Decomposition Problem Research Articles

Neuromorphic Electronic Module, focused on the Use of Memristor ECB, for Image Recognition

Currently, the expansion of the range of tasks solved by neural networks occurs mainly due to the complication of their structure, an increase in the number of neurons and synapses. Networks with thousands of neurons and tens to hundreds of thousands of synapses can achieve impressive results in the areas of speech processing, image identification, computer vision, etc., but at the same time, their use and training require significant computing power and energy costs. This is unacceptable for embedded autonomous systems, which, as follows from current trends, will constitute one of the most important applications for neural networks on a chip and must perform their tasks using a minimum number of elements and with minimal energy consumption. In this article a method for increasing the efficiency of hardware implementation and minimizing the number of electronic synaptic elements of asynchronous spiking neural networks (ASNN) in solving image identification problems was developed. To achieve this goal, a theoretical analysis of ASNN architectural solutions was carried out, the number of electronic synaptic elements was minimized due to the decomposition of the image identification problem, an ASNN software model was developed, neuron parameters were optimized and the neural network was learned (the weights of electronic synaptic elements were sat) on a software model. An ASNN electrical circuit was developed and the results of SPICE modeling were obtained. A hardware implementation of an asynchronous spiking neural network on serial electronic components was performed. The effectiveness of the proposed method was demonstrated in the process of optimizing the parameters of neurons and learning the neural network on the developed software model and confirmed by the results of SPICE modeling of the developed electrical circuit of the ASNN and the results of measuring the signals of the neural network implemented on serial electronic components.

A Normal Form Algorithm for Tensor Rank Decomposition

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system of polynomial equations allows us to leverage recent numerical linear algebra tools from computational algebraic geometry. We characterize the complexity of our algorithm in terms of an algebraic property of this polynomial system—the multigraded regularity. We prove effective bounds for many tensor formats and ranks, which are of independent interest for overconstrained polynomial system solving. Moreover, we conjecture a general formula for the multigraded regularity, yielding a (parameterized) polynomial time complexity for the tensor rank decomposition problem in the considered setting. Our numerical experiments show that our algorithm can outperform state-of-the-art numerical algorithms by an order of magnitude in terms of accuracy, computation time, and memory consumption.

Software System for End-Products Accounting in Bakery Production Lines Based on Distributed Video Streams Analysis

Among the main requirements of modern surveillance systems are stability in the face of negative influences and intellectualization. The purpose of intellectualization is that the surveillance system should perform not only the main functions such as monitoring and stream recording but also have to provide effective stream processing. The requirement for this processing is that the system operation has to be automated, and the operator's influence should be minimal. Modern intelligent surveillance systems require the development of grouping methods. The context of the grouping method here is associated with a decomposition of the target problem. Depending on the purpose of the system, the target problem can represent several subproblems, each of which usually accomplishes by artificial intelligence or data mining methods.

Randomized sampling techniques based low-tubal-rank plus sparse tensor recovery

Recently, tensor robust principal component analysis (TRPCA) based on the tensor singular value decomposition (t-SVD) framework has gained considerable attention owing to its ability to decompose a data tensor into a low-tubal-rank component and a sparse residual component. Although the tensor principal component pursuit (TPCP) program is a powerful and foremost approach for solving the TRPCA problem, it utilizes all the data to extract the intrinsic component, which causes it to be constrained by the scale of the data and makes it unsuitable for high-dimensional settings in big data applications. In this paper, using randomized sampling techniques, we propose a randomized optimization algorithm with lower computational complexity that transforms a large-scale tensor decomposition problem into two low-dimensional column/row subspace pursuit problems. In addition, the exact recovery guarantee of the proposed method is established. The obtained results suggest that the sufficient number of randomly selected columns/rows grows linearly with the changes in the rank and the coherency factor of the low-tubal-rank component. Furthermore, experimental results show that the proposed approach outperforms the full-scale TPCP in terms of decomposition efficiency on synthetic data and real color video data.

