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This paper focuses on minimum-time path tracking, a subproblem in motion planning of robotic systems. We generate a time-optimal velocity profile for robotic manipulators taking into account kinematic and dynamic constraints. Based on the special structure of the constraints (called peaked constraints), profile generation is formulated as a linear programming (LP) problem. The LP-based control problem is solved by a sequential optimization method. The presented algorithm has reduced computational time compared to a general LP solver. [ABSTRACT FROM AUTHOR]

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate. [ABSTRACT FROM AUTHOR]

In this paper we provide a theoretical and numerical comparison of convergence rates of forward-backward, Douglas-Rachford, and Peaceman-Rachford algorithms for minimizing the sum of a convex proper lower semicontinuous function and a strongly convex differentiable function with Lipschitz continuous gradient. Our results extend the comparison made in [1], when both functions are smooth, to the context where only one is assumed differentiable. Optimal step-sizes and rates of the three algorithms are compared theoretically and numerically in the context of texture segmentation problem, obtaining very sharp estimations and illustrating the high efficiency of Peaceman-Rachford splitting. [ABSTRACT FROM AUTHOR]

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors. [ABSTRACT FROM AUTHOR]

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called “prosumers,” i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we first prove the strong monotonicity of the game. Then, the GNG is converted into an equivalent optimization problem. An algorithm based on Nesterov's methods is thereby devised to solve the equivalent problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 1888 prosumers. [ABSTRACT FROM AUTHOR]

Weighted multi-view clustering (MVC) aims to combine the complementary information of multi-view data (such as image data with different types of features) in a weighted manner to obtain a consistent clustering result. However, when the cluster-wise weights across views are vastly different, most existing weighted MVC methods may fail to fully utilize the complementary information, because they are based on view-wise weight learning and can not learn the fine-grained cluster-wise weights. Additionally, extra parameters are needed for most of them to control the weight distribution sparsity or smoothness, which are hard to tune without prior knowledge. To address these issues, in this paper we propose a novel and effective Cluster-weighted mUlti-view infoRmation bottlEneck (CURE) clustering algorithm, which can automatically learn the cluster-wise weights to discover the discriminative clusters across multiple views and thus can enhance the clustering performance by properly exploiting the cluster-level complementary information. To learn the cluster-wise weights, we design a new weight learning scheme by exploring the relation between the mutual information of the joint distribution of a specific cluster (containing a group of data samples) and the weight of this cluster. Finally, a novel draw-and-merge method is presented to solve the optimization problem. Experimental results on various multi-view datasets show the superiority and effectiveness of our cluster-wise weighted CURE over several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Black-box optimization algorithms typically start a search from scratch, assuming little prior knowledge about the task at hand. In practice, this approach can be prohibitive for computationally expensive problems, as a large number of costly function evaluations are often needed before a suitable (near-optimal) solution is found. Under this observation, recent efforts have incorporated transfer learning capabilities into sequential model-based Bayesian optimization (BO) solvers, resulting in substantial performance speed-ups by leveraging information from related past problems. However, a common simplifying assumption in existing approaches is that the search spaces of a previously encountered source and the ongoing target task bear the same features and dimensionality, with the difference lying in their respective objective functions. In this article, we present a generalized transfer BO algorithm that relaxes the aforementioned assumption. Our method jointly transforms source features while training probabilistic transfer regression models for the target, thus applying to practical use-cases where (in addition to the difference in objective functions) the number of features could change across the source and target tasks; for example, features can be added and/or removed. The theoretical basis of our proposal is analyzed, and its empirical performance is demonstrated on synthetic benchmark functions as well as in realistic examples spanning engineering design and the automated configuration of a machine learning model. Note to Practitioners—Problems of industrial interest have a tendency of being repetitive in nature. For this reason, domain experts are always in high demand, as they are able to harness their experience of similar problems to come up with fast solutions in difficult situations. However, domain experts are not easy to find. Given this fact, the present paper puts forth a method for automating the process of knowledge extraction (through experiential learning) and transfer across problems in the domain of computationally expensive black-box optimization. The key novelty and motivation of this work lies in enabling the adaptive transfer of knowledge even when the number of features changes across the source and target problems. Our proposed approach is verified experimentally on a range of benchmarks as well as real-world problems of a computationally expensive nature, highlighting the utility of an optimization engine that is able to learn from experience without the need for constant human intervention. [ABSTRACT FROM AUTHOR]

