Open AccessArticle
Efficient Deep Learning-Based Automated Pathology Identification in Retinal Optical Coherence Tomography Images
Algorithms 2018, 11(6), 88; https://doi.org/10.3390/a11060088 -
Abstract
We present an automatic method based on transfer learning for the identification of dry age-related macular degeneration (AMD) and diabetic macular edema (DME) from retinal optical coherence tomography (OCT) images. The algorithm aims to improve the classification performance of retinal OCT images and
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We present an automatic method based on transfer learning for the identification of dry age-related macular degeneration (AMD) and diabetic macular edema (DME) from retinal optical coherence tomography (OCT) images. The algorithm aims to improve the classification performance of retinal OCT images and shorten the training time. Firstly, we remove the last several layers from the pre-trained Inception V3 model and regard the remaining part as a fixed feature extractor. Then, the features are used as input of a convolutional neural network (CNN) designed to learn the feature space shifts. The experimental results on two different retinal OCT images datasets demonstrate the effectiveness of the proposed method. Full article
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Open AccessEditorial
Special Issue on Algorithms for Scheduling Problems
Algorithms 2018, 11(6), 87; https://doi.org/10.3390/a11060087 -
Abstract
This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main
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This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main topics include sequencing and scheduling with additional constraints (setup times or costs, precedence constraints, resource constraints, and batch production environment) and production planning and scheduling problems arising in real-world applications. Full article
Open AccessArticle
Performance Optimal PI controller Tuning Based on Integrating Plus Time Delay Models
Algorithms 2018, 11(6), 86; https://doi.org/10.3390/a11060086 -
Abstract
A method for tuning PI controller parameters, a prescribed maximum time delay error or a relative time delay error is presented. The method is based on integrator plus time delay models. The integral time constant is linear in the relative time delay error,
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A method for tuning PI controller parameters, a prescribed maximum time delay error or a relative time delay error is presented. The method is based on integrator plus time delay models. The integral time constant is linear in the relative time delay error, and the proportional constant is seen inversely proportional to the relative time delay error. The keystone in the method is the method product parameter, i.e., the product of the PI controller proportional constant, the integral time constant, and the integrator plus time delay model, velocity gain. The method product parameter is found to be constant for various PI controller tuning methods. Optimal suggestions are given for choosing the method product parameter, i.e., optimal such that the integrated absolute error or, more interestingly, the Pareto performance objective (i.e., integrated absolute error for combined step changes in output and input disturbances) is minimised. Variants of the presented tuning method are demonstrated for tuning PI controllers for motivated (possible) higher order process model examples, i.e., the presented method is combined with the model reduction step (process–reaction curve) in Ziegler–Nichols. Full article
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Open AccessArticle
ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems
Algorithms 2018, 11(6), 85; https://doi.org/10.3390/a11060085 -
Abstract
This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and
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This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example. Full article
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Open AccessArticle
Efficient Approximation for Restricted Biclique Cover Problems
Algorithms 2018, 11(6), 84; https://doi.org/10.3390/a11060084 -
Abstract
Covering the edges of a bipartite graph by a minimum set of bipartite complete graphs (bicliques) is a basic graph theoretic problem, with numerous applications. In particular, it is used to characterize parsimonious models of a set of observations (each biclique corresponds to
