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In this article, a new hypervolume-based evolutionary multiobjective optimization algorithm (EMOA), namely, R2HCA-EMOA (R2-based hypervolume contribution approximation EMOA), is proposed for many-objective optimization. The core idea of the algorithm is to use an R2 indicator variant to approximate the hypervolume contribution. The basic framework of the proposed algorithm is the same as SMS-EMOA. In order to make the algorithm computationally efficient, a utility tensor structure is introduced for the calculation of the R2 indicator variant. Moreover, a normalization mechanism is incorporated into R2HCA-EMOA to enhance the performance of the algorithm. Through experimental studies, R2HCA-EMOA is compared with three hypervolume-based EMOAs and several other state-of-the-art EMOAs on 5-, 10-, and 15-objective DTLZ, WFG problems, and their minus versions. Our results show that R2HCA-EMOA is more efficient than the other hypervolume-based EMOAs, and is superior to all the compared state-of-the-art EMOAs. [ABSTRACT FROM AUTHOR]

The group Lasso is an extension of the Lasso for feature selection on (predefined) nonoverlapping groups of features. The nonoverlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. Our methods and theoretical results are then generalized to tackle the general overlapping group Lasso formulation based on the $(\ell_q)$ norm. We further extend our algorithm to solve a nonconvex overlapping group Lasso formulation based on the capped norm regularization, which reduces the estimation bias introduced by the convex penalty. We have performed empirical evaluations using both a synthetic and the breast cancer gene expression dataset, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms. Results also demonstrate the effectiveness of the nonconvex formulation for overlapping group Lasso. [ABSTRACT FROM AUTHOR]

Existing minimum-symbol-error-rate equalizers were derived based on the symbol-error-rate objective function. Due to the complexity of the objective function the derivation is not straightforward. In this paper we present a new approach to derive the minimum-symbol-error-rate adaptive equalizers. The problem is formulated as minimizing the norm between two subsequent parameter vectors under the constraint of symbol-error-rate minimization. The constrained optimization problem then is solved with the Lagrange multiplier method, which results in an adaptive algorithm with normalization. Simulation results show that the proposed algorithm outperforms the existing adaptive minimum-symbol-error-rate equalizer in convergence speed and steady-state performance. [ABSTRACT FROM AUTHOR]

Recently, the hybridization between evolutionary algorithms and other metaheuristics has shown very good performances in many kinds of multiobjective optimization problems (MOPs), and thus has attracted considerable attentions from both academic and industrial communities. In this paper, we propose a novel hybrid multiobjective evolutionary algorithm (HMOEA) for real-valued MOPs by incorporating the concepts of personal best and global best in particle swarm optimization and multiple crossover operators to update the population. One major feature of the HMOEA is that each solution in the population maintains a nondominated archive of personal best and the update of each solution is in fact the exploration of the region between a selected personal best and a selected global best from the external archive. Before the exploration, a selfadaptive selection mechanism is developed to determine an appropriate crossover operator from several candidates so as to improve the robustness of the HMOEA for different instances of MOPs. Besides the selection of global best from the external archive, the quality of the external archive is also considered in the HMOEA through a propagating mechanism. Computational study on the biobjective and three-objective benchmark problems shows that the HMOEA is competitive or superior to previous multiobjective algorithms in the literature. [ABSTRACT FROM AUTHOR]

Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the optimality of Gaussian signalling, an optimal transmit covariance matrix is known for some special cases only and the general case remains an open problem. An iterative custom-made algorithm to find a globally-optimal transmit covariance matrix in the general case is developed in this paper, with guaranteed convergence to a global optimum. While the original optimization problem is not convex and hence difficult to solve, its minimax reformulation can be solved via the convex optimization tools, which is exploited here. The proposed algorithm is based on the barrier method extended to deal with a minimax problem at hand. Its convergence to a global optimum is proved for the general case (degraded or not) and a bound for the optimality gap is given for each step of the barrier method. The performance of the algorithm is demonstrated via numerical examples. In particular, 20 to 40 Newton steps are already sufficient to solve the sufficient optimality conditions with very high precision (up to the machine precision level), even for large systems. Even fewer steps are required if the secrecy capacity is the only quantity of interest. The algorithm can be significantly simplified for the degraded channel case and can also be adopted to include the per-antenna power constraints (instead or in addition to the total power constraint). It also solves the dual problem of minimizing the total power subject to the secrecy rate constraint. [ABSTRACT FROM PUBLISHER]