Connected vehicles will change the modes of future transportation management and organization, especially at an intersection without traffic light. Centralized coordination methods globally coordinate vehicles approaching the intersection from all sections by considering their states altogether. However, they need substantial computation resources since they own a centralized controller to optimize the trajectories for all approaching vehicles in real-time. In this paper, we propose a centralized coordination scheme of automated vehicles at an intersection without traffic signals using reinforcement learning (RL) to address low computation efficiency suffered by current centralized coordination methods. We first propose an RL training algorithm, model accelerated proximal policy optimization (MA-PPO), which incorporates a prior model into proximal policy optimization (PPO) algorithm to accelerate the learning process in terms of sample efficiency. Then we present the design of state, action and reward to formulate centralized coordination as an RL problem. Finally, we train a coordinate policy in a simulation setting and compare computing time and traffic efficiency with a coordination scheme based on model predictive control (MPC) method. Results show that our method spends only 1/400 of the computing time of MPC and increase the efficiency of the intersection by 4.5 times. [ABSTRACT FROM AUTHOR]

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. It is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLP D-OPF model for the same distribution system. [ABSTRACT FROM AUTHOR]

Subset selection, aiming to select the best subset from a ground set with respect to some objective function, is a fundamental problem with applications in many areas, such as combinatorial optimization, machine learning, data mining, computer vision, information retrieval, etc. Along with the development of data collection and storage, the size of the ground set grows larger. Furthermore, in many subset selection applications, the objective function evaluation is subject to noise. We thus study the large-scale noisy subset selection problem in this paper. The recently proposed DPOSS algorithm based on multiobjective evolutionary optimization is a powerful distributed solver for large-scale subset selection. Its performance, however, has been only validated in the noise-free environment. In this paper, we first prove its approximation guarantee under two common noise models, i.e., multiplicative noise and additive noise, disclosing that the presence of noise degrades the performance of DPOSS largely. Next, we propose a new distributed multiobjective evolutionary algorithm called DPONSS for large-scale noisy subset selection. We prove that the approximation guarantee of DPONSS under noise is significantly better than that of DPOSS. We also conduct experiments on the application of sparse regression, where the objective evaluation is often estimated using a sample data, bringing noise. The results on various real-world data sets, whose size can reach millions, clearly show the excellent performance of DPONSS. [ABSTRACT FROM AUTHOR]

Dictionary learning has emerged as a powerful tool for a range of image processing applications and a proper dictionary always plays a key issue to the final achievable performance. In this paper, a class-oriented discriminative dictionary learning (CODDL) method is presented for image classification applications. It takes a comprehensive consideration of multiple optimization objectives, emphasizing class discrimination of both dictionary atoms and representation coefficients. The atoms of the learned dictionary should be grouped into class level sub-dictionaries. Meanwhile, the sparse representation coefficients of an input sample should be concentrated on the sub-dictionary of the class it belongs to. Then, based on the learned class-oriented discriminative dictionary, the structured representation coefficients can thus be used for image classification with a simple and efficient classification scheme. The superior performance of the proposed algorithm is demonstrated through extensive experiments. [ABSTRACT FROM AUTHOR]

Existing decentralized coded caching solutions cannot guarantee small loads in the general scenario with arbitrary file sizes and cache sizes. In this paper, we propose an optimization framework for decentralized coded caching in the general scenario to minimize the worst-case load and average load (under an arbitrary file popularity), respectively. Specifically, we first propose a class of decentralized coded caching schemes for the general scenario, which are specified by a general caching parameter and include several known schemes as special cases. Then, we optimize the caching parameter to minimize the worst-case load and average load, respectively. Each of the two optimization problems is a challenging nonconvex problem with a nondifferentiable objective function. For each optimization problem, we develop an iterative algorithm to obtain a stationary point using techniques for solving Complementary Geometric Programming (GP). We also obtain a low-complexity approximate solution by solving an approximate problem with a differentiable objective function which is an upper bound on the original nondifferentiable one, and characterize the performance loss caused by the approximation. Finally, we present two information-theoretic converse bounds on the worst-case load and average load (under an arbitrary file popularity) in the general scenario, respectively. To the best of our knowledge, this is the first work that provides optimization-based decentralized coded caching schemes and information-theoretic converse bounds for the general scenario. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new Bayesian model to solve the Robust PCA problem - recovering the underlying low-rank matrix and sparse matrix from their noisy compositions. We first derive and analyze a new objective function, which is proven to be equivalent to the fundamental objective of minimizing the “rank+sparsity”. To solve this objective, we develop a concise Sparse Bayesian Learning (SBL) method that makes minimal assumptions and effectively deals with the requirements of the problem. The concise modeling allows simple and effective Empirical Bayesian inference via maximum a posteriori expectation-maximization (MAP-EM). We further propose a modified SBL method that additionally utilizes the sparsity pattern information of the outliers in the Robust PCA problem. Simulation studies demonstrate the superiority of the proposed methods over the existing state-of-the-art methods. The efficacy of the proposed methods is further verified through two image processing tasks. [ABSTRACT FROM AUTHOR]

In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted l 1 norm, we utilize the l p norm of the array weight vector, where $0

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms. [ABSTRACT FROM AUTHOR]

