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16th Genetic and Evolutionary Computation Conference (GECCO)

作者： Probst, Melte Rothlauf, Franz Grahl, Joern Johannes Gutenberg Univ Mainz Dept Informat Syst & Business Adm D-55122 Mainz Germany

ISBN: (纸本)9781450326629

We present a parallel version of RBM-EDA. RBM-EDA is an Estimation of Distribution Algorithm (FDA) that models dependencies between decision variables using a Restricted Boltzmann Machine (RBM). In contrast to other EDAs, RBM-EDA mainly uses matrix-matrix ultiplications for model estimation and sampling. Hence, for implementation, standard libraries for linear algebra can be used. This allows an easy parallelization and leads to a high utilization of parallel architectures. The probabilistic model of the parallel version and the version on a single core are identical. We explore the speedups gained from running RBM-EDA on a Graphics Processing Unit. For problems of bounded difficulty like deceptive traps, parallel RBM-EDA is faster by several orders of magnitude (up to 750 times) in comparison to a single-threaded implementation on a CPU. As the speedup grows linearly with problem size, parallel RBM-EDA may be particularly useful for large problems.

关键词： Parallelization Restricted Boltzmann Machines Estimation of Distribution Algorithms Machine Learning combinatorial optimization problems GPU Neural Networks

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Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data

Combining Geometric and Topological Ideas with Machine Learn...

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作者： Zhao, Qi University of California San Diego

学位级别：Ph.D., Doctor of Philosophy

Recently there has been an increasing number of learning problems arising in complex data domains, like graph-structured data, such as social networks and knowledge graphs. Various machine learning approaches have been developed to handle different kinds of data like PointNet for point clouds and graph neural networks for graph-structured data. At the same time, to tame the complexity in data, geometry and topology form natural platforms. In particular, computational geometry and the emerging field of topological data analysis (TDA) have been effective at capturing hidden structure and shape features from data, as well as providing efficient algorithms for them. In this thesis, we aim to integrate geometric ideas and topological concepts with machine learning pipelines to further augment their power and performance. In the first part of the thesis, we show how topological ideas, in particular, the so-called persistent homology, can help with analyzing graph-structured data. Persistent homology provides a flexible and versatile way to summarize complex shapes (including graphs) by a simple multiscale summary. In the first line of work, we designed an effective metric learning approach for persistence-based summaries of graphs, and showed how this improved graph classification tasks. In the second line, we show how topological summaries can be used to further improve graph neural networks' performance. In the second part, we investigate how geometric algorithmic ideas can be combined with neural networks (NNs) to tackle hard optimization problems in geometric setting. In recent years, NNs have shown promise in helping solve combinatorial optimization problems. However, such approaches often tend to be ad hoc. Instead of solving problems in a completely data-driven manner using NNs, we propose to design mixed algorithmic-NN frameworks, where NNs are used as components within an algorithmic framework. In particular, this allows us to leverage elegant algorithmic ideas f

关键词： combinatorial optimization problems Computational geometry Graph neural networks Machine learning Topological data analysis

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On approximation hardness of the minimum 2SAT-DELETION problem

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29th International Symposium on Mathematical Foundations of Computer Science

作者： Chlebík, M Chlebíková, J MPI Math Sci D-04103 Leipzig Germany Comenius Univ Dept Informat Educ Fac Math Phys & Informat Bratislava 84248 Slovakia

ISBN: (纸本)3540228233

The MINIMUM 2SAT-DELETION problem is to delete the minimum number of clauses in a 2SAT instance to make it satisfiable. It is one of the prototypes in the approximability hierarchy of minimization problems [8], and its approximability is largely open. We prove a lower approximation bound of 8root5 - 15 approximate to 2.88854, improving the previous bound of 10root5 - 21 approximate to 1.36067 by Dinur and Safra [5]. For highly restricted instances with exactly 4 occurrences of every variable we provide a lower bound of 3/2. Both inapproximability results apply to instances with no mixed Clauses (the literals in every clause are both either negated, or unnegated). We further prove that any k-approximation algorithm for MINIMUM 2SAT-DELETION polynomially reduces to a (2 - 2/k+1)-approximation algorithm for the MINIMUM VERTEX COVER problem. One ingredient of these improvements is our proof that for the MINIMUM VERTEX COVER problem restricted to graphs with a perfect matching its threshold on polynomial time approximability is the same as for the general MINIMUM VERTEX COVER problem. This improves also on results of Chen and Kanj [3].

关键词： Vertex cover perfect matching satisfiability combinatorial optimization problems approximation algorithm inapproximability Nemhauser-Trotter Theorem

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Chaotic Neural Network with Trigonometric Function Self-feedback 39

Chaotic Neural Network with Trigonometric Function Self-feed...

