution quality at the expense of a slight increase in computing time, while providing solutions that are easier to check by the network operator.

Hybrid genetic algorithms (GAs) for the graph partitioning problem are described. The algorithms include a fast local improvement heuristic. One of the novel features of these algorithms is the schema preprocessing phase that improves GAs' space searching capability, which in turn improves the performance of GAs. Experimental tests on graph problems with published solutions showed that the new genetic algorithms performed comparable to or better than the multistart Kernighan-Lin algorithm and the simulated annealing algorithm. Analyses of some special classes of graphs are also provided showing the usefulness of schema preprocessing and supporting the experimental results.

SummaryThis paper presents how parallel advanced graph partitioning algorithms can be designed and improved with the use of global application states monitoring of distributed programs. The proposed algorithms have been implemented inside a novel distributed program design framework Program Execution Governed by Asynchronous Supervision of States in Distributed Applications (PEGASUS DA). This framework provides system support for the design of execution control in distributed applications based on automated global state monitoring. Two strategies for the control design of advanced parallel/distributed graph partitioning algorithms are presented and discussed. In the first one, the parallel algorithm control runs on top of the popular graph partitioning METIS tool. The second control strategy is based on genetic programming so that partitioning primitives and the overall algorithmic control can be freely designed by the user. Advanced partitioning methods have been conveniently embedded inside the global state monitoring driven PEGASUS DA framework which controls partitioning distributed actions at the level of processes and threads. The use of the framework allowed easy design and testing of different graph optimization strategies. The presented graph partitioning methods are illustrated by experiments with benchmark graphs. The experiments have comparatively assessed the obtained graph partitioning quality (visible improvement has been observed) and have identified benefits of the proposed approach for programmers.

Graph partitioning is a fundamental problem in several scientific and engineering applications. In this paper, we describe heuristics that improve the state-of-the-art practical algorithms used in graph-partitioning software in terms of both partitioning speed and quality. An important use of graph partitioning is in ordering sparse matrices for obtaining direct solutions to sparse systems of linear equations arising in engineering and optimization applications. The experiments reported in this paper show that the use of these heuristics results in a considerable improvement in the quality of sparse-matrix orderings over conventional ordering methods, especially for sparse matrices arising in linear programming problems. In addition, our graph-partitioning-based ordering algorithm is more parallelizable than minimum-degree-based ordering algorithms, and it renders the ordered matrix more amenable to parallel factorization.

The m‐way graph partitioning problem is of central importance in combinatorial optimization. It has many important applications in fields such as VLSI circuit design, task allocation in distributed computing systems, and network partitioning. In this paper, we propose an efficient genetic algorithm to solve this problem. The proposed method searches a large solution space and finds the best possible solution by adjusting the intensification and diversification automatically during the optimization process. The proposed method is tested on a large number of instances and compared with some existing algorithms. The experimental results show that the proposed algorithm is superior to its competitors in terms of computation time and solution quality. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Graph matching, set covering and partitioning problems are both theoretically and practically important in decision support systems. Numerous situations have been modeled as graph matching, set covering and partitioning problems. These situations include applications in the areas of task assignment, marriage problem, airline crew scheduling, truck deliveries or vehicle routing, political redistricting, etc. Relational database systems currently support these applications merely by providing some programming languages which are used to write the programs associated with the data. These programming languages are complete as opposed to existing query languages like SQL. These languages, since they are complete, have the usual complexity of a powerful language and lack the simplicity of query languages. This increases application development effort. Relational operators and the query language SQL are extended in this present work in order to enable these problems to be stated and solved directly by the relational database systems leading to benefits of improved data independence, increased productivity, and better performance. The relational operators are extended with six operators, i.e., match, maxmatch, cover, mincover, partition, and minpartition. Properties of these operators are described. Some of these operators may possibly take a very long time in finding a solution. Genetic algorithms are proposed. These algorithms are bounded by a polynomial time. These algorithms therefore enable DBMS to be capable of responding to queries involving proposed operators in a given time constraint. The database operations and query languages extended in this research provide a powerful tool for users as a database‐query tool which supports some decision support systems for information retrieval from a database.

With the rapid expansion of social networks, efficiently mining and analyzing massive graph data has become a fundamental challenge in social network research. Graph partitioning plays a pivotal role in enhancing the performance of such analyses. However, conventional graph partitioning methods predominantly rely on local structural information and often overlook the rich attribute information associated with vertices in social network graphs. To overcome this limitation, this paper introduces GP-DQN (Graph Partitioning via Double Deep Q-Network), a large-scale graph partitioning algorithm that jointly considers structural correlations, attribute disparities among user vertices, and partition load balancing. GP-DQN encodes partition load metrics and vertex attributes into vector representations and employs a Graph Convolutional Network (GCN) to aggregate both vertex features and neighborhood structures, thereby improving the accuracy and scalability of the partitioning process. A tailored reward function is designed to guide partitioning actions, where a Double Deep Q-Network (DDQN) predicts the expected partitioning rewards based on GCN-extracted features for assigning each vertex to different partitions. The partitioning strategy is iteratively optimized using both immediate and expected rewards, ultimately achieving balanced load distribution while minimizing the number of edge cuts. Experimental results demonstrate that GP-DQN produces well-balanced partitions with significantly fewer edge cuts, leading to enhanced computational efficiency within each partition.

