Graph Partitioning Based on the Combined Approach

2020 ◽  
Vol 26 (12) ◽  
pp. 667-672
Author(s):  
V. V. Kureichik ◽  
◽  
Vl. Vl. Kureichik ◽  
Keyword(s):  
Graph Partitioning ◽  
Optimization Problems ◽  
Experimental Studies ◽  
Optimization Method ◽  
Combined Approach ◽  
Software Module ◽  
Combinatorial Optimization Problems ◽  
Partitioning Problem ◽  
Complex Optimization ◽  
Combined Algorithm

The article considers one of the most important combinatorial optimization problems — the problem of graph partitioning. It belongs to the class of NP-complex optimization problems. The article presents the partitioning problem statement. Due to the complexity of this task, the article proposes a new search strategy based on a combined approach. The combined approach is to divide the decision-making process into two levels. At the first level, the bee optimization method is used to quickly obtain subdomains with a high value of the objective function, and at the second level, an evolutionary algorithm is used to improve obtained solutions. To implement this approach, the authors developed a combined algorithm that can obtain sets of quasi-optimal solutions in polynomial time and avoid looping in local regions at the same time. A software module is developed and algorithms for partitioning graphs into parts are implemented. A computational experiment has been carried out when dividing into 8 parts of test circuits (benchmarks) by IBM. An analysis of experimental studies showed that the developed combined algorithm is on average 5 % higher than the partition results obtained by well-known hMetis, PGAComplex algorithms with comparable solution time, which indicates the effectiveness of the proposed approach. The time complexity of the developed combined algorithm is approximately O (n2).

Modified Firefly Algorithm With Chaos Theory for Feature Selection

2019 ◽  
Vol 10 (2) ◽  
pp. 1-20 ◽  
Author(s):  
Sujata Dash ◽  
Ruppa Thulasiram ◽  
Parimala Thulasiraman
Keyword(s):  
Feature Selection ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Heuristic Method ◽  
High Dimensional ◽  
Support Vector ◽  
Combinatorial Optimization Problems ◽  
Meta Search ◽  
Combined Algorithm

Conventional algorithms such as gradient-based optimization methods usually struggle to deal with high-dimensional non-linear problems and often land up with local minima. Recently developed nature-inspired optimization algorithms are the best approaches for finding global solutions for combinatorial optimization problems like microarray datasets. In this article, a novel hybrid swarm intelligence-based meta-search algorithm is proposed by combining a heuristic method called conditional mutual information maximization with chaos-based firefly algorithm. The combined algorithm is computed in an iterative manner to boost the sharing of information between fireflies, enhancing the search efficiency of chaos-based firefly algorithm and reduces the computational complexities of feature selection. The meta-search model is implemented using a well-established classifier, such as support vector machine as the modeler in a wrapper approach. The chaos-based firefly algorithm increases the global search mobility of fireflies. The efficiency of the model is studied over high-dimensional disease datasets and compared with standard firefly algorithm, particle swarm optimization, and genetic algorithm in the same experimental environment to establish its superiority of feature selection over selected counterparts.

A New Sequential Multi-Disciplinary Optimization Method for Bi-Level Decomposed Systems

2015 ◽  
Author(s):  
Jianhua Zhou ◽  
Mian Li ◽  
Min Xu
Keyword(s):  
Optimization Problems ◽  
Optimization Method ◽  
Global Variables ◽  
Initial Stage ◽  
Shared Variables ◽  
Consistency Constraints ◽  
Full Optimization ◽  
Complex Optimization ◽  
Coupling Variables

Multi-discipline optimization (MDO) has been proposed to handle complex optimization problems with multiple disciplines or subsystems. These problems are with global and coupling variables that are shared by more than one subsystem, which is one of the major challenges for these problems. Diverse methods that can be classified as of single- and multi-levels have been developed aiming to solve those problems. Most of these methods do not give optimization autonomies to each subsystem concerning these shared variables. This study proposed that for decomposed bi-level MDO problems, each subsystem is given full optimization autonomy in the initial stage to decide possible best solutions individually. Then all the obtained solutions are given to the system that will process the information and dispatch shared variables to each subsystem. Based on these dispatched variables, subsystems will sequentially perform the corresponding optimization with respect to their local (and global) variables with additional consistency constraints. There is no nested optimization between the system and subsystems. Six numerical and engineering examples are tested and comparisons with other methods are made to demonstrate the efficiency and applicability of the proposed approach.