A novel two-stage TSO–DSO coordination approach for managing congestion and voltages

This paper proposes a novel approach to TSO–DSO coordination in day-ahead operation planning for the procurement of ancillary services (AS) such as congestion management and voltage control. The approach overcomes two major issues hindering practical applicability of existing TSO–DSO coordination mechanisms, namely the computational complexity due to the large number of times the TSO and DSO problems are resolved as well as the inability to map analytically the cost and amount of flexibility at DSO level into TSO problem. To this end, a two-fold novelty of our approach consists of the decomposition of the overall AS problem into two sequential stages, which seek the procurement of: (i) “active power related” AS (i.e., for congestion management) and then (ii) the “reactive power related” AS (i.e., for voltage support), respectively as well as a fast approximation of the cost of aggregated active and reactive power flexibilities of active distribution systems (ADSs). Unlike existing mechanisms, the proposed approach considers real-world challenging aspects such as the N-1 security at TSO level and operation uncertainties at both TSO and DSO levels. Accordingly, the approach relies on tailored versions of stochastic multi-period AC security-constrained optimal power flow (S-MP-SCOPF) at TSO level and stochastic multi-period AC optimal power flow (S-MP-OPF) at DSO level, which are formulated as non-linear programming (NLP) problems. The importance and performance of the proposed approach are illustrated on a power system connecting a 60-bus transmission system (under 33 N-1 contingencies) with five 34-bus ADSs.

Exploring students’ learning support use in digital game-based math learning: A mixed-methods approach using machine learning and multi-cases study

Digital game-based math learning environments (math DGBLE) are promising platforms that provide students with opportunities to master conceptual understanding and cultivate mathematical thinking, on which the contemporary mathematics education places an emphasis. Literature on learning support in digital game-based learning (DGBL) rarely investigate learners' support-use behaviors and interaction patterns in relation to math learning. We addressed this research gap in this exploratory mixed-methods study. We designed and developed a packet of learning supports (i.e., Task Planner and Math Story) in a math DGBLE. Task Planner is designed to assist learners' systematic and planned efforts for math problem solving whereas Math Story features historical stories and real-life applications of math concepts. With the data collected via mixed-methods approach, we extracted six clusters of learning-support-use behaviors via unsupervised machine learning technique (i.e., Gaussian Mixture Model), including 1) skills development and application of mathematical problem decomposition, 2) conceptual knowledge development, 3) metacognitive mathematical connections, 4) metacognitive regulation, 5) information selection using cognitive aids, and 6) sustained motivation for necessary aversive practices. Qualitative multi-cases study revealed nuanced details regarding learners’ interactions with the learning supports in DGBLE. Results showed that the designed in-game learning supports facilitated individual meaningful and mindful math problem-solving experiences. The findings suggested that a mixed-methods research design integrating machine learning with multi-cases study could act as a tool for learner behavior and interaction pattern research that informs the design of adaptive and effective DGBL.

Multiple Classifiers-Assisted Evolutionary Algorithm Based on Decomposition for High-Dimensional Multiobjective Problems

Surrogate-assisted multiobjective evolutionary algorithms (MOEAs) have advanced the field of computationally expensive optimization, but their progress is often restricted to low-dimensional problems. This manuscript presents a multiple classifiers-assisted evolutionary algorithm based on decomposition, which is adapted for high-dimensional expensive problems in terms of the following two insights. Compared to approximation-based surrogates, the accuracy of classification-based surrogates is robust for few high-dimensional training samples. Furthermore, multiple local classifiers can hedge the risk of overfitting issues. Accordingly, the proposed algorithm builds multiple classifiers with support vector machines (SVMs) on a decomposition-based multiobjective algorithm, wherein each local classifier is trained for a corresponding scalarization function. Experimental results confirm that the proposed algorithm is competitive to the state-of-the-art algorithms and computationally efficient as well.

Reconfigurable Intelligent Surface-Aided 6G Massive Access: Coupled Tensor Modeling and Sparse Bayesian Learning

This paper investigates a reconfigurable intelligent surface (RIS)-aided unsourced random access (URA) scheme for the sixth-generation (6G) wireless networks with massive sporadic traffic devices. First of all, this paper proposes a novel joint active device separation (the message recovery of active device) and channel estimation architecture for the RIS-aided URA. Specifically, the RIS passive reflection is optimized before the successful device separation. Then, by associating the data sequences to multiple rank-one tensors and exploiting the angular sparsity of the RIS-BS channel, the detection problem is cast as a high-order coupled tensor decomposition problem without the need of exploiting pilot sequences. However, the inherent coupling among multiple sparse device-RIS channels, together with the unknown number of active devices make the detection problem at hand deviate from the widely-used coupled tensor decomposition format. To overcome this challenge, this paper judiciously devises a probabilistic model that captures both the element-wise sparsity from the angular channel model and the low-rank property due to the sporadic nature of URA. Then, based on such a probabilistic model, a iterative detection algorithm is developed under the framework of sparse variational inference, where each update iteration is obtained in a closed-form and the number of active devices can be automatically estimated for effectively avoiding the overfitting of noise. Extensive simulation results confirm the excellence of the proposed URA algorithm, especially for the case of a large number of reflecting elements for accommodating a significantly large number of devices.