This work investigates the design of linear precoders in cooperative multi-cell MIMO downlink coverage for finite-alphabet source signals. Traditional design of multi-cell MIMO downlink precoder relies on Gaussian input assumption, which may lead to performance loss when true data inputs consist of discrete non-Gaussian symbols. This work presents optimized precoders for finite-alphabet input by maximizing the sum rate under per-base station power constraints. Specifically, we propose two distributed algorithms: a finite-alphabet signal Gaussian interference gradient projection algorithm and a block diagonalization alternating optimization algorithm while supporting interference cancellation. Our numerical results demonstrate considerable performance gain in terms of approximate transmission data rate as well as decoded bit error rate over precoding schemes designed by using the non-realistic Gaussian input assumption. [ABSTRACT FROM PUBLISHER]

Proper patrol route planning increases the effectiveness of police patrolling and improves public security. In this paper, we present a new approach for real-time patrol route planning in dynamic environments. We first build a mathematical formulation for the patrol route planning problem under a single patrol unit setting and then propose a fast algorithm developed from the cross entropy (CE) method to meet the real-time computation requirements needed for practical applications. We next generalized the result to the patrol team case. Since the size of feasible team routes grows exponentially as the number of patrol units increases, we propose an approximate CE (ACE) algorithm that balances convergence time with optimality. Compared with the CE algorithm, the ACE algorithm can reduce the convergence time by as much as 48.9% with a less than 1% performance loss. [ABSTRACT FROM PUBLISHER]

The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross nonlinearities applied to the measurements. In this paper we introduce a new algorithm—restricted-step shrinkage (RSS)—to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for nonconvex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes a novel low-complexity reduced-rank linear interference suppression technique for direct-sequence code-division multiple access (DS-CDMA) systems based on the set-membership joint iterative optimization of receive parameters. Set-membership filtering is applied to the design and adaptation of the dimensionality-reducing projection matrix and the reduced-rank interference suppression filter. The specification of error bounds on the projection matrix and reduced-rank filter lead to the formation of two constraint sets from which estimates of the adaptive structures are selected at each time instant. The result is a low-complexity sparsely updating reduced-rank technique that does not require eigendecomposition or subspace tracking procedures. We develop least squares and stochastic gradient-type algorithms and a low-complexity rank-selection algorithm and also devise a time-varying adaptive error bound implementation. We present a stability and mean-square-error convergence analysis of the proposed algorithms along with a study of their complexity. The proposed schemes are applied to interference suppression in the uplink of a multiuser spread-spectrum DS-CDMA system, and the results confirm the validity of the analysis and the effective operation of the schemes. Performance comparisons are given against existing reduced-rank and full-rank algorithms, which act to highlight the improvements obtained by the proposed technique and algorithms. [ABSTRACT FROM PUBLISHER]

In evolutionary multiobjective optimization, the task of the optimizer is to obtain an accurate and useful approximation of the true Pareto-optimal front. Proximity to the front and diversity of solutions within the approximation set are important requirements. Most established multiobjective evolutionary algorithms (MOEAs) have mechanisms that address these requirements. However, in many-objective optimization, where the number of objectives is greater than 2 or 3, it has been found that these two requirements can conflict with one another, introducing problems such as dominance resistance and speciation. In this paper, two diversity management mechanisms are introduced to investigate their impact on overall solution convergence. They are introduced separately, and in combination, and tested on a set of test functions with an increasing number of objectives (6–20). It is found that the inclusion of one of the mechanisms improves the performance of a well-established MOEA in many-objective optimization problems, in terms of both convergence and diversity. The relevance of this for many-objective MOEAs is discussed. [ABSTRACT FROM AUTHOR]

This paper examines the application of the immune algorithm for the problem of optimal placement of fault indicators to minimize the total cost of customer service outage and investment cost of fault indicators. The reliability index of each service zone is derived to solve the expected energy not served due to fault contingency, and the customer interruption cost is then determined according to the customer type and power consumption within the service zone. To demonstrate the effectiveness of the proposed IA methodology and solve the optimal placement of fault indicators, a practical distribution feeder of Taiwan Power Company is selected for computer simulation to explore the cost benefit of fault indicator placement. [ABSTRACT FROM AUTHOR]