scholarly journals Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Junyi Huang ◽  
Yisheng Fang ◽  
Zhichao Ruan
Keyword(s):  
Spatial Light Modulator ◽  
Large Scale ◽  
Single Phase ◽  
Optimization Problems ◽  
Light Modulator ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
Partitioning Problem ◽  
Statistical Systems ◽  
Antiferromagnetic Model

AbstractRecently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground-state-search acceleration of an antiferromagnetic model with 40000 spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

scholarly journals Multilevel Combinatorial Optimization across Quantum Architectures

2021 ◽  
Vol 2 (1) ◽  
pp. 1-29
Author(s):  
Hayato Ushijima-Mwesigwa ◽  
Ruslan Shaydulin ◽  
Christian F. A. Negre ◽  
Susan M. Mniszewski ◽  
Yuri Alexeev ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems ◽  
Large Scale Problems ◽  
Quantum Processor ◽  
Partitioning Problem ◽  
Real World Datasets ◽  
Near Future

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution. Reproducibility : Our code and data are available at Reference [1].

scholarly journals Improved upper bounds in clique partitioning problem

2019 ◽  
pp. 93-104
Author(s):  
Alexander B. Belyi ◽  
Stanislav L. Sobolevsky ◽  
Alexander N. Kurbatski ◽  
Carlo Ratti
Keyword(s):  
Exact Solution ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Weighted Graph ◽  
Upper Bounds ◽  
Clique Partitioning ◽  
Clustering Problem ◽  
Combinatorial Optimization Problems ◽  
Clique Partitioning Problem ◽  
Partitioning Problem

In this work, a problem of partitioning a complete weighted graph into cliques in such a way that sum of edge weights between vertices belonging to the same clique is maximal is considered. This problem is known as a clique partitioning problem. It arises in many applications and is a varian of classical clustering problem. However, since the problem, as well as many other combinatorial optimization problems, is NP-hard, finding its exact solution often appears hard. In this work, a new method for constructing upper bounds of partition quality function values is proposed, and it is shown how to use these upper bounds in branch and bound technique for finding an exact solution. Proposed method is based on the usage of triangles constraining maximal possible quality of partition. Novelty of the method lies in possibility of using triangles overlapping by edges, which allows to find much tighter bounds than when using only non-overlapping subgraphs. Apart from constructing initial estimate, a method of its recalculation, when fixing edges on each step of branch and bound method, is described. Test results of proposed algorithm on generated sets of random graphs are provided. It is shown, that version that uses new bounds works several times faster than previously known methods.

scholarly journals Genetic Algorithms as Computational Methods for Finite-Dimensional Optimization

2021 ◽  
pp. 5-14
Author(s):  
Nataliya Gulayeva ◽  
Volodymyr Shylo ◽  
Mykola Glybovets
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Numerical Methods ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Direct Search ◽  
Mathematical Programming Problem ◽  
Combinatorial Optimization Problems