In a low-statistics PET imaging context, the positive bias in regions of low activity is a burning issue. To overcome this problem, algorithms without the built-in non-negativity constraint may be used. They allow negative voxels in the image to reduce, or even to cancel the bias. However, such algorithms increase the variance and are difficult to interpret since the resulting images contain negative activities, which do not hold a physical meaning when dealing with radioactive concentration. In this paper, a post-processing approach is proposed to remove these negative values while preserving the local mean activities. Its original idea is to transfer the value of each voxel with negative activity to its direct neighbors under the constraint of preserving the local means of the image. In that respect, the proposed approach is formalized as a linear programming problem with a specific symmetric structure, which makes it solvable in a very efficient way by a dual-simplex-like iterative algorithm. The relevance of the proposed approach is discussed on simulated and on experimental data. Acquired data from an yttrium-90 phantom show that on images produced by a non-constrained algorithm, a much lower variance in the cold area is obtained after the post-processing step, at the price of a slightly increased bias. More specifically, when compared with the classical OSEM algorithm, images are improved, both in terms of bias and of variance. [ABSTRACT FROM AUTHOR]

Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for autonomous aircraft. If the design is safe, as it is supposed to be, accident cases are hard to find. Such analysis needs some variance reduction technique and several algorithms exist for that; however, specific model features may cause difficulties in practice, such as the case of system models where independent agents have to autonomously accomplish missions within finite time, and likely with the presence of human agents. For handling these scenarios, this paper presents a novel estimation approach, based on the combination of the well-established variation reduction technique of interacting particles system with the long-standing optimization algorithm denominated DIviding RECTangles. When combined, these two techniques yield statistically significant results for extremely low probabilities. In addition, this novel approach allows the identification of intermediate events and simplifies the evaluation of sensitivity of the estimated probabilities to certain system parameters. [ABSTRACT FROM AUTHOR]

This paper revisits the circular formation control problem proposed in [G. S. Seyboth, J. Wu, J. Qin, C. Yu, and F. Allgower, “Collective circular motion of unicycle type vehicles with nonidentical constant velocities,” IEEE Transactions on Control of Network Systems, vol. 1, no. 2, pp. 167–176, Jun. 2014.] for multiple nonholonomic mobile robots with nonidentical constant forward speeds. Specifically, we study two types of circular formations: First, a circular motion with synchronized/balanced phase configuration; and second, a concentric circular formation with both circular orbits control and phase synchronization/balancing. Existing works on the above problems utilize a fixed-gain control input, which increases the workload of the engineers for selecting favorable algorithm parameters. To reduce this workload, we study the above problems from a new perspective by utilizing optimization methods, based on which two variable-gain control algorithms are proposed such that much greater flexibility on the selection of algorithm parameters is acquired. The global convergence properties of the proposed algorithms are analyzed under some mild assumptions. Both simulations and field experiments are presented to validate the effectiveness of the proposed formation algorithms. [ABSTRACT FROM AUTHOR]

2-D linear discriminant analysis (2DLDA) has been widely used in pattern recognition and image classification. 2DLDA selects discriminative features from the up and left corner of images. However, 2DLDA uses the Frobenius norm (F-norm), which is sensitive to noise or outliers in data, as a metric. In this paper, we propose a novel framework, called horizontal and vertical nuclear norm-based 2DLDA (HVNN-2DLDA) for image representation. In the proposed framework, HVNN-2DLDA methods (i.e., HNN-2DLDA and VNN-2DLDA) are proposed, and both use the nuclear norm as a criterion. The nuclear norm can provide more structure and global information for the reconstruction of noisy images. HNN-2DLDA and VNN-2DLDA represent images in the row and column directions, respectively. In addition, by combining the row and column directions, we propose a bilateral nuclear norm-based 2DLDA method called BNN-2DLDA. The advantage of BNN-2DLDA over HNN-2DLDA and VNN-2DLDA is that an image sample can be represented by both the row and the column directions instead of only the row or column direction. HVNN-2DLDA learns a set of local optimal projection vectors by maximizing the ratio of the nuclear norm of the between-class scatter matrix and the nuclear norm of the within-class scatter matrix. To verify the robustness and recognition performance in image classification of HVNN-2DLDA, six public image databases are used for experiments. The experimental results demonstrate the effectiveness and the feasibility of the proposed framework. [ABSTRACT FROM AUTHOR]

In this paper, we study the cost-aware target viral marketing (CTVM) problem, a generalization of influence maximization. CTVM asks for the most cost-effective users to influence the most relevant users. In contrast to the vast literature, we attempt to offer exact solutions. As the problem is NP-hard, thus, exact solutions are intractable, we propose TipTop, a $(1-\epsilon)$ -optimal solution for arbitrary $\epsilon >0$ that scales to very large networks, such as Twitter. At the heart of TipTop lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using integer programming. Furthermore, TipTop lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available. [ABSTRACT FROM AUTHOR]