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Covering the edges of a bipartite graph by a minimum set of bipartite complete graphs (bicliques) is a basic graph theoretic problem, with numerous applications. In particular, it is used to characterize parsimonious models of a set of observations (each biclique corresponds to a factor or feature that relates the observations in the two sets of nodes connected by the biclique). The decision version of the minimum biclique cover problem is NP-Complete, and unless P=NP, the cover size cannot be approximated in general within less than a sub-linear factor of the number of nodes (or edges) in the graph. In this work, we consider two natural restrictions to the problem, motivated by practical applications. In the first case, we restrict the number of bicliques a node can belong to. We show that when this number is at least 5, the problem is still NP-hard. In contrast, we show that when nodes belong to no more than two bicliques, the problem has efficient approximations. The second model we consider corresponds to observing a set of independent samples from an unknown model, governed by a possibly large number of factors. The model is defined by a bipartite graph G=(L,R,E), where each node in L is assigned to an arbitrary subset of up to a constant f factors, while the nodes in R (the independent observations) are assigned to random subsets of the set of k factors where k can grow with size of the graph. We show that this practical version of the biclique cover problem is amenable to efficient approximations. Full article
Open AccessArticle
A Combined Syntactical and Statistical Approach for R Peak Detection in Real-Time Long-Term Heart Rate Variability Analysis
Algorithms 2018, 11(6), 83; https://doi.org/10.3390/a11060083 -
Abstract
Long-term heart rate variability (HRV) analysis is useful as a noninvasive technique for autonomic nervous system activity assessment. It provides a method for assessing many physiological and pathological factors that modulate the normal heartbeat. The performance of HRV analysis systems heavily depends on
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Long-term heart rate variability (HRV) analysis is useful as a noninvasive technique for autonomic nervous system activity assessment. It provides a method for assessing many physiological and pathological factors that modulate the normal heartbeat. The performance of HRV analysis systems heavily depends on a reliable and accurate detection of the R peak of the QRS complex. Ectopic beats caused by misdetection or arrhythmic events can introduce bias into HRV results, resulting in significant problems in their interpretation. This study presents a novel method for long-term detection of normal R peaks (which represent the normal heartbeat in electrocardiographic signals), intended specifically for HRV analysis. The very low computational complexity of the proposed method, which combines and exploits the advantages of syntactical and statistical approaches, enables real-time applications. The approach was validated using the Massachusetts Institute of Technology–Beth Israel Hospital Normal Sinus Rhythm and the Fantasia database, and has a sensitivity, positive predictivity, detection error rate, and accuracy of 99.998, 99.999, 0.003, and 99.996%, respectively. Full article
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Open AccessArticle
Research on Fault Diagnosis of a Marine Fuel System Based on the SaDE-ELM Algorithm
Algorithms 2018, 11(6), 82; https://doi.org/10.3390/a11060082 -
Abstract
Since the traditional fault diagnosis method of the marine fuel system has a low accuracy of identification, the algorithm solution can easily fall into local optimum, and they are not fit for the research on the fault diagnosis of a marine fuel system.
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Since the traditional fault diagnosis method of the marine fuel system has a low accuracy of identification, the algorithm solution can easily fall into local optimum, and they are not fit for the research on the fault diagnosis of a marine fuel system. Hence, a fault diagnosis method for a marine fuel system based on the SaDE-ELM algorithm is proposed. First, the parameters of initializing extreme learning machine are adopted by a differential evolution algorithm. Second, the fault diagnosis of the marine fuel system is realized by the fault diagnosis model corresponding to the state training of marine fuel system. Based on the obtained fault data of a marine fuel system, the proposed method is verified. The experimental results show that this method produces higher recognition accuracy and faster recognition speed that are superior to the traditional BP neural network, SVM support vector machine diagnosis algorithm, and the un-optimized extreme learning machine algorithm. The results have important significance relevant to fault diagnosis for a marine fuel system. The algorithm based on SaDE-ELM is an effective and practical method of fault diagnosis for a marine fuel system. Full article
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Open AccessArticle
A Randomized Algorithm for Optimal PID Controllers
Algorithms 2018, 11(6), 81; https://doi.org/10.3390/a11060081 -
Abstract
A randomized algorithm is suggested for the syntheses of optimal PID controllers for MIMO coupled systems, where the optimality is with respect to the H -norm, the H2 -norm and the LQR functional, with possible system-performance specifications defined by regional pole-placement.
