Algorithms

12 pages, 247 KiB

Open AccessEditor’s ChoiceArticle

The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

by Derek H. Smith, Roberto Montemanni and Stephanie Perkins

Algorithms 2020, 13(10), 253; https://doi.org/10.3390/a13100253 - 4 Oct 2020

Cited by 8 | Viewed by 3289

Let

G = (V, E)

be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A [...] Read more.

Let

G = (V, E)

be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances. Full article

(This article belongs to the Special Issue Algorithms for Graphs and Networks)

18 pages, 404 KiB

Open AccessEditor’s ChoiceArticle

A Survey on Shortest Unique Substring Queries

by Paniz Abedin, M. Oğuzhan Külekci and Shama V. Thankachan

Algorithms 2020, 13(9), 224; https://doi.org/10.3390/a13090224 - 6 Sep 2020

Cited by 4 | Viewed by 4163

Abstract

The shortest unique substring (SUS) problem is an active line of research in the field of string algorithms and has several applications in bioinformatics and information retrieval. The initial version of the problem was proposed by Pei et al. [ICDE’13]. Over the years, [...] Read more.

The shortest unique substring (SUS) problem is an active line of research in the field of string algorithms and has several applications in bioinformatics and information retrieval. The initial version of the problem was proposed by Pei et al. [ICDE’13]. Over the years, many variants and extensions have been pursued, which include positional-SUS, interval-SUS, approximate-SUS, palindromic-SUS, range-SUS, etc. In this article, we highlight some of the key results and summarize the recent developments in this area. Full article

(This article belongs to the Special Issue Algorithms in Bioinformatics)

17 pages, 471 KiB

Open AccessEditor’s ChoiceArticle

Exact Method for Generating Strategy-Solvable Sudoku Clues

by Kohei Nishikawa and Takahisa Toda

Algorithms 2020, 13(7), 171; https://doi.org/10.3390/a13070171 - 16 Jul 2020

Cited by 2 | Viewed by 11056

Abstract

A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introduce a rigorous framework [...] Read more.

A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introduce a rigorous framework to discuss solvability for Sudoku instances with respect to strategies. This allows us to handle not only known strategies but also general strategies under a few reasonable assumptions. We propose an exact method for determining Sudoku clues for a given set of clue positions that is solvable with a given set of strategies. This is the first exact method except for a trivial brute-force search. Besides the clue generation, we present an application of our method to the problem of determining the minimum number of strategy-solvable Sudoku clues. We conduct experiments to evaluate our method, varying the position and the number of clues at random. Our method terminates within 1 min for many grids. However, as the number of clues gets closer to 20, the running time rapidly increases and exceeds the time limit set to 600 s. We also evaluate our method for several instances with 17 clue positions taken from known minimum Sudokus to see the efficiency for deciding unsolvability. Full article

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24 pages, 1066 KiB

Open AccessEditor’s ChoiceArticle

Binary Time Series Classification with Bayesian Convolutional Neural Networks When Monitoring for Marine Gas Discharges

by Kristian Gundersen, Guttorm Alendal, Anna Oleynik and Nello Blaser

Algorithms 2020, 13(6), 145; https://doi.org/10.3390/a13060145 - 19 Jun 2020

Cited by 13 | Viewed by 5632

Abstract

The world’s oceans are under stress from climate change, acidification and other human activities, and the UN has declared 2021–2030 as the decade for marine science. To monitor the marine waters, with the purpose of detecting discharges of tracers from unknown locations, large [...] Read more.

The world’s oceans are under stress from climate change, acidification and other human activities, and the UN has declared 2021–2030 as the decade for marine science. To monitor the marine waters, with the purpose of detecting discharges of tracers from unknown locations, large areas will need to be covered with limited resources. To increase the detectability of marine gas seepage we propose a deep probabilistic learning algorithm, a Bayesian Convolutional Neural Network (BCNN), to classify time series of measurements. The BCNN will classify time series to belong to a leak/no-leak situation, including classification uncertainty. The latter is important for decision makers who must decide to initiate costly confirmation surveys and, hence, would like to avoid false positives. Results from a transport model are used for the learning process of the BCNN and the task is to distinguish the signal from a leak hidden within the natural variability. We show that the BCNN classifies time series arising from leaks with high accuracy and estimates its associated uncertainty. We combine the output of the BCNN model, the posterior predictive distribution, with a Bayesian decision rule showcasing how the framework can be used in practice to make optimal decisions based on a given cost function. Full article