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39th Chinese Control Conference (CCC)

作者： Xu, Yaoqun Xu, Nan Qiu, Zeguo Harbin Univ Commerce Inst Syst Engn Harbin 150028 Peoples R China Harbin Univ Commerce Sch Management Harbin 150028 Peoples R China

ISBN: (纸本)9789881563903

A new chaotic neural network is constructed by introducing trigonometric function into the self-feedback term of the transient chaotic neural network;By analyzing the inverse bifurcation graph and the maximum Lyapunov exponent of the single neuron, the chaotic dynamic characteristics of the network are analyzed;The energy function of the chaotic neural network is constructed. Its stability is analyzed and the condition of gradual stability of the network is given;The network parameters for solving the traveling salesman problem are set. The simulation results show that the new model can avoid local minima effectively and is effective for solving combinatorial optimization problems.

关键词： Chaotic neural network trigonometric function self-feedback Lyapunov exponents energy function combinatorial optimization problems

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A Saturation Binary Neural Network for Bipartite Subgraph Problem

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7th International Conference on Intelligent Computing (ICIC)

作者： Zhang, Cui Zhao, Li-Qing Wang, Rong-Long Liaoning Inst Sci & Technol Dept Autocontrol Benxi Peoples R China Univ Fukui Grad Sch Engn Fukui Japan

ISBN: (纸本)9783642245527;9783642245534

In this paper, we propose a saturation binary neuron model and use it to construct a Hopfield-type neural network called saturation binary neural network to solve the bipartite sub-graph problem. A large number of instances have been simulated to verify the proposed algorithm, with the simulation result showing that our algorithm finds the solution quality is superior to the compared algorithms.

关键词： Saturation binary neuron model Saturation binary neural network combinatorial optimization problems Bipartite sub-graph problem

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Hierarchical scheduling method corresponding to multiple macros of task graph

Hierarchical scheduling method corresponding to multiple mac...

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IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM)

作者： Hasegawa, Motoki Kai, Munenori Seikei Univ Grad Sch Sci & Technol Musashino Tokyo Japan

ISBN: (纸本)9781538607008

One of the key methods for the optimization of parallel processing in a program is task scheduling. This intends to minimize implementation time for the entire program by determining schedule for optimally allocating tasks, which are processing units comprising the program, to available processor elements into pieces. Due to complexity of calculation and being a large-scale problem, the optimization problem is extremely challenging to solve with the current algorithms in a practical amount of time. Authors studied the method of partially optimizing task graph as a technique of task scheduling for large-scale problems. This paper reports on scheduling method that supports hierarchical macro for task groups.

关键词： Task Scheduling combinatorial optimization problems High Performance Search

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An approach to Quantum Annealing-based workforce assignment in manufacturing systems 56

An approach to Quantum Annealing-based workforce assignment ...

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56th CIRP International Conference on Manufacturing Systems, CIRP CMS 2023

作者： Wu, Xiangqian Schworm, Philipp Yi, Li Glatt, Moritz Aurich, Jan C. RPTU Kaiserslautern P.O. Box 3049 Kaiserslautern67653 Germany

Workforce assignment (WA) is a crucial aspect of production planning and control. However, current global crises have led to workforce absence and skill shortages. To tackle these challenges, a short-term WA approach is necessary for manufacturing systems flexibility and workforce health. Conventional methods for WA face complexity issues due to complex manufacturing systems, requiring substantial computation time. A Quantum Annealing-based WA approach is proposed in this paper to allocate tasks and shifts to workers. The proposed method is validated in a use case, showing improved solution quality compared to traditional methods. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientifc committee of the 56th CIRP International Conference on Manufacturing Systems 2023.

关键词： combinatorial optimization problems manufacturing systems Quantum Annealing shift planning Workforce assignment

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A bidirectional graph neural network for traveling salesman problems on arbitrary symmetric graphs

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2021年 97卷 104061-104061页

作者： Hu, Yujiao Zhang, Zhen Yao, Yuan Huyan, Xingpeng Zhou, Xingshe Lee, Wee Sun Northwestern Polytech Univ Dept Comp Sci Xian Peoples R China Northwestern Polytech Univ Sch Comp Sci Xian Peoples R China Natl Univ Singapore Dept Comp Sci Singapore Singapore