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A randomized algorithm is suggested for the syntheses of optimal PID controllers for MIMO coupled systems, where the optimality is with respect to the H -norm, the H2 -norm and the LQR functional, with possible system-performance specifications defined by regional pole-placement. Other notions of optimality (e.g., mixed H2/H design, controller norm or controller sparsity) can be handled similarly with the suggested algorithm. The suggested method is direct and thus can be applied to continuous-time systems as well as to discrete-time systems with the obvious minor changes. The presented algorithm is a randomized algorithm, which has a proof of convergence (in probability) to a global optimum. Full article
Open AccessFeature PaperArticle
Scheduling a Single Machine with Primary and Secondary Objectives
Algorithms 2018, 11(6), 80; https://doi.org/10.3390/a11060080 -
Abstract
We study a scheduling problem in which jobs with release times and due dates are to be processed on a single machine. With the primary objective to minimize the maximum job lateness, the problem is strongly NP-hard. We describe a general algorithmic scheme
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We study a scheduling problem in which jobs with release times and due dates are to be processed on a single machine. With the primary objective to minimize the maximum job lateness, the problem is strongly NP-hard. We describe a general algorithmic scheme to minimize the maximum job lateness, with the secondary objective to minimize the maximum job completion time. The problem of finding the Pareto-optimal set of feasible solutions with these two objective criteria is strongly NP-hard. We give the dominance properties and conditions when the Pareto-optimal set can be formed in polynomial time. These properties, together with our general framework, provide the theoretical background, so that the basic framework can be expanded to (exponential-time) implicit enumeration algorithms and polynomial-time approximation algorithms (generating the Pareto sub-optimal frontier with a fair balance between the two objectives). Some available in the literature experimental results confirm the practical efficiency of the proposed framework. Full article
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Open AccessArticle
A Fire Detection Algorithm Based on Tchebichef Moment Invariants and PSO-SVM
Algorithms 2018, 11(6), 79; https://doi.org/10.3390/a11060079 -
Abstract
Automatic fire detection, which can detect and raise the alarm for fire early, is expected to help reduce the loss of life and property as much as possible. Due to its advantages over traditional methods, image processing technology has been applied gradually in
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Automatic fire detection, which can detect and raise the alarm for fire early, is expected to help reduce the loss of life and property as much as possible. Due to its advantages over traditional methods, image processing technology has been applied gradually in fire detection. In this paper, a novel algorithm is proposed to achieve fire image detection, combined with Tchebichef (sometimes referred to as Chebyshev) moment invariants (TMIs) and particle swarm optimization-support vector machine (PSO-SVM). According to the correlation between geometric moments and Tchebichef moments, the translation, rotation, and scaling (TRS) invariants of Tchebichef moments are obtained first. Then, the TMIs of candidate images are calculated to construct feature vectors. To gain the best detection performance, a PSO-SVM model is proposed, where the kernel parameter and penalty factor of support vector machine (SVM) are optimized by particle swarm optimization (PSO). Then, the PSO-SVM model is utilized to identify the fire images. Compared with algorithms based on Hu moment invariants (HMIs) and Zernike moment invariants (ZMIs), the experimental results show that the proposed algorithm can improve the detection accuracy, achieving the highest detection rate of 98.18%. Moreover, it still exhibits the best performance even if the size of the training sample set is small and the images are transformed by TRS. Full article
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Open AccessArticle
A Modified Artificial Bee Colony Algorithm Based on the Self-Learning Mechanism
Algorithms 2018, 11(6), 78; https://doi.org/10.3390/a11060078 -
Abstract
Artificial bee colony (ABC) algorithm, a novel category of bionic intelligent optimization algorithm, was achieved for solving complex nonlinear optimization problems. Previous studies have shown that ABC algorithm is competitive to other biological-inspired optimization algorithms, but there still exist several insufficiencies due to
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Artificial bee colony (ABC) algorithm, a novel category of bionic intelligent optimization algorithm, was achieved for solving complex nonlinear optimization problems. Previous studies have shown that ABC algorithm is competitive to other biological-inspired optimization algorithms, but there still exist several insufficiencies due to the inefficient solution search equation (SSE), which does well in exploration but poorly in exploitation. To improve accuracy of the solutions, this paper proposes a modified ABC algorithm based on the self-learning mechanism (SLABC) with five SSEs as the candidate operator pool; among them, one is good at exploration and two of them are good at exploitation; another SSE intends to balance exploration and exploitation; moreover, the last SSE with Lévy flight step-size which can generate smaller step-size with high frequency and bigger step-size occasionally not only can balance exploration and exploitation but also possesses the ability to escape from the local optimum. This paper proposes a simple self-learning mechanism, wherein the SSE is selected according to the previous success ratio in generating promising solutions at each iteration. Experiments on a set of 9 benchmark functions are carried out with the purpose of evaluating the performance of the proposed method. The experimental results illustrated that the SLABC algorithm achieves significant improvement compared with other competitive algorithms. Full article