(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)

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26 pages, 388 KiB

Open AccessEditor’s ChoiceArticle

Late Acceptance Hill-Climbing Matheuristic for the General Lot Sizing and Scheduling Problem with Rich Constraints

by Andreas Goerler, Eduardo Lalla-Ruiz and Stefan Voß

Algorithms 2020, 13(6), 138; https://doi.org/10.3390/a13060138 - 9 Jun 2020

Cited by 15 | Viewed by 5567

Abstract

This paper considers the general lot sizing and scheduling problem with rich constraints exemplified by means of rework and lifetime constraints for defective items (GLSP-RP), which finds numerous applications in industrial settings, for example, the food processing industry and the pharmaceutical industry. To [...] Read more.

This paper considers the general lot sizing and scheduling problem with rich constraints exemplified by means of rework and lifetime constraints for defective items (GLSP-RP), which finds numerous applications in industrial settings, for example, the food processing industry and the pharmaceutical industry. To address this problem, we propose the Late Acceptance Hill-climbing Matheuristic (LAHCM) as a novel solution framework that exploits and integrates the late acceptance hill climbing algorithm and exact approaches for speeding up the solution process in comparison to solving the problem by means of a general solver. The computational results show the benefits of incorporating exact approaches within the LAHCM template leading to high-quality solutions within short computational times. Full article

(This article belongs to the Special Issue Optimization Algorithms for Allocation Problems)

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30 pages, 871 KiB

Open AccessEditor’s ChoiceArticle

Short-Term Wind Speed Forecasting Using Statistical and Machine Learning Methods

by Lucky O. Daniel, Caston Sigauke, Colin Chibaya and Rendani Mbuvha

Algorithms 2020, 13(6), 132; https://doi.org/10.3390/a13060132 - 26 May 2020

Cited by 19 | Viewed by 6059

Abstract

Wind offers an environmentally sustainable energy resource that has seen increasing global adoption in recent years. However, its intermittent, unstable and stochastic nature hampers its representation among other renewable energy sources. This work addresses the forecasting of wind speed, a primary input needed [...] Read more.

Wind offers an environmentally sustainable energy resource that has seen increasing global adoption in recent years. However, its intermittent, unstable and stochastic nature hampers its representation among other renewable energy sources. This work addresses the forecasting of wind speed, a primary input needed for wind energy generation, using data obtained from the South African Wind Atlas Project. Forecasting is carried out on a two days ahead time horizon. We investigate the predictive performance of artificial neural networks (ANN) trained with Bayesian regularisation, decision trees based stochastic gradient boosting (SGB) and generalised additive models (GAMs). The results of the comparative analysis suggest that ANN displays superior predictive performance based on root mean square error (RMSE). In contrast, SGB shows outperformance in terms of mean average error (MAE) and the related mean average percentage error (MAPE). A further comparison of two forecast combination methods involving the linear and additive quantile regression averaging show the latter forecast combination method as yielding lower prediction accuracy. The additive quantile regression averaging based prediction intervals also show outperformance in terms of validity, reliability, quality and accuracy. Interval combination methods show the median method as better than its pure average counterpart. Point forecasts combination and interval forecasting methods are found to improve forecast performance. Full article

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19 pages, 570 KiB

Open AccessEditor’s ChoiceArticle

A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems

by Luca Bergamaschi

Algorithms 2020, 13(4), 100; https://doi.org/10.3390/a13040100 - 21 Apr 2020

Cited by 16 | Viewed by 4622

Abstract

The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems

A_{k} x_{k} = b_{k}, k = 1, \dots

arising in many scientific applications, such [...] Read more.