Merged Differential Grouping for Large-Scale Global Optimization

The divide-and-conquer strategy has been widely used in cooperative co-evolutionary algorithms to deal with large-scale global optimization problems, where a target problem is decomposed into a set of lower-dimensional and tractable subproblems to reduce the problem complexity. However, such a strategy usually demands a large number of function evaluations to obtain an accurate variable grouping. To address this issue, a merged differential grouping (MDG) method is proposed in this article based on the subset–subset interaction and binary search. In the proposed method, each variable is first identified as either a separable variable or a nonseparable variable. Afterward, all separable variables are put into the same subset, and the nonseparable variables are divided into multiple subsets using a binary-tree-based iterative merging method. With the proposed algorithm, the computational complexity of interaction detection is reduced to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(\max \{n,n_{ns}\times \log _{2} k\})$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{ns}(\leq n)$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k( &lt; n)$ </tex-math></inline-formula> indicate the numbers of decision variables, nonseparable variables, and subsets of nonseparable variables, respectively. The experimental results on benchmark problems show that MDG is very competitive with the other state-of-the-art methods in terms of efficiency and accuracy of problem decomposition.

On product decomposition

Given a finite set W in k¯n where k¯ is the algebraic closure of a field k one would like to determine if W can be decomposed as ∏i=1nVi where Vi⊂k¯ under a linear transformation, that is, W→λ∏i=1nVi where λ∈Gln(k¯). We assume that W is presented as W=Z(F), the zero set of a polynomial system F in n variables over k. We study algebraic characterization of such product decomposition. For decomposition into component sets of the same cardinality we obtain a stronger characterization and show that the decomposition in this case is essentially unique (up to permutation and scalar multiplication of coordinates). We investigate computational problems that arise from the decomposition problem.

A surrogate-assisted variable grouping algorithm for general large-scale global optimization problems

Problem decomposition plays an important role when applying cooperative coevolution (CC) to large-scale global optimization problems. However, most learning-based decomposition algorithms only apply to additively separable problems, while the others insensitive to problem type perform low decomposition accuracy and efficiency. Given this limitation, this study designs a general-separability-oriented detection criterion, and further proposes a novel decomposition algorithm called surrogate-assisted variable grouping (SVG). The new criterion detects the separability between a variable and some other variables by checking whether its optimum changes with the latter. Consistent with the definition of general separability, this criterion endows SVG with strong applicability and high accuracy. To reduce expensive fitness evaluations, SVG locates the optimum of a variable with the help of a surrogate model rather than the original high-dimensional model. Moreover, it converts the variable-grouping process into a search process in a binary tree by taking variable subsets as tree nodes. This facilitates the reutilization of historical separability information, thereby reducing separability detection times. Experimental results on a general benchmark suite indicate that compared with six state-of-the-art decomposition algorithms, SVG achieves higher accuracy and efficiency on both additively and nonadditively separable problems. Furthermore, it can significantly enhance the optimization performance of CC.

A Novel Self-Adaptive Cooperative Coevolution Algorithm for Solving Continuous Large-Scale Global Optimization Problems

Unconstrained continuous large-scale global optimization (LSGO) is still a challenging task for a wide range of modern metaheuristic approaches. A cooperative coevolution approach is a good tool for increasing the performance of an evolutionary algorithm in solving high-dimensional optimization problems. However, the performance of cooperative coevolution approaches for LSGO depends significantly on the problem decomposition, namely, on the number of subcomponents and on how variables are grouped in these subcomponents. Also, the choice of the population size is still an open question for population-based algorithms. This paper discusses a method for selecting the number of subcomponents and the population size during the optimization process (“on fly”) from a predefined pool of parameters. The selection of the parameters is based on their performance in the previous optimization steps. The main goal of the study is the improvement of coevolutionary decomposition-based algorithms for solving LSGO problems. In this paper, we propose a novel self-adapt evolutionary algorithm for solving continuous LSGO problems. We have tested this algorithm on 15 optimization problems from the IEEE LSGO CEC’2013 benchmark suite. The proposed approach, on average, outperforms cooperative coevolution algorithms with a static number of subcomponents and a static number of individuals.