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Open AccessArticle
A Novel Design of Sparse Prototype Filter for Nearly Perfect Reconstruction Cosine-Modulated Filter Banks
Algorithms 2018, 11(5), 77; https://doi.org/10.3390/a11050077 -
Abstract
Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR) cosine-modulated filter
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Cosine-modulated filter banks play a major role in digital signal processing. Sparse FIR filter banks have lower implementation complexity than full filter banks, while keeping a good performance level. This paper presents a fast design paradigm for sparse nearly perfect-reconstruction (NPR) cosine-modulated filter banks. First, an approximation function is introduced to reduce the non-convex quadratically constrained optimization problem to a linearly constrained optimization problem. Then, the desired sparse linear phase FIR prototype filter is derived through the orthogonal matching pursuit (OMP) performed under the weighted l2 norm. The simulation results demonstrate that the proposed scheme is an effective paradigm to design sparse NPR cosine-modulated filter banks. Full article
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Open AccessArticle
PHEFT: Pessimistic Image Processing Workflow Scheduling for DSP Clusters
Algorithms 2018, 11(5), 76; https://doi.org/10.3390/a11050076 -
Abstract
We address image processing workflow scheduling problems on a multicore digital signal processor cluster. We present an experimental study of scheduling strategies that include task labeling, prioritization, resource selection, and digital signal processor scheduling. We apply these strategies in the context of executing
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We address image processing workflow scheduling problems on a multicore digital signal processor cluster. We present an experimental study of scheduling strategies that include task labeling, prioritization, resource selection, and digital signal processor scheduling. We apply these strategies in the context of executing the Ligo and Montage applications. To provide effective guidance in choosing a good strategy, we present a joint analysis of three conflicting goals based on performance degradation. A case study is given, and experimental results demonstrate that a pessimistic scheduling approach provides the best optimization criteria trade-offs. The Pessimistic Heterogeneous Earliest Finish Time scheduling algorithm performs well in different scenarios with a variety of workloads and cluster configurations. Full article
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Open AccessArticle
A New Oren–Nayar Shape-from-Shading Approach for 3D Reconstruction Using High-Order Godunov-Based Scheme
Algorithms 2018, 11(5), 75; https://doi.org/10.3390/a11050075 -
Abstract
3D shape reconstruction from images has been an important topic in the field of robot vision. Shape-From-Shading (SFS) is a classical method for determining the shape of a 3D surface from a one intensity image. The Lambertian reflectance is a fundamental assumption in
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3D shape reconstruction from images has been an important topic in the field of robot vision. Shape-From-Shading (SFS) is a classical method for determining the shape of a 3D surface from a one intensity image. The Lambertian reflectance is a fundamental assumption in conventional SFS approaches. Unfortunately, when applied to characterize the reflection attribute of the diffuse reflection, the Lambertian model is tested to be inexact. In this paper, we present a new SFS approach for 3D reconstruction of diffuse surfaces whose reflection attribute is approximated by the Oren–Nayar reflection model. The partial differential Image Irradiance Equation (IIR) is set up with this model under a single distant point light source and an orthographic camera projection whose direction coincides with the light source. Then, the IIR is converted into an eikonal equation by solving a quadratic equation that includes the 3D surface shape. The viscosity solution of the resulting eikonal equation is approximated by using the high-order Godunov-based scheme that is accelerated by means of an alternating sweeping strategy. We conduct the experiments on synthetic and real-world images, and the experimental results illustrate the effectiveness of the presented approach. Full article
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Open AccessArticle
Using Metaheuristics on the Multi-Depot Vehicle Routing Problem with Modified Optimization Criterion
Algorithms 2018, 11(5), 74; https://doi.org/10.3390/a11050074 -
Abstract
This article deals with the modified Multi-Depot Vehicle Routing Problem (MDVRP). The modification consists of altering the optimization criterion. The optimization criterion of the standard MDVRP is to minimize the total sum of routes of all vehicles, whereas the criterion of modified MDVRP
