Solving the m‐way graph partitioning problem using a genetic algorithm

Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem. We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.

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.

HEURISTIC SOLUTION PROCEDURES FOR THE GRAPH PARTITIONING PROBLEM

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. >

This research proposes an efficient parallel graph partitioning algorithm for the big data environment, aiming to solve the bottlenecks of traditional clustering techniques in terms of processing speed and scalability. The algorithm adopts a multi-level graph partitioning framework, decomposing the network information processing task into multiple levels, gradually simplifying the graph structure and backtracking refinement, thereby significantly reducing the computational complexity while ensuring the partitioning quality. The algorithm focuses on balancing the node cohesion within partitions and the edge cutting cost of inter-partition communication. By constructing a global objective function, it minimizes the number of edges across partitions and the workload differences among various sub-graphs, thereby achieving a more balanced partitioning result. The research results show that this algorithm achieves a resource utilization rate of 0.95. In the Hadoop cluster environment, 95% of the computing resources are effectively used for actual task processing, which is significantly higher than that of the competing algorithms. The energy efficiency ratio reaches 0.98, indicating that the number of tasks completed per unit of energy consumption is close to the optimal level, which is superior to the 0.78 to 0.67 range of existing methods, reflecting the advantages of this algorithm in green computing. The load imbalance rate is only 0.00395, and the point weight imbalance rate is 0.00141, which are much lower values than those of the comparison algorithm. This indicates that the algorithm achieves a high degree of balance in task allocation and node weight distribution, effectively avoiding resource waste and performance bottlenecks.

Task allocation for Unmanned Aerial Vehicle (UAV) swarms is a complex challenge. Effective distribution of tasks among multiple UAVs necessitates the optimization of conflicting objectives, such as task balance, flight distance, cost, and target benefits. This multi-objective optimization problem is inherently intricate due to strong interdependencies, nonlinear relationships, and dynamic environments. Traditional methods, including heuristic algorithms, supervised machine learning, and basic reinforcement learning mechanisms, often suffer from low efficiency and strict requirements for data sources or supervision mechanisms. They also struggle to adapt to problems with large discrete action spaces. To address this challenge, this paper proposes a novel approach that integrates swarm intelligence simulation with reinforcement learning. The core of this approach is a reinforcement learning algorithm based on the Deep Deterministic Policy Gradient (DDPG) framework. A key innovation is a customized DDPG variant specifically designed to handle the large, discrete action spaces inherent in UAV task allocation. Additionally, a behavior tree model is employed to simulate UAV swarm interactions, providing a realistic and verifiable environment for evaluating task allocation strategies. This simulation generates a rich dataset for training and testing reinforcement learning algorithms. The combined approach efficiently addresses the multi-objective optimization problem, enabling optimal task distribution for numerous UAVs. Compared to existing heuristic methods, the proposed approach demonstrates superior computational efficiency and solution quality, while maintaining reasonable convergence stability and environmental adaptability. Simulation-based validation ensures the approach’s robustness in dynamic environments, a critical factor for practical applications. Overall, the integration of simulation and reinforcement learning provides a powerful framework for tackling the complex task allocation problem in UAV swarms.

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

: Our Phase I work resulted in a software prototype for MFD page organization, a technique for translating MFD page organizations into graph partitioning problems, and a genetic algorithm for carrying out the graph partitioning. We apply our system to a scenario taken from the Comanche attack helicopter task analysis. The system out-performs other published algorithms for graph partitioning.

Genetic algorithm for the personnel assignment problem with multiple objectives

Task allocation is one of the cor e steps to effectively exploit the capabilities of cooperative control of multiple Uninhabited Aerospace Vehicle (UAV) teams. Task allocation is an NP -complete problem. In this paper, we present a new task allocation algorithm that is based on the principl es of genetic algorithm (GA). GA is a class of adaptive search algorithms derived from biological population genetics. We discuss the adaptation and implementation of the GA search strategy to the task allocation problem in the cooperative control of multi ple UAVs. Simulation results indicate that the GA strategy is a feasible approach for the task allocation problem .

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.

The Traveling Salesman Problem (TSP) represents an extensively researched challenge in combinatorial optimization. Genetic Algorithms (GAs), recognized for their nature-inspired approach, stand as potent heuristics for resolving combinatorial optimization problems. Nevertheless, GA exhibits inherent deficiencies, notably premature convergence, which diminishes population diversity and consequential inefficiencies in computational processes. Such drawbacks may result in protracted operations and potential misallocation of computational resources, particularly when confronting intricate NP-hard optimization problems. To address these challenges, the current study underscores the pivotal role of the selection operator in ameliorating GA efficiency. The proposed methodology introduces a novel parameter operator within the Stochastic Universal Selection (SUS) framework, aimed at constricting the search space and optimizing genetic operators for parent selection. This innovative approach concentrates on selecting individuals based on their fitness scores, thereby mitigating challenges associated with population sorting and individual ranking while concurrently alleviating computational complexity. Experimental results robustly validate the efficacy of the proposed approach in enhancing both solution quality and computational efficiency, thereby positioning it as a noteworthy contribution to the domain of combinatorial optimization.

This paper presents a design CAD tool for automated design of digital CMOS VLSI circuits. In order to fit the circuit performance into desired specifications, a multi-objective optimization approach based on genetic algorithms (GA) is proposed and the transistor sizes are calculated based on the analytical equations describing the behavior of the circuit. The optimization algorithm is developed in MATLAB and the performance of the designed circuit is verified using HSPICE simulations based on 0.18µm CMOS technology parameters. Different digital integrated circuits were successfully designed and verified using the proposed design tool. It is also shown in this paper that, the design results obtained from the proposed algorithm in MATLAB, have a very good agreement with the obtained circuit simulation results in HSPICE.

PurposeThe purpose of this paper is to introduce a general equation for eigensolution. Eigenvalues and eigenvectors of graphs have many applications in combinatorial optimization and structural mechanics. Some important applications of graph products consist of nodal ordering and graph partitioning for structuring the structural matrices and finite element subdomaining, respectively.Design/methodology/approachIn the existing methods for the eigensolution of Laplacian matrices, members have been added to the model of a graph product such that for its Laplacian matrix an algebraic relation between blocks become possible. These methods are categorized as topological approaches. Here, using concepts of linear algebra a general algebraic method is developed.FindingsA new algebraic method is introduced for calculating the eigenvalues of Laplacian matrices in graph products.Originality/valueThe present method provides a simple tool for calculating the eigenvalues of the Laplacian matrices without using the configurational model and merely by using the Laplacian matrices. The developed formula for calculating the eigenvalues contains approximate terms which can be managed by the analyst.

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.