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based upon multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based upon an alternating direction optimization method. The standard regularization [or maximum a posteriori (MAP)] restoration criterion, which combines the Poisson log-likelihood with a (nonsmooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is nonquadratic and nonseparable, the regularizer is nonsmooth, and there is a nonnegativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for several types of regularizers: total-variation, frame-based analysis, and frame-based synthesis. We attack these problems with an instance of the alternating direction method of multipliers (ADMM), which belongs to the family of augmented Lagrangian algorithms. We study sufficient conditions for convergence and show that these are satisfied, either under total-variation or frame-based (analysis and synthesis) regularization. The resulting algorithms are shown to outperform alternative state-of-the-art methods, both in terms of speed and restoration accuracy. [ABSTRACT FROM AUTHOR]

To promote research on dynamic constrained multiobjective optimization, we first propose a group of generic test problems with challenging characteristics, including different modes of the true Pareto front (e.g., convexity–concavity and connectedness–disconnectedness) and the changing feasible region. Subsequently, motivated by the challenges presented by dynamism and constraints, we design a dynamic constrained multiobjective optimization algorithm with a nondominated solution selection operator, a mating selection strategy, a population selection operator, a change detection method, and a change response strategy. The designed nondominated solution selection operator can obtain a nondominated population with diversity when the environment changes. The mating selection strategy and population selection operator can adaptively handle infeasible solutions. If a change is detected, the proposed change response strategy reuses some portion of the old solutions in combination with randomly generated solutions to reinitialize the population, and a steady-state update method is designed to improve the retained previous solutions. The experimental results show that the proposed test problems can be used to clearly distinguish the performance of algorithms, and that the proposed algorithm is very competitive for solving dynamic constrained multiobjective optimization problems in comparison with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This article proposes a modified grey wolf optimization (MGWO) which has improved rate of convergence and avoids local optima stagnation. This is achieved by improving the exploration–exploitation balance in conventional grey wolf optimization (GWO). Moreover, the use of weighted-distance strategy allows quick identification of the global optima in the proposed MGWO. This optimization is then applied for the control of a three-phase, 11-level hybrid cascaded multilevel inverter (HC-MLI). Selective harmonic elimination pulsewidth modulation technique is implemented through MGWO which generates optimal switching angles for the HC-MLI so as to eliminate lower order harmonics such as 5th, 7th, 11th, and 13th from the output voltage. In MGWO optimized HC-MLI, balancing of capacitor voltage is made possible at higher modulation index by making use of the available redundant switching states. The performance of the proposed work is validated through simulation and experimentation on a 1.5 kW prototype. The results obtained through simulation show that the MGWO algorithm is more efficient and accurate than other reported algorithms such as GWO, genetic algorithm, and particle swarm optimization in terms of performance, harmonic reduction, and convergence rate. [ABSTRACT FROM AUTHOR]

We study the properties of the Frank–Wolfe algorithm to solve the m-Exact-Sparse reconstruction problem, where a signal $y$ must be expressed as a sparse linear combination of a predefined set of atoms, called dictionary. We prove that when the signal is sparse enough with respect to the coherence of the dictionary, then the iterative process implemented by the Frank–Wolfe algorithm only recruits atoms from the support of the signal, is the smallest set of atoms from the dictionary that allows for a perfect reconstruction of $y$. We also prove that under this same condition, there exists an iteration beyond which the algorithm converges exponentially. [ABSTRACT FROM AUTHOR]

We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for the objective function, QDGD achieves a vanishing mean solution error under customary conditions for quantizers. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the numerical results. [ABSTRACT FROM AUTHOR]

Langasite (LGS) is a promising material for SAW applications at high temperature. However, the temperature coefficients of LGS material constants are not accurate enough to perform reliable simulations, and therefore to make good use of available design tools, above 300°C. In the first part of the paper, we describe a new possible way to derive these coefficients in a wider temperature range. The method is based on Simulated Annealing, a well-known optimization algorithm. The algorithm converges toward a set of optimized temperature coefficients of the stiffness constants which are used to perform accurate simulations up to at least 800°C. In the second part, a deeper analysis of the algorithm outputs demonstrates some of its strengths but also some of its main limitations. Possible solutions are described to predict and then improve the accuracy of the optimized coefficient values. In particular, one solution making use of additional BAW target curves is tested. A promising solution to extend the optimization to the temperature coefficients of piezoelectric constants is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid algorithm based on artificial bee colony (ABC) algorithm and differential evolution (DE) algorithm called ABC-DE is proposed to inherit their advantages and overcome their drawbacks. In ABC-DE algorithm, employed bees employ the mutation and crossover strategies of DE to enforce their exploration ability while onlooker bees keep their original updating strategy to retain the exploitation ability. Classical test functions have been provided to testify the ABC-DE algorithm. Furthermore, ABC-DE is applied to different types of time-modulated arrays (TMAs) pattern synthesis problems, including the syntheses of low equal-ripple sidelobe level (SLL) pattern, deep null level pattern, multiple-beams patterns and satellite footprint pattern. Experiment results reveal that ABC-DE has a promising performance in the convergence rate and the exploration ability when compared with other improved evolutionary algorithms, which indicates that the proposed algorithm can be an effective approach for TMAs synthesis problems. [ABSTRACT FROM PUBLISHER]