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This article deals with the modified Multi-Depot Vehicle Routing Problem (MDVRP). The modification consists of altering the optimization criterion. The optimization criterion of the standard MDVRP is to minimize the total sum of routes of all vehicles, whereas the criterion of modified MDVRP (M-MDVRP) is to minimize the longest route of all vehicles, i.e., the time to conduct the routing operation is as short as possible. For this problem, a metaheuristic algorithm—based on the Ant Colony Optimization (ACO) theory and developed by the author for solving the classic MDVRP instances—has been modified and adapted for M-MDVRP. In this article, an additional deterministic optimization process which further enhances the original ACO algorithm has been proposed. For evaluation of results, Cordeau’s benchmark instances are used. Full article
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Open AccessArticle
The NIRS Brain AnalyzIR Toolbox
Algorithms 2018, 11(5), 73; https://doi.org/10.3390/a11050073 -
Abstract
Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low-levels of light (650–900 nm) to measure changes in cerebral blood volume and oxygenation. Over the last several decades, this technique has been utilized in a growing number of functional and resting-state
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Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low-levels of light (650–900 nm) to measure changes in cerebral blood volume and oxygenation. Over the last several decades, this technique has been utilized in a growing number of functional and resting-state brain studies. The lower operation cost, portability, and versatility of this method make it an alternative to methods such as functional magnetic resonance imaging for studies in pediatric and special populations and for studies without the confining limitations of a supine and motionless acquisition setup. However, the analysis of fNIRS data poses several challenges stemming from the unique physics of the technique, the unique statistical properties of data, and the growing diversity of non-traditional experimental designs being utilized in studies due to the flexibility of this technology. For these reasons, specific analysis methods for this technology must be developed. In this paper, we introduce the NIRS Brain AnalyzIR toolbox as an open-source Matlab-based analysis package for fNIRS data management, pre-processing, and first- and second-level (i.e., single subject and group-level) statistical analysis. Here, we describe the basic architectural format of this toolbox, which is based on the object-oriented programming paradigm. We also detail the algorithms for several of the major components of the toolbox including statistical analysis, probe registration, image reconstruction, and region-of-interest based statistics. Full article
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Open AccessArticle
Gray Wolf Optimization Algorithm for Multi-Constraints Second-Order Stochastic Dominance Portfolio Optimization
Algorithms 2018, 11(5), 72; https://doi.org/10.3390/a11050072 -
Abstract
In the field of investment, how to construct a suitable portfolio based on historical data is still an important issue. The second-order stochastic dominant constraint is a branch of the stochastic dominant constraint theory. However, only considering the second-order stochastic dominant constraints does
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In the field of investment, how to construct a suitable portfolio based on historical data is still an important issue. The second-order stochastic dominant constraint is a branch of the stochastic dominant constraint theory. However, only considering the second-order stochastic dominant constraints does not conform to the investment environment under realistic conditions. Therefore, we added a series of constraints into basic portfolio optimization model, which reflect the realistic investment environment, such as skewness and kurtosis. In addition, we consider two kinds of risk measures: conditional value at risk and value at risk. Most important of all, in this paper, we introduce Gray Wolf Optimization (GWO) algorithm into portfolio optimization model, which simulates the gray wolf’s social hierarchy and predatory behavior. In the numerical experiments, we compare the GWO algorithm with Particle Swarm Optimization (PSO) algorithm and Genetic Algorithm (GA). The experimental results show that GWO algorithm not only shows better optimization ability and optimization efficiency, but also the portfolio optimized by GWO algorithm has a better performance than FTSE100 index, which prove that GWO algorithm has a great potential in portfolio optimization. Full article
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Open AccessArticle
Improving Monarch Butterfly Optimization Algorithm with Self-Adaptive Population
Algorithms 2018, 11(5), 71; https://doi.org/10.3390/a11050071 -
Abstract
Inspired by the migration behavior of monarch butterflies in nature, Wang et al. proposed a novel, promising, intelligent swarm-based algorithm, monarch butterfly optimization (MBO), for tackling global optimization problems. In the basic MBO algorithm, the butterflies in land 1 (subpopulation 1) and land