Deep learning has recently been shown to provide great achievement to the traveling salesman problem (TSP) on the Euclidean graphs. These methods usually fully represent the graph by a set of coordinates, and then captures graph information from the coordinates to generate the solution. The TSP on arbitrary symmetric graphs models more realistic applications where the working graphs maybe sparse, or the distance between points on the graphs may not satisfy the triangle inequality. When prior learning-based methods being applied to the TSP on arbitrary symmetric graphs, they are not capable to capture graph features that are beneficial to produce near-optimal solutions. Moreover, they suffer from serious exploration problems. This paper proposes a bidirectional graph neural network (BGNN) for the arbitrary symmetric TSP. The network learns to produce the next city to visit sequentially by imitation learning. The bidirectional message passing layer is designed as the most important component of BGNN. It is able to encode graphs based on edges and partial solutions. By this way, the proposed approach is much possible to construct near-optimal solutions for the TSP on arbitrary symmetric graphs, and it is able to be combined with informed search to further improve performance.

关键词： Deep learning Graph neural network Traveling salesman problem combinatorial optimization problems Planning

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Self-adaptive Equilibrium Optimizer for solving global, combinatorial, engineering, and Multi-Objective problems

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期195卷 116552-116552页

作者： Houssein, Essam H. Celik, Emre Mahdy, Mohamed A. Ghoniem, Rania M. Minia Univ Fac Comp & Informat Al Minya Egypt Duzce Univ Engn Fac Elect Elect Engn Dept Duzce Turkey Beni Suef Univ Fac Comp & Artificial Intelligence Bani Suwayf Egypt Princess Nourah Bint Abdulrahman Univ Coll Comp & Informat Sci Dept Informat Technol POB 84428 Riyadh 11671 Saudi Arabia Mansoura Univ Dept Comp Mansoura 35516 Egypt

This paper proposes a self-adaptive Equilibrium Optimizer (self-EO) to perform better global, combinatorial, engineering, and multi-objective optimization problems. The new self-EO algorithm integrates four effective exploring phases, which address the potential shortcomings of the original EO. We validate the performances of the proposed algorithm over a large spectrum of optimization problems, i.e., ten functions of the CEC'20 benchmark, three engineering optimization problems, two combinatorial optimization problems, and three multi-objective problems. We compare the self-EO results to those obtained with nine other metaheuristic algorithms (MAs), including the original EO. We employ different metrics to analyze the results thoroughly. The self-EO analyses suggest that the self-EO algorithm has a greater ability to locate the optimal region, a better trade-off between exploring and exploiting mechanisms, and a faster convergence rate to (near)-optimal solutions than other algorithms. Indeed, the self-EO algorithm reaches better results than the other algorithms for most of the tested functions.

关键词： Equilibrium Optimizer Enhanced Equilibrium Optimizer (self-EO) Multi-Objective self-EO (MO-self-EO) Engineering design problems combinatorial optimization problems Metaheuristic algorithms (MAs)

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FPGA Implementation of Hardware-Oriented Chaotic Boltzmann Machines

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IEEE ACCESS 2020年 8卷 204360-204377页

作者： Kawashima, Ichiro Morie, Takashi Tamukoh, Hakaru Kyushu Inst Technol Grad Sch Life Sci & Syst Engn Kitakyushu Fukuoka 8080196 Japan

Boltzmann machines (BMs) are useful in various applications but are limited by their requirement to generate random numbers. In contrast, chaotic Boltzmann machines (CBMs) are neural networks that imitate the stochastic behavior of BMs with the chaotic dynamics and deterministic behavior, without random numbers. CBMs can potentially require fewer hardware resources than the original algorithms due to the unnecessity of random number generators. In this study, hardware-oriented algorithms and a differential multiply-accumulation operation are proposed to overcome the difficulties of implementing CBMs on field-programmable gate arrays (FPGAs). A hardware-oriented algorithm for CBMs, which includes fixed-point operations and shift operations, is proposed to reduce hardware resource utilization in the implemented circuits. In particular, the differential multiply-accumulate operation allows us to implement the multiply-accumulate operation with block random access memory and digital signal processors to reduce the consumption of lookup tables and flip-flops in FPGAs without losing the calculation speed. Our proposed approach was evaluated in numerical simulations, logical synthesis, and FPGA implementation. The calculation speed of FPGA-implemented CBMs was compared with software-implemented CBMs, which resulted in 1 / 6,500 of calculation time reduction in a 300-neuron CBM. Moreover, 2,048 neurons of CBM were realized by the logical synthesis. Therefore, the proposed hardware implementation of CBMs was shown to be feasible. The proposed CBMs can solve combinatorial optimization problems at a larger scale with fewer resources.

关键词： Chaotic Boltzmann machines combinatorial optimization problems Ising model field-programmable gate array

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