In a distribution system when fault occurs, prior operation of any other relay which is not designated as the primary relay causes undesired shedding of a healthy line. This phenomena of unwanted relay operation is termed as sympathetic tripping. For appropriate relay operation, issue of sympathetic tripping is required to be considered while addressing relay coordination problem. This paper proposes a phase fault protection scheme, which mitigates the issue of sympathetic tripping in the meshed network. The undesired relay operation in the network is restricted by imposing some additional constraints on the conventional relay coordination problem. The proposed nonlinear optimization problem is solved by using Shannon–Wiener differential evolution algorithm. Procured optimal relay settings will provide efficient protection against each phase fault without causing sympathetic tripping. The efficacy of the proposed algorithm is examined on modified IEEE-8-bus system, IEEE-14-bus system, and IEEE-30-bus system. The obtained results are verified by using GE Mutilin, model-750/760 overcurrent relay in ETAP (industrial simulation software). [ABSTRACT FROM AUTHOR]

Optimally designed arrays are used to obtain high gain and directivity. Based on the desired application, different radiation patterns can be generated. These patterns have generally a main beam and some sidelobes. These last ones are undesirable because they can cause electromagnetic interference and compatibility issues. Therefore, sidelobe levels (SLLs) reduction is one of the most important factors for the design of antenna arrays and arrays must be designed in a way to reduce SLLs. In this paper, the optimal design of circular antenna arrays (CAA) for maximum SLLs reduction is investigated using a newly developed metaheuristic that is the most valuable player algorithm. This algorithm is inspired from sport and it has been proven to be an excellent optimization algorithm for mathematical benchmarks. Three cases with different number of arrays are investigated. For comparison purposes, ten other well-known optimization algorithms are used. The design results obtained show the superiority of the proposed algorithm for the optimal design of CAA and for sidelobe reduction over many other algorithms. [ABSTRACT FROM AUTHOR]

Confronted with considerable intermittence and variability of wind power, prediction intervals (PIs) serve as a crucial tool to assist power system decision-making under uncertainties. Conventional PIs rely on predetermining the lower and upper quantile proportions and therefore suffer from conservative interval width. This paper innovatively develops a chance constrained extreme learning machine (CCELM) model to generate quality nonparametric proportion-free PIs of wind power generation, which minimizes the expected interval width subject to the PI coverage probability constraint. Due to the independency on the preset PI bounds proportions, the proposed CCELM model merits high adaptivity and taps the latent potentialities for PI shortening. The convexity of extreme learning machine renders the sample average approximation counterpart of stochastic CCELM model equivalent to a parameter searching task in parametric optimization problem with polyhedral feasible region. A novel difference of convex functions optimization based bisection search (DCBS) algorithm is proposed to efficiently construct the CCELM model, which successfully realizes machine learning by means of solving linear programming problems sequentially. Comprehensive numerical experiments based on actual wind farm data demonstrate the significant effectiveness and efficiency of the developed CCELM model and DCBS algorithm. [ABSTRACT FROM AUTHOR]

Recently, sparse representation-based classification (SRC) has been widely studied and has produced state-of-the-art results in various classification tasks. Learning useful and computationally convenient representations from complex redundant and highly variable visual data is crucial for the success of SRC. However, how to find the best feature representation to work with SRC remains an open question. In this paper, we present a novel discriminative projection learning approach with the objective of seeking a projection matrix such that the learned low-dimensional representation can fit SRC well and that it has well discriminant ability. More specifically, we formulate the learning algorithm as a bilevel optimization problem, where the optimization includes an $\ell _{1}$ -norm minimization problem in its constraints. Through the bilevel optimization model, the relationship between sparse representation and the desired feature projection can be explicitly exploited during the learning process. Therefore, SRC can achieve a better performance in the transformed subspace. The optimization model can be solved by using a stochastic gradient ascent algorithm, and the desired gradient is computed using implicit differentiation. Furthermore, our method can be easily extended to learn a dictionary. The extensive experimental results on a series of benchmark databases show that our method outperforms many state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized algorithm for solving a consensus optimization problem defined in a static networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form. Examples of such problems include decentralized constrained quadratic programming and compressed sensing problems, as well as many regularization problems arising in inverse problems, signal processing, and machine learning, which have decentralized applications. This paper addresses the need for efficient decentralized algorithms that take advantages of proximal operations for the nonsmooth terms. We propose a proximal gradient exact first-order algorithm (PG-EXTRA) that utilizes the composite structure and has the best known convergence rate. It is a nontrivial extension to the recent algorithm EXTRA. At each iteration, each agent locally computes a gradient of the smooth part of its objective and a proximal map of the nonsmooth part, as well as exchanges information with its neighbors. The algorithm is “exact” in the sense that an exact consensus minimizer can be obtained with a fixed step size, whereas most previous methods must use diminishing step sizes. When the smooth part has Lipschitz gradients, PG-EXTRA has an ergodic convergence rate of O\left(1\over k\right) in terms of the first-order optimality residual. When the smooth part vanishes, PG-EXTRA reduces to P-EXTRA, an algorithm without the gradients (so no “G” in the name), which has a slightly improved convergence rate at o\left(1\over k\right) in a standard (non-ergodic) sense. Numerical experiments demonstrate effectiveness of PG-EXTRA and validate our convergence results [ABSTRACT FROM PUBLISHER]