A relax-and-fix Pareto-based algorithm for a bi-objective vaccine distribution network considering a mix-and-match strategy in pandemics

Mass vaccination in pandemics is one of the most effective strategies to halt disease transmission. A well-organized vaccination plan is essential for guaranteeing its success in cases with limited vaccines. On the other hand, most vaccines need more than one dose for appropriate immunity, intensifying the vaccine shortage probability and complicating decision-making. This study presents a bi-objective mixed-integer linear model for a vaccine distribution chain problem, simultaneously considering economic and social objectives, with multi-dose vaccination adaptable even for booster doses. Moreover, the compatible vaccines in each vaccination process are considered a mix-and-match strategy to diversify vaccination alternatives and alleviate the vaccine shortage risk. It is shown that the problem is NP-hard, and we develop two heuristic and meta-heuristic algorithms to solve real-size instances in a reasonable time. Both algorithms use problem size reduction and problem decomposition techniques to produce an approximate Pareto front for the problem. The heuristic algorithm employs relax-and-fix and fix-and-optimize techniques, and an epsilon-constraint method to solve the multi-objective problem. The proposed meta-heuristic algorithm is based on the hybrid of two well-known evolutionary algorithms, particle swarm optimization, and genetic algorithm. It also uses a multi-objective framework called PESA-II to generate the Pareto front. Both proposed heuristic and meta-heuristic algorithms can employ parallel computing, which significantly reduces computational time. Finally, we investigate the proposed algorithms’ performance using 30 random problem instances and a case study from Iran. The results demonstrate that heuristic and meta-heuristic algorithms have obtained a reasonable solution with a maximum of 6.9% and 16.3% cost objective function gap respectively. The heuristic algorithm is superior to the meta-heuristic in terms of Pareto front quality metrics.

Order based algorithms for the core maintenance problem on edge-weighted graphs

The cohesive subgraph k-core is a maximal connected subgraph with the minimum degree δ≥k of a simple graph, where integer k≥0. Define the core number of a vertex w as the maximum k such that w is contained in a k-core. The core decomposition problem which is calculating the core numbers of all vertices in static graphs, and the core maintenance problem which is updating the core numbers in dynamic graphs are our main concern. Although, core numbers can be updated by the core decomposition algorithms, only a small part of vertices' core numbers have changed after the change of a graph. Thus, it is necessary to update core numbers locally to reduce the cost. In this paper, we study the core maintenance problem on edge-weighted graphs by using the vertex sequence k-order which is ordered by the order that the core decomposition algorithm removes vertices. We design the core maintenance algorithms for inserting one edge at a time and the method of updating the k-order, which reduce the searching range and the time cost evidently. For the removing case, we use the existing subcore algorithm to do the core maintenance and modify it with the method of updating k-order we design. Finally, we do extensive experiments to evaluate the effectiveness and the efficiency of our algorithms, which shows that the order based algorithm has a better performance than the existing for the core maintenance on edge-weighted graphs.

On Improving Adaptive Problem Decomposition Using Differential Evolution for Large-Scale Optimization Problems

Modern computational mathematics and informatics for Digital Environments deal with the high dimensionality when designing and optimizing models for various real-world phenomena. Large-scale global black-box optimization (LSGO) is still a hard problem for search metaheuristics, including bio-inspired algorithms. Such optimization problems are usually extremely multi-modal, and require significant computing resources for discovering and converging to the global optimum. The majority of state-of-the-art LSGO algorithms are based on problem decomposition with the cooperative co-evolution (CC) approach, which divides the search space into a set of lower dimensional subspaces (or subcomponents), which are expected to be easier to explore independently by an optimization algorithm. The question of the choice of the decomposition method remains open, and an adaptive decomposition looks more promising. As we can see from the most recent LSGO competitions, winner-approaches are focused on modifying advanced DE algorithms through integrating them with local search techniques. In this study, an approach that combines multiple ideas from state-of-the-art algorithms and implements Coordination of Self-adaptive Cooperative Co-evolution algorithms with Local Search (COSACC-LS1) is proposed. The self-adaptation method tunes both the structure of the complete approach and the parameters of each algorithm in the cooperation. The performance of COSACC-LS1 has been investigated using the CEC LSGO 2013 benchmark and the experimental results has been compared with leading LSGO approaches. The main contribution of the study is a new self-adaptive approach that is preferable for solving hard real-world problems because it is not overfitted with the LSGO benchmark due to self-adaptation during the search process instead of a manual benchmark-specific fine-tuning.

Inertial accelerated SGD algorithms for solving large-scale lower-rank tensor CP decomposition problems

The stochastic gradient descent (SGD) method has been applied to the tensor CANDECOMP/PARAFAC (CP) decomposition problem to reduce the computational cost. However, SGD usually takes numerous iterations to converge. In this paper, we propose inertial accelerated SGD methods for the subproblems of CP decomposition concerning one block factor. We consider two methods for the selection of a block index in the subproblem: the stochastic manner with replacement and the randomly permuted order without replacement. First, we propose an inertial accelerated block-randomized SGD algorithm for CP decomposition (iBrasCPD) and show each cluster point is a stochastic stationary point. Then we introduce a randomized permutation inertial stochastic algorithm (RP-iSPALM) for randomized order without replacement. Under some mild conditions, we show the global convergence and convergence rate of RP-iSPALM under the Kurdyka-Łojasiewicz (KL) property. Numerical experiments on six real datasets demonstrate that our proposed algorithms are efficient and can achieve better performance than the existing state-of-the-art methods.