Introduction. As early as 1744, the great Leonhard Euler noted that nothing at all took place in the universe in which some rule of maximum or minimum did not appear [12]. Great many today’s scientific and engineering problems faced by humankind are of optimization nature. There exist many different methods developed to solve optimization problems, the number of these methods is estimated to be in the hundreds and continues to grow. A number of approaches to classify optimization methods based on various criteria (e.g. the type of optimization strategy or the type of solution obtained) are proposed, narrower classifications of methods solving specific types of optimization problems (e.g. combinatorial optimization problems or nonlinear programming problems) are also in use. Total number of known optimization method classes amounts to several hundreds. At the same time, methods falling into classes far from each other may often have many common properties and can be reduced to each other by rethinking certain characteristics. In view of the above, the pressing task of the modern science is to develop a general approach to classify optimization methods based on the disclosure of the involved search strategy basic principles, and to systematize existing optimization methods. The purpose is to show that genetic algorithms, usually classified as metaheuristic, population-based, simulation, etc., are inherently the stochastic numerical methods of direct search. Results. Alternative statements of optimization problem are given. An overview of existing classifications of optimization problems and basic methods to solve them is provided. The heart of optimization method classification into symbolic (analytical) and numerical ones is described. It is shown that a genetic algorithm scheme can be represented as a scheme of numerical method of direct search. A method to reduce a given optimization problem to a problem solvable by a genetic algorithm is described, and the class of problems that can be solved by genetic algorithms is outlined. Conclusions. Taking into account the existence of a great number of methods solving optimization problems and approaches to classify them it is necessary to work out a unified approach for optimization method classification and systematization. Reducing the class of genetic algorithms to numerical methods of direct search is the first step in this direction. Keywords: mathematical programming problem, unconstrained optimization problem, constrained optimization problem, multimodal optimization problem, numerical methods, genetic algorithms, metaheuristic algorithms.

scholarly journals Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing

2021 ◽  
Author(s):  
Zhichao Ruan ◽  
Huang Junyi ◽  
Yisheng Fang
Keyword(s):  
Spatial Light Modulator ◽  
Large Scale ◽  
Single Phase ◽  
Optimization Problems ◽  
Light Modulator ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
Partitioning Problem ◽  
Statistical Systems ◽  
Antiferromagnetic Model

Abstract Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

Decomposition-Based Assembly Synthesis for Maximum Structural Strength and Modularity

2004 ◽  
Vol 126 (2) ◽  
pp. 244-253 ◽  
Author(s):  
O. L. Cetin ◽  
K. Saitou
Keyword(s):  
Graph Partitioning ◽  
Structural Strength ◽  
Optimization Method ◽  
Structural Topology ◽  
Acceptable Solution ◽  
Frame Design ◽  
Computational Overhead ◽  
Conceptual Design Phase ◽  
Bicycle Frame ◽  
Partitioning Problem

This study presents a systematic decomposition process to carry out assembly synthesis as a tool during the conceptual design phase of a product. Two configurations obtained by structural topology optimization are decomposed automatically into assemblies consisting of multiple members with simpler geometries. Generating topology graphs for both products, the search for an optimal decomposition can then be posed as a graph partitioning problem. Considering the complexity and the corresponding computational overhead of the problem, a steady-state genetic algorithm is employed as the optimization method. The final objective function attempts to find a solution that brings about two structures with maximum structural strength, maximum assemblability, and one or more components that can be shared by both products. The software implementation is carried out and a bicycle frame design problem is solved using the procedure. It is observed that the algorithm manages to find an acceptable solution, allowing the commonality of one component in both end products and still maintaining a good structural strength and assemblability.

scholarly journals An Improved Artificial Bee Colony Algorithm Based on Elite Strategy and Dimension Learning

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 289
Author(s):  
Songyi Xiao ◽  
Wenjun Wang ◽  
Hui Wang ◽  
Dekun Tan ◽  
Yun Wang ◽  
...  
Keyword(s):  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Optimization Method ◽  
Computational Results ◽  
Bee Colony ◽  
Elite Strategy ◽  
Large Jump ◽  
Complex Optimization

Artificial bee colony is a powerful optimization method, which has strong search abilities to solve many optimization problems. However, some studies proved that ABC has poor exploitation abilities in complex optimization problems. To overcome this issue, an improved ABC variant based on elite strategy and dimension learning (called ABC-ESDL) is proposed in this paper. The elite strategy selects better solutions to accelerate the search of ABC. The dimension learning uses the differences between two random dimensions to generate a large jump. In the experiments, a classical benchmark set and the 2013 IEEE Congress on Evolutionary (CEC 2013) benchmark set are tested. Computational results show the proposed ABC-ESDL achieves more accurate solutions than ABC and five other improved ABC variants.

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