This paper focuses on precoding design for sum-rate maximization while considering the effects of residual self-interference for multiuser multiple-input–multiple-output (MU-MIMO) full-duplex (FD) systems. The problem formulation leads to a nonconvex matrix-variable optimization problem, where we develop two efficient sum-rate maximization algorithms using sequential convex programming (SCP), namely, the difference of convex functions (DC)-based and the sequential convex approximations for matrix-variable programming (SCAMP) algorithms. In addition, we derive the achievable sum rate under the effect of residual self-interference. Simulation results show that, even in cases of high self-interference and high estimation error, the SCAMP algorithm provides approximately 20%–30% sum-rate improvements over both conventional optimized half-duplex (HD) transmission and the existing state-of-the-art FD algorithm in a wide range of scenarios. Finally, the convergence results indicate that the DC-based algorithm tends to initially give the best performance; however, at convergence, the SCAMP algorithm tends to significantly outperform the other algorithms. [ABSTRACT FROM AUTHOR]

In this article, we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration, and jerk constraints. Such a problem arises in industrial contexts, such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and nonconvex jerk constraints, which, thus, represent the main source of the difficulty. While existing nonlinear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this article. At each iteration, a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach that strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proven through different computational experiments. Note to Practitioners—This article was motivated by the needs of LGV manufacturers. In particular, it presents an algorithm for computing the minimum-time speed law for an LGV along a preassigned path, respecting assigned velocity, acceleration, and jerk constraints. The solution algorithm should be: 1) fast, since speed planning is made continuously throughout the workday, not only when an LGV receives a new task but also during the execution of the task itself, since conditions may change, e.g., if the LGV has to be halted for security reasons and 2) reliable, i.e., it should return solutions of high quality, because a better speed profile allows to save time and even small percentage improvements, say a 5% improvement, has a considerable impact on the productivity of the warehouse, and, thus, determines a significant economic gain. The algorithm that we propose meets these two requirements, and we believe that it can be a useful tool for LGV manufacturers and users. It is obvious that the proposed method also applies to the speed planning problem for vehicles other than LGVs, e.g., road vehicles. [ABSTRACT FROM AUTHOR]

This paper formulates an optimization-based algorithm for the compensation of unwanted current terms by means of distributed electronic power converters, such as active power filters and grid-connected inverters. The compensation goal consists in achieving suitable load conformity factors, defined at the source side and within a feasible power region in terms of the power converter capability. Based on the measured load quantities and on a certain objective function, the algorithm tracks the expected source currents, which are thereupon used to calculate proper scaling coefficients and, therefore, the compensation current references. It improves the power quality at the point of common coupling and enables full exploitation of distributed energy resources, increasing their efficiency. The compensation is based on a decoupled current decomposition and on an optimization-based algorithm. In this paper, the strategy is applied to nonlinear and unbalanced three-phase four-wire circuit, under nonsinusoidal and asymmetrical voltage conditions. The steady-state and dynamic behaviors have been analyzed by theoretical, simulation, and experimental results. Furthermore, the proposed approach is also compared to other compensation strategies showing its effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents an incremental timing-driven placement tool, named OWARU. It optimizes timing critical paths through a free space-aware path smoothing: the gates on such paths are relocated to free spaces around the smoothed paths, while incremental static timing analysis is involved to accurately assess timing changes due to the relocation. OWARU is extended to accommodate gate sizing and layer assignment to demonstrate the effectiveness of unified physical synthesis optimizations and incremental placement. The goal is to show that OWARU is an ideal platform for timing closure at later stages of a physical design flow. OWARU is applied on a set of test circuits from 14-nm high-performance commercial microprocessors, which originally failed in timing closure. On average, the worst slack is improved by 63.6%, which corresponds to 5.0% of the clock period; total negative slack is improved by 69.1%. [ABSTRACT FROM AUTHOR]

Video contents are inherently heterogeneous. To exploit different feature modalities in a diverse video collection for video summarization, we propose to formulate the task as a multiview representative selection problem. The goal is to select visual elements that are representative of a video consistently across different views (i.e., feature modalities). We present in this paper the multiview sparse dictionary selection with centroid co-regularization method, which optimizes the representative selection in each view, and enforces that the view-specific selections to be similar by regularizing them towards a consensus selection. We also introduce a diversity regularizer to favor a selection of diverse representatives. The problem can be efficiently solved by an alternating minimizing optimization with the fast iterative shrinkage thresholding algorithm. Experiments on synthetic data and benchmark video datasets validate the effectiveness of the proposed approach for video summarization, in comparison with other video summarization methods and representative selection methods such as K-medoids, sparse dictionary selection, and multiview clustering. [ABSTRACT FROM PUBLISHER]