The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems

A_{k} x_{k} = b_{k}, k = 1, \dots

arising in many scientific applications, such as discretization of transient Partial Differential Equations (PDEs), solution of eigenvalue problems, (Inexact) Newton methods applied to nonlinear systems, rational Krylov methods for computing a function of a matrix. In this paper, we will analyze a number of techniques of updating a given initial preconditioner by a low-rank matrix with the aim of improving the clustering of eigenvalues around 1, in order to speed-up the convergence of the Preconditioned Conjugate Gradient (PCG) method. We will also review some techniques to efficiently approximate the linearly independent vectors which constitute the low-rank corrections and whose choice is crucial for the effectiveness of the approach. Numerical results on real-life applications show that the performance of a given iterative solver can be very much enhanced by the use of low-rank updates. Full article

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19 pages, 11395 KiB

Open AccessEditor’s ChoiceArticle

How to Identify Varying Lead–Lag Effects in Time Series Data: Implementation, Validation, and Application of the Generalized Causality Algorithm

by Johannes Stübinger and Katharina Adler

Algorithms 2020, 13(4), 95; https://doi.org/10.3390/a13040095 - 16 Apr 2020

Cited by 3 | Viewed by 7366

Abstract

This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead–lag effects between two given time series. This [...] Read more.

This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead–lag effects between two given time series. This procedure allows an elastic adjustment of the time axis to find similar but phase-shifted sequences—structural breaks in their relationship are also captured. A large-scale simulation study validates the outperformance in the vast majority of parameter constellations in terms of efficiency, robustness, and feasibility. Finally, the presented methodology is applied to real data from the areas of macroeconomics, finance, and metal. Highest similarity show the pairs of gross domestic product and consumer price index (macroeconomics), S&P 500 index and Deutscher Aktienindex (finance), as well as gold and silver (metal). In addition, the algorithm takes full use of its flexibility and identifies both various structural breaks and regime patterns over time, which are (partly) well documented in the literature. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications)

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9 pages, 2485 KiB

Open AccessEditor’s ChoiceArticle

Beyond Newton: A New Root-Finding Fixed-Point Iteration for Nonlinear Equations

by Ankush Aggarwal and Sanjay Pant

Algorithms 2020, 13(4), 78; https://doi.org/10.3390/a13040078 - 29 Mar 2020

Cited by 3 | Viewed by 6143

Abstract

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is Newton’s method. However, its convergence depends heavily on the initial guess, with poor choices often leading to slow convergence or even divergence. In [...] Read more.

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is Newton’s method. However, its convergence depends heavily on the initial guess, with poor choices often leading to slow convergence or even divergence. In this short note, we seek to enlarge the basin of attraction of the classical Newton’s method. The key idea is to develop a relatively simple multiplicative transform of the original equations, which leads to a reduction in nonlinearity, thereby alleviating the limitation of Newton’s method. Based on this idea, we derive a new class of iterative methods and rediscover Halley’s method as the limit case. We present the application of these methods to several mathematical functions (real, complex, and vector equations). Across all examples, our numerical experiments suggest that the new methods converge for a significantly wider range of initial guesses. For scalar equations, the increase in computational cost per iteration is minimal. For vector functions, more extensive analysis is needed to compare the increase in cost per iteration and the improvement in convergence of specific problems. Full article

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65 pages, 1890 KiB

Open AccessEditor’s ChoiceReview

Energy Efficient Routing in Wireless Sensor Networks: A Comprehensive Survey

by Christos Nakas, Dionisis Kandris and Georgios Visvardis

Algorithms 2020, 13(3), 72; https://doi.org/10.3390/a13030072 - 24 Mar 2020

Cited by 133 | Viewed by 17931

Abstract

Wireless Sensor Networks (WSNs) are among the most emerging technologies, thanks to their great capabilities and their ever growing range of applications. However, the lifetime of WSNs is extremely restricted due to the delimited energy capacity of their sensor nodes. This is why [...] Read more.

Wireless Sensor Networks (WSNs) are among the most emerging technologies, thanks to their great capabilities and their ever growing range of applications. However, the lifetime of WSNs is extremely restricted due to the delimited energy capacity of their sensor nodes. This is why energy conservation is considered as the most important research concern for WSNs. Radio communication is the utmost energy consuming function in a WSN. Thus, energy efficient routing is necessitated to save energy and thus prolong the lifetime of WSNs. For this reason, numerous protocols for energy efficient routing in WSNs have been proposed. This article offers an analytical and up to date survey on the protocols of this kind. The classic and modern protocols presented are categorized, depending on i) how the network is structured, ii) how data are exchanged, iii) whether location information is or not used, and iv) whether Quality of Service (QoS) or multiple paths are or not supported. In each distinct category, protocols are both described and compared in terms of specific performance metrics, while their advantages and disadvantages are discussed. Finally, the study findings are discussed, concluding remarks are drawn, and open research issues are indicated. Full article