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Inspired by the migration behavior of monarch butterflies in nature, Wang et al. proposed a novel, promising, intelligent swarm-based algorithm, monarch butterfly optimization (MBO), for tackling global optimization problems. In the basic MBO algorithm, the butterflies in land 1 (subpopulation 1) and land 2 (subpopulation 2) are calculated according to the parameter p, which is unchanged during the entire optimization process. In our present work, a self-adaptive strategy is introduced to dynamically adjust the butterflies in land 1 and 2. Accordingly, the population size in subpopulation 1 and 2 are dynamically changed as the algorithm evolves in a linear way. After introducing the concept of a self-adaptive strategy, an improved MBO algorithm, called monarch butterfly optimization with self-adaptive population (SPMBO), is put forward. In SPMBO, only generated individuals who are better than before can be accepted as new individuals for the next generations in the migration operation. Finally, the proposed SPMBO algorithm is benchmarked by thirteen standard test functions with dimensions of 30 and 60. The experimental results indicate that the search ability of the proposed SPMBO approach significantly outperforms the basic MBO algorithm on most test functions. This also implies the self-adaptive strategy is an effective way to improve the performance of the basic MBO algorithm. Full article
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Open AccessArticle
Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis
Algorithms 2018, 11(5), 70; https://doi.org/10.3390/a11050070 -
Abstract
Functional Near InfraRed Spectroscopy (fNIRS) connectivity analysis is often performed using the measured oxy-haemoglobin (HbO2) signal, while the deoxy-haemoglobin (HHb) is largely ignored. The in-common information of the connectivity networks of both HbO2 and HHb is not regularly reported, or
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Functional Near InfraRed Spectroscopy (fNIRS) connectivity analysis is often performed using the measured oxy-haemoglobin (HbO2) signal, while the deoxy-haemoglobin (HHb) is largely ignored. The in-common information of the connectivity networks of both HbO2 and HHb is not regularly reported, or worse, assumed to be similar. Here we describe a methodology that allows the estimation of the symmetry between the functional connectivity (FC) networks of HbO2 and HHb and propose a differential symmetry index (DSI) indicative of the in-common physiological information. Our hypothesis is that the symmetry between FC networks associated with HbO2 and HHb is above what should be expected from random networks. FC analysis was done in fNIRS data collected from six freely-moving healthy volunteers over 16 locations on the prefrontal cortex during a real-world task in an out-of-the-lab environment. In addition, systemic data including breathing rate (BR) and heart rate (HR) were also synchronously collected and used within the FC analysis. FC networks for HbO2 and HHb were established independently using a Bayesian networks analysis. The DSI between both haemoglobin (Hb) networks with and without systemic influence was calculated. The relationship between the symmetry of HbO2 and HHb networks, including the segregational and integrational characteristics of the networks (modularity and global efficiency respectively) were further described. Consideration of systemic information increases the path lengths of the connectivity networks by 3%. Sparse networks exhibited higher asymmetry than dense networks. Importantly, our experimental connectivity networks symmetry between HbO2 and HHb departs from random (t-test: t(509) = 26.39, p < 0.0001). The DSI distribution suggests a threshold of 0.2 to decide whether both HbO2 and HHb FC networks ought to be studied. For sparse FC networks, analysis of both haemoglobin species is strongly recommended. Our DSI can provide a quantifiable guideline for deciding whether to proceed with single or both Hb networks in FC analysis. Full article
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Open AccessArticle
A Multi-Stage Algorithm for a Capacitated Vehicle Routing Problem with Time Constraints
Algorithms 2018, 11(5), 69; https://doi.org/10.3390/a11050069 -
Abstract
The Vehicle Routing Problem (VRP) is one of the most optimized tasks studied and it is implemented in a huge variety of industrial applications. The objective is to design a set of minimum cost paths for each vehicle in order to serve a
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The Vehicle Routing Problem (VRP) is one of the most optimized tasks studied and it is implemented in a huge variety of industrial applications. The objective is to design a set of minimum cost paths for each vehicle in order to serve a given set of customers. Our attention is focused on a variant of VRP, the capacitated vehicle routing problem when applied to natural gas distribution networks. Managing natural gas distribution networks includes facing a variety of decisions ranging from human resources and material resources to facilities, infrastructures, and carriers. Despite the numerous papers available on vehicle routing problem, there are only a few that study and analyze the problems occurring in capillary distribution operations such as those found in a metropolitan area. Therefore, this work introduces a new algorithm based on the Saving Algorithm heuristic approach which aims to solve a Capacitated Vehicle Routing Problem with time and distance constraints. This joint algorithm minimizes the transportation costs and maximizes the workload according to customer demand within the constraints of a time window. Results from a real case study in a natural gas distribution network demonstrates the effectiveness of the approach. Full article
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