Generating units, participating in the secondary frequency control of a control area, are usually spinning units already connected to the network and operating outside their range of optimal performance. This paper deals with an alternative method of providing secondary frequency control called Rapid-Start (RS). It consists in assigning a regulation band to several off-line units (RS units) which are capable of being started and connected rapidly, therefore allowing the online units to operate closer to their nominal power. As RS operation may have economic benefits, an appropriate algorithm to start up an RS unit needs to be developed. This paper proposes a methodology to evaluate, compare, and choose the most appropriate RS algorithm among the ones developed for a certain AGC control area. An optimization model provides a reference by determining the hypothetically ideal start-ups and shut-downs of RS units. In addition, the definition of performance indexes to evaluate, compare, and choose the different RS algorithms is proposed. The proposed methodology is illustrated for a secondary frequency control zone within the Spanish power system by using real data signals. [ABSTRACT FROM PUBLISHER]

Identification of variable interaction is essential for an efficient implementation of a divide-and-conquer algorithm for large-scale black-box optimization. In this paper, we propose an improved variant of the differential grouping (DG) algorithm, which has a better efficiency and grouping accuracy. The proposed algorithm, DG2, finds a reliable threshold value by estimating the magnitude of roundoff errors. With respect to efficiency, DG2 reuses the sample points that are generated for detecting interactions and saves up to half of the computational resources on fully separable functions. We mathematically show that the new sampling technique achieves the lower bound with respect to the number of function evaluations. Unlike its predecessor, DG2 checks all possible pairs of variables for interactions and has the capacity to identify overlapping components of an objective function. On the accuracy aspect, DG2 outperforms the state-of-the-art decomposition methods on the latest large-scale continuous optimization benchmark suites. DG2 also performs reliably in the presence of imbalance among contribution of components in an objective function. Another major advantage of DG2 is the automatic calculation of its threshold parameter ( $\epsilon $ ), which makes it parameter-free. Finally, the experimental results show that when DG2 is used within a cooperative co-evolutionary framework, it can generate competitive results as compared to several state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem's inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. The proposed algorithm is used to generate the feasible spaces of two small test cases. [ABSTRACT FROM PUBLISHER]

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in term of their canonical dual solutions. The existence and uniqueness of these analytical solutions are proved. NP-hardness of the knapsack problems is discussed. A powerful CDT algorithm combined with an alternative iteration and a volume reduction method is proposed for solving the NP-hard bilevel knapsack problems. Application is illustrated by benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. [ABSTRACT FROM AUTHOR]

In order to obtain a good optimization method for the electrical transformer design with optimal selection of parameters, performance evaluation of three evolutionary algorithms (EAs), namely, genetic algorithm (GA), differential evolution algorithm, and nondominated sorting GA (NSGA-II), is carried out. The aim of this paper is to optimize parameters of transformer design (core thicknesses, primary-turn number, secondary-turn number, primary conductor area, and secondary conductor area) for minimization of total power losses (no-load losses and load losses) in three-phase transformer topology while maintaining high efficiency and low cost. The method used for this optimization scheme combines the finite-element method (FEM) and EAs to provide an accurate selection of parameters together with the optimized magnetic flux density and decreased loss. Experimental results show that NSGA-II+FEM model successfully provides a global feasible solution by minimizing total loss and related cost while improving the efficiency of three-phase transformer, rendering it suitable for application in the design environment of industrial transformers. [ABSTRACT FROM AUTHOR]

In this paper, four iterative algorithms for learning analysis operators are presented. They are built upon the same optimization principle underlying both Analysis K-SVD and Analysis SimCO. The forward and sequential analysis operator learning (AOL) algorithms are based on projected gradient descent with optimally chosen step size. The implicit AOL algorithm is inspired by the implicit Euler scheme for solving ordinary differential equations and does not require to choose a step size. The fourth algorithm, singular value AOL, uses a similar strategy as Analysis K-SVD while avoiding its high computational cost. All algorithms are proven to decrease or preserve the target function in each step and a characterization of their stationary points is provided. Further they are tested on synthetic and image data, compared to Analysis SimCO and found to give better recovery rates and faster decay of the objective function, respectively. In a final denoising experiment the presented algorithms are again shown to perform similar to or better than the state-of-the-art algorithm ASimCO. [ABSTRACT FROM AUTHOR]