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17 pages, 2260 KiB

Open AccessEditor’s ChoiceArticle

Observability of Uncertain Nonlinear Systems Using Interval Analysis

by Thomas Paradowski, Sabine Lerch, Michelle Damaszek, Robert Dehnert and Bernd Tibken

Algorithms 2020, 13(3), 66; https://doi.org/10.3390/a13030066 - 16 Mar 2020

Cited by 11 | Viewed by 4868

Abstract

In the field of control engineering, observability of uncertain nonlinear systems is often neglected and not examined. This is due to the complex analytical calculations required for the verification. Therefore, the aim of this work is to provide an algorithm which numerically analyzes [...] Read more.

In the field of control engineering, observability of uncertain nonlinear systems is often neglected and not examined. This is due to the complex analytical calculations required for the verification. Therefore, the aim of this work is to provide an algorithm which numerically analyzes the observability of nonlinear systems described by finite-dimensional, continuous-time sets of ordinary differential equations. The algorithm is based on definitions for distinguishability and local observability using a rank check from which conditions are deduced. The only requirements are the uncertain model equations of the system. Further, the methodology verifies observability of nonlinear systems on a given state space. In case that the state space is not fully observable, the algorithm provides the observable set of states. In addition, the results obtained by the algorithm allows insight into why the remaining states cannot be distinguished. Full article

(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control)

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12 pages, 368 KiB

Open AccessEditor’s ChoiceArticle

Optimization of Constrained Stochastic Linear-Quadratic Control on an Infinite Horizon: A Direct-Comparison Based Approach

by Ruobing Xue, Xiangshen Ye and Weiping Wu

Algorithms 2020, 13(2), 49; https://doi.org/10.3390/a13020049 - 24 Feb 2020

Viewed by 4082

Abstract

In this paper we study the optimization of the discrete-time stochastic linear-quadratic (LQ) control problem with conic control constraints on an infinite horizon, considering multiplicative noises. Stochastic control systems can be formulated as Markov Decision Problems (MDPs) with continuous state spaces and therefore [...] Read more.

In this paper we study the optimization of the discrete-time stochastic linear-quadratic (LQ) control problem with conic control constraints on an infinite horizon, considering multiplicative noises. Stochastic control systems can be formulated as Markov Decision Problems (MDPs) with continuous state spaces and therefore we can apply the direct-comparison based optimization approach to solve the problem. We first derive the performance difference formula for the LQ problem by utilizing the state separation property of the system structure. Based on this, we successfully derive the optimality conditions and the stationary optimal feedback control. By introducing the optimization, we establish a general framework for infinite horizon stochastic control problems. The direct-comparison based approach is applicable to both linear and nonlinear systems. Our work provides a new perspective in LQ control problems; based on this approach, learning based algorithms can be developed without identifying all of the system parameters. Full article

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13 pages, 6398 KiB

Open AccessEditor’s ChoiceArticle

Optimal Learning and Self-Awareness Versus PDI

by Brendon Smeresky, Alex Rizzo and Timothy Sands

Algorithms 2020, 13(1), 23; https://doi.org/10.3390/a13010023 - 11 Jan 2020

Cited by 33 | Viewed by 7470

Abstract

This manuscript will explore and analyze the effects of different paradigms for the control of rigid body motion mechanics. The experimental setup will include deterministic artificial intelligence composed of optimal self-awareness statements together with a novel, optimal learning algorithm, and these will be [...] Read more.

This manuscript will explore and analyze the effects of different paradigms for the control of rigid body motion mechanics. The experimental setup will include deterministic artificial intelligence composed of optimal self-awareness statements together with a novel, optimal learning algorithm, and these will be re-parameterized as ideal nonlinear feedforward and feedback evaluated within a Simulink simulation. Comparison is made to a custom proportional, derivative, integral controller (modified versions of classical proportional-integral-derivative control) implemented as a feedback control with a specific term to account for the nonlinear coupled motion. Consistent proportional, derivative, and integral gains were used throughout the duration of the experiments. The simulation results will show that akin feedforward control, deterministic self-awareness statements lack an error correction mechanism, relying on learning (which stands in place of feedback control), and the proposed combination of optimal self-awareness statements and a newly demonstrated analytically optimal learning yielded the highest accuracy with the lowest execution time. This highlights the potential effectiveness of a learning control system. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

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