Clustering algorithms divide data into meaningful or useful groups, called clusters, such that the intra-cluster similarity is maximized and the inter-cluster similarity is minimized.These discovered clusters can be used to explain the characteristics of the underlying data distribution and thus serve as the foundation for various data mining and analysis techniques.The applications of clustering include characterization of different customer groups based upon purchasing patterns, categorization of documents on the World Wide Web, grouping of genes and proteins that have similar functionality, grouping of spatial locations prone to earth quakes from seismological data, etc. What is CLUTOCLUTO is a software package for clustering low and high dimensional datasets and for analyzing the characteristics of the various clusters.CLUTO provides three different classes of clustering algorithms that operate either directly in the object's feature space or in the object's similarity space.These algorithms are based on the partitional, agglomerative, and graphpartitioning paradigms.A key feature in most of CLUTO's clustering algorithms is that they treat the clustering problem as an optimization process which seeks to maximize or minimize a particular clustering criterion function defined either globally or locally over the entire clustering solution space.CLUTO provides a total of seven different criterion functions that can be used to drive both partitional and agglomerative clustering algorithms, that are described and analyzed in [6,5].Most of these criterion functions have been shown to produce high quality clustering solutions in high dimensional datasets, especially those arising in document clustering.In addition to these criterion functions, CLUTO provides some of the more traditional local criteria (e.g., single-link, complete-link, and UPGMA) that can be used in the context of agglomerative clustering.Furthermore, CLUTO provides graph-partitioning-based clustering algorithms that are well-suited for finding clusters that form contiguous regions that span different dimensions of the underlying feature space.An important aspect of partitional-based criterion-driven clustering algorithms is the method used to optimize this criterion function.CLUTO uses a randomized incremental optimization algorithm that is greedy in nature, has low computational requirements, and has been shown to produce high-quality clustering solutions [6].CLUTO's graphpartitioning-based clustering algorithms utilize high-quality and efficient multilevel graph partitioning algorithms derived from the METIS and hMETIS graph and hypergraph partitioning algorithms [4,3].CLUTO also provides tools for analyzing the discovered clusters to understand the relations between the objects assigned to each cluster and the relations between the different clusters, and tools for visualizing the discovered clustering solutions.CLUTO can identify the features that best describe and/or discriminate each cluster.These set of features can be used to gain a better understanding of the set of objects assigned to each cluster and to provide concise summaries about the cluster's contents.Moreover, CLUTO provides visualization capabilities that can be used to see the relationships between the clusters, objects, and features.CLUTO's algorithms have been optimized for operating on very large datasets both in terms of the number of objects as well as the number of dimensions.This is especially true for CLUTO's algorithms for partitional clustering.These algorithms can quickly cluster datasets with several tens of thousands objects and several thousands of dimensions.Moreover, since most high-dimensional datasets are very sparse, CLUTO directly takes into account this sparsity and requires memory that is roughly linear on the input size.CLUTO's distribution consists of both stand-alone programs (vcluster and scluster) for clustering and analyzing these clusters, as well as, a library via which an application program can access directly the various clustering and analysis algorithms implemented in CLUTO. Outline of CLUTO's ManualCLUTO's manual is organized as follows.Section 2 describe the major changes from the previous release.Section 3 describes the stand-alone programs provided by CLUTO, and discusses its various options and analysis capabilities.Section 4 describes the type of clusters that CLUTO's algorithms can find, and discusses their scalability.Section 5 de-

In parallel computing based on finite element analysis, domain decomposition is a key technique for its preprocessing. Generally, a domain decomposition of a mesh can be realized through partitioning of a graph which is converted from a finite element mesh. This paper discusses the method for graph partitioning and the way to actualize mesh partitioning. Relevant softwares are introduced, and the data structure and key functions of Metis and ParMetis are introduced. The writing, compiling, and testing of the mesh partitioning interface program based on these key functions are performed. The results indicate some objective law and characteristics to guide the users who use the graph partitioning algorithm and software to write PFEM program, and ideal partitioning effects can be achieved by actualizing mesh partitioning through the program. The interface program can also be used directly by the engineering researchers as a module of the PFEM software. So that it can reduce the application of the threshold of graph partitioning algorithm, improve the calculation efficiency, and promote the application of graph theory and parallel computing.