As one of the most commonly used clustering methods, the fuzzy C-means (FCM) clustering strategy extends the notion of hard clustering to associate each pattern with every cluster using a membership function. Although a lot of efforts have been made by the clustering community, it is still unclear how to evaluate the fuzziness of different versions of FCM. To fill this theoretical blank, by observing a family of objective functions, a definition of fuzzy degree is provided to quantify the fuzziness of different versions of FCM according to their dedicated objective functions. Then, a general fuzzy C-means (GFCM) clustering algorithm is proposed to solve the clustering problem of using FCM under different distance metrics and fuzzy degrees. From the perspective of fuzzy attribute, the using of this fuzzy degree can be used to reveal the essential difference among a group of FCM-based clustering algorithms, and the proposed GFCM achieves the aim of using objective functions to control the fuzziness of clustering results. Additionally, some properties and relations of these FCM-based clustering algorithms under different fuzzy degrees are discussed and the convergence and stability of the proposed GFCM are proved. Finally, extensive experiments have been performed to demonstrate that by comparison with the effect caused by distance metric, the choices of fuzzy degree have a more significant effect and improvement on the performances of a FCM-based clustering algorithm. [ABSTRACT FROM AUTHOR]

Complex networks have been widely adopted to represent a variety of complicated systems. Given a complex network, it is of great significance to perform accurate clustering for better understanding its intrinsic organization. To this end, a fuzzy-based clustering algorithm, i.e., FCAN, has been developed. Though effective, FCAN suffers from the disadvantage of slow convergence, which in return constrains its efficiency. To address this issue, this article proposes a fast fuzzy clustering algorithm, namely, F $^2$ CAN, which incorporates a generalized momentum method into FCAN. Its fast convergence is rigorous justified in theory. Empirical studies on five datasets from real applications demonstrate that F $^2$ CAN achieves a better performance when compared with FCAN and several state-of-the-art clustering algorithms in terms of convergence rate and clustering accuracy simultaneously. Hence, F $^2$ CAN has potential for addressing the clustering analysis of large-scale complex networks emerging from industrial applications. [ABSTRACT FROM AUTHOR]

Fuzzy c-means (FCM) algorithms with spatial information have been widely applied in the field of image segmentation. However, most of them suffer from two challenges. One is that the introduction of fixed or adaptive single neighboring information with narrow receptive field limits contextual constraints leading to clutter segmentations. The other is that the incorporation of superpixels with wide receptive field enlarges spatial coherency leading to block effects. To address these challenges, we propose fuzzy STUDENT’S t-distribution model based on richer spatial combination (FRSC) for image segmentation. In this article, we make two significant contributions. The first is that both the narrow and wide receptive fields are integrated into the objective function of FRSC, which is convenient to mine image features and distinguish local difference. The second is that the rich spatial combination under STUDENT’S t-distribution ensures that spatial information is introduced into the updated parameters of FRSC, which is helpful in finding a balance between the noise-immunity and detail-preservation. Experimental results on synthetic and publicly available images further demonstrate that the proposed FRSC addresses successfully the limitations of FCM algorithms with spatial information, and provides better segmentation results than state-of-the-art clustering algorithms. [ABSTRACT FROM AUTHOR]

This paper seeks to improve the computational time needed to solve transmission switching problems. Transmission switching provides an effective way to reduce operating costs in power system operations by altering the topology of the transmission network. However, determining the optimal set of lines to switch creates an enormous computational burden. Transmission switching formulations add binary decision variables for many transmission lines in the system to indicate if they are switched. This creates a very weak formulation that is difficult to solve. Altering the transmission topology by switching lines can affect the reliability of the network, for instance, by creating islands. Additional reliability constraints need to be added to the problem formulation. These constraints can potentially make an already difficult problem even harder. This paper takes a different approach to the transmission switching problem. Rather than preventing islanding by using constraints in the problem formulation, we look at how they can be used to improve the solution process. Specifically, we develop a cutting plane algorithm to generate valid inequalities and fix variables based on the fact that optimal solutions to the transmission switching problem that do not contain islands exist. [ABSTRACT FROM AUTHOR]

Many automation or manufacturing systems are too complex to be modeled by analytical approaches and can only resort to fast-running simulation. Stochastic Nelder–Mead simplex method (SNM) is a newly developed methodology for simulation optimization with expected-value-based objective functions. Quantile, as an important alternative to the usual expected value, provides additional information about the distribution of system performance. In particular, it is useful in describing the tail behavior of the distribution. In this paper, we exploit the structure of SNM and extend it to solve simulation optimization problems with quantile-based objective functions and inequality constraints. The proposed method, called SNM-QC, utilizes the same search strategy as SNM but further incorporates effective quantile estimation techniques and penalty function approaches to solve the problem. We prove that SNM-QC has the desirable global convergence guarantee, i.e., the algorithm is guaranteed to converge to the true optima with probability one. One advantage of SNM-QC is that it is a direct search method that determines the moving direction simply by comparing a set of solutions rather than estimating gradient, thus it can handle many practical problems where gradient does not exist or is difficult to estimate. An extensive numerical study shows that the performance of SNM-QC is promising compared to the existing heuristics. Two illustrative applications are provided in the end to demonstrate the viability of SNM-QC in practical settings. [ABSTRACT FROM AUTHOR]