New Constructions of Existential Unforgeable Aggregate Signature Scheme from CSP

In future, hundreds of years of mathematical problems that the security of public key cryptography algorithms rely on may be defeated by quantum algorithms. How can a digital signature scheme gracefully balance security and efficiency? This study uses the conjugate search problem and the left self-distributive system to combine and uses the RSA-like algorithm as the underlying structure to propose a new aggregated signature scheme. We, through the EUF game, under the random metaphor model, prove that the security of the scheme satisfies the adaptation unforgeability under selective message attack, the scheme can be finally reduced to the discrete logarithm problem or large prime number decomposition problem. In addition, we can achieve antiquantum attack and exhaustive attack by performing matrix calculations on the message, defining and changing the structure of the matrix by encoding, and setting thresholds for the matrix dimension and the length of the private key. In terms of efficiency, the message signature implementation is linear compared with the expansion rate in terms of storage and computing overhead, and the generation and verification of the final signature pair have nothing to do with the number of users. In addition, the length of the signature is fixed and the size is only the length of a single group, which effectively reduces the generation of public and private key pairs and saves a lot of storage space. The storage space and computational complexity are also effectively improved compared with other solutions.

A data driven Dantzig–Wolfe decomposition framework

We face the issue of finding alternative paradigms for the resolution of generic Mixed Integer Programs (MIP), by considering the perspective option of general purpose solvers which switch to decomposition methods when pertinent. Currently, the main blocking factor in their design is the problem of automatic decomposition of MIPs, that is to produce good MIP decompositions algorithmically, looking only at the algebraic structure of the MIP instance. We propose to employ Dantzig–Wolfe reformulation and machine learning methods to obtain a fully data driven automatic decomposition framework. We also design strategies and introduce algorithmic techniques in order to make such a framework computationally effective. An extensive experimental analysis shows our framework to grant substantial improvements, in terms of both solutions quality and computing time, with respect to state-of-the-art automatic decomposition techniques. It also allows us to gain insights into the relative impact of different techniques. As a side product of our research, we provide a dataset of more than 31 thousand random decompositions of MIPLIB instances, with 121 features, including computations of their root node relaxation.

DIVRS: Data integrity verification based on ring signature in cloud storage

Nowadays, cloud service is becoming an indispensable part of people’s lives and a growing number of users store data on servers. Although this way can reduce storage and maintenance costs, data owners lose the control and possession of the data, which will result in some additional security issues, such as data corruption. It means that cloud server providers may delete or tamper with the infrequently used data to economize on storage space. Therefore, it is essential to provide an audit service to verify integrity of data stored on the cloud. Most of the existing audit schemes are based on the difficult problems of large integer decomposition and discrete logarithms. With the development of quantum computers, these schemes will face the security threat, because quantum computers can easily solve these difficult problems. In short, it is essential to design a data audit scheme that is resistant to quantum attacks. Therefore, we design a novel data audit scheme to achieve post-quantum security, in which the ring signature based on the problem of learning with errors is employed. In addition, two data possession games are designed to prove the security of the DIVRS. Experiment results show that the communication and computing costs are acceptable, and the time spent in each phase of the DIVRS is shorter than that of the comparison schemes.

Pinning control of networks: Dimensionality reduction through simultaneous block-diagonalization of matrices.

In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the "pinned nodes." Previous work has mainly focused on the case that (i) and (ii) are of the same type. We decouple the stability analysis of the target synchronous solution into subproblems of the lowest dimension by using the techniques of simultaneous block diagonalization of matrices. Interestingly, we obtain two different types of blocks, driven and undriven. The overall dimension of the driven blocks is equal to the dimension of an appropriately defined controllable subspace, while all the remaining undriven blocks are scalar. Our main result is a decomposition of the stability problem into four independent sets of equations, which we call quotient controllable, quotient uncontrollable, redundant controllable, and redundant uncontrollable. Our analysis shows that the number and location of the pinned nodes affect the number and the dimension of each set of equations. We also observe that in a large variety of complex networks, the stability of the target synchronous solution is de facto only determined by a single quotient controllable block.