Existing studies in black-box optimization suffer from low generalizability, caused by a typically selective choice of problem instances used for training and testing of different optimization algorithms. Among other issues, this practice promotes overfitting and poor-performing user guidelines. We address this shortcoming by introducing in this work a general-purpose algorithm selection wizard that was designed and tested on a previously unseen breadth of black-box optimization problems, ranging from academic benchmarks to real-world applications, from discrete over numerical to mixed-integer problems, from small to very large-scale problems, from noisy over dynamic to static problems, etc. Not only did we use the already very extensive benchmark environment available in Nevergrad, but we also extended it significantly by adding a number of additional benchmark suites, including Pyomo, Photonics, large-scale global optimization (LSGO), and MuJoCo. Our wizard achieves competitive performance on all benchmark suites. It significantly outperforms previous state-of-the-art algorithms on some of the suites, including YABBOB and LSGO. Its excellent performance is obtained without any task-specific parametrization. The algorithm selection wizard, all of its base solvers, as well as the benchmark suites are available for reproducible research in the open-source Nevergrad platform. [ABSTRACT FROM AUTHOR]

This paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases. A computationally efficient iterative algorithm for the continuous phase case (IA-CPC) is proposed to sequentially optimize the quadratic objective function. The quadratic optimization problem is turned into multiple one-dimensional optimization problems with closed-form solutions. For the discrete phase case, we present an iterative block optimization algorithm. Specifically, we partition the design variables into $K$ blocks, and then, we sequentially optimize each block via exhaustive search while fixing the remaining $K-1$ blocks. Finally, we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method-like and semidefinite relaxation related techniques. [ABSTRACT FROM PUBLISHER]

In order to optimize hydro power plants generator scheduling according to 24-h system demand, a parallel self-adaptive differential evolution algorithm has been applied. The proposed algorithm presents a novel approach to considering the multi-population and utilization of the preselection step for the improvements of the algorithm's global search capabilities. A preselection step with the best, middle, and worst populations' individuals establishes the new trial vectors. This algorithm has been verified on two different models. The first one consists of eight power plants with real parameters, and the second one consists of four power plants, mostly used as a test model in scientific papers. The main goal of the optimization process is to satisfy system demand for 24 h with a decreased usage of water quantity per electrical energy unit. The initial and final states of the reservoirs must also be satisfied. [ABSTRACT FROM PUBLISHER]

Ultradense heterogeneous networks (HetNets) are emerging as an inevitable approach to tackle the capacity crunch in cellular networks. However, imbalanced load among small and macrocells and poor resource utilization as a consequence in HetNets remains a long-standing problem. This paper addresses this problem by presenting a solution for maximization of coverage and capacity while minimizing load imbalance among macro and small cells. Most recent studies on the topic focus on either optimization of coverage, capacity or load, or a combination of two of these three intertwined objectives. We formulate the optimization problem as a function of two hard parameters namely antenna tilt and transmit power, and a soft parameter, cell individual offset, that affect the coverage, capacity, and load directly. The resulting solution is a combination of the otherwise conflicting coverage and capacity optimization (CCO) and load balancing (LB) self-organizing network (SON) functions. In the presented joint CCO-LB solution, a conflict free operation of CCO and LB is ensured by designing a novel load aware user association methodology and resolving the effects of shadowing on coverage probability using stochastic approximation. The problem is proven to be nonconvex and is solved using genetic algorithm, sequential quadratic programming, and pattern search algorithms. The proposed CCO-LB solution is compared against two recently proposed CCO and CCO-LB solutions in the literature. Results show that the proposed solution can yield significant gain in terms of throughput, spectral efficiency, and load distribution. [ABSTRACT FROM AUTHOR]

This paper proposes a new distance-based distributionally robust unit commitment (DB-DRUC) model via Kullback–Leibler (KL) divergence, considering volatile wind power generation. The objective function of the DB-DRUC model is to minimize the expected cost under the worst case wind distributions restricted in an ambiguity set. The ambiguity set is a family of distributions within a fixed distance from a nominal distribution. The distance between two distributions is measured by KL divergence. The DB-DRUC model is a “min-max-min” programming model; thus, it is intractable to solve. Applying reformulation methods and stochastic programming technologies, we reformulate this “min-max-min” DB-DRUC model into a one-level model, referred to as the reformulated DB-DRUC (RDB-DRUC) model. Using the generalized Benders decomposition, we then propose a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model. The iterative algorithm for the RDB-DRUC model guarantees global convergence within finite iterations. Case studies are carried out to demonstrate the effectiveness, global optimality, and finite convergence of a proposed solution strategy. [ABSTRACT FROM AUTHOR]

Bounded component analysis (BCA) is a recently introduced approach including independent component analysis as a special case under the assumption of source boundedness. In this paper, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as well as independent sources from their mixtures. The stationary points are identified and characterized as either perfect separators, which are the global maxima of the proposed optimization scheme or saddle points. The important result emerging from the analysis is that there are no local optima that can prevent the proposed BCA algorithms from converging to perfect separators. [ABSTRACT FROM PUBLISHER]