Nonnegative matrix factorization (NMF), which can lead to nonsubtractive parts-based representation, has been demonstrated to be effective for dimensionality reduction of hyperspectral imagery (HSI). However, existing NMF methods applied to HSI use only a single spectral feature and do not take into consideration spatial information, such as texture or morphological features, while it has been widely acknowledged that exploiting multiple features can improve performance. Consequently, a variant of orthogonal NMF, which can not only achieve a nonnegative factorization but also exploit the complementary information that arises among heterogeneous features, is proposed for hyperspectral dimensionality reduction. The proposed method, which couples orthogonal NMF with a previous multiple-features-combining algorithm, yields a discriminative low-dimensional feature representation that matches the intuition that parts should sum to produce a whole. An efficient multiplicative updating procedure is derived, and its local convergence is guaranteed theoretically. Experimental results on two hyperspectral data sets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

While the convergence rate of any optimization algorithm can be increased by selecting a larger stepsize parameter, this also magnifies the parameter estimation variance. This research introduces an analytical methodology for comparing the estimation variance when optimizing Soft-Max models using two different loss functions (Cross Entropy and Mean Square Error). This method can be used to adjust the stepsize parameters of algorithms with different loss functions so that they attain equal estimation variances after converging; this provides a fair starting point for a comparison of the convergence rates of the algorithms. The polyphonic pitch detection problem is used as a case study, and the performance of the models trained by the cross entropy loss function and the mean square error loss function are compared with each other and with a k-nearest neighbor classifier. [ABSTRACT FROM PUBLISHER]

Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets. [ABSTRACT FROM AUTHOR]

This paper reports on enhancing the thermal performance of multiple-chip modules (MCMs) that contain a number of chips under natural convection by optimizing the chip placement layout. To attain this goal, an innovative hybrid optimization approach (HOA) incorporating a genetic algorithm (GA) into an algorithm based on a response surface method (RSM) is introduced for improving the performance of both these algorithms. The GA in the proposed HOA is responsible for not only evolving the population toward better fitness value but also, based on the newly evolved populations at each GA generation, for continuously updating the RS mathematical model for better approximation of the chip junction temperature. The sum of the mathematical expressions representing the total system temperature defines the objective of the optimization problems. For each GA generation, a constrained quadratic optimization subproblem is formed, based on the newly updated approximate RS mathematical model as the objective function along with the specified constraints. The solution of the optimization subproblem is sought through a mathematical programming model. As the genetic RS optimization progresses, a sequence of approximate solutions associated with the continuously updated RS mathematical models is constructed. The iterative process continues until convergence of the approximate solutions is attained. To demonstrate the effectiveness of the developed algorithm, several thermal design problems associated with two types of MCMs with equal/unequal power are performed. The obtained results are compared with those derived using two conventional approaches—the GA-based and the RSM-based optimization techniques. Results show that the developed algorithm can provide good optimal solutions with much less computational effort, and the larger the scale of the design problems, the more significant the improvement in the computation cost. [ABSTRACT FROM PUBLISHER]

The area of sparse approximation of signals is drawing tremendous attention in recent years. Typically, sparse solutions of underdetermined linear systems of equations are required. Such solutions are often achieved by minimizing an l1 penalized least squares functional. Various iterative-shrinkage algorithms have recently been developed and are quite effective for handling these problems, often surpassing traditional optimization techniques. In this paper, we suggest a new iterative multilevel approach that reduces the computational cost of existing solvers for these inverse problems. Our method takes advantage of the typically sparse representation of the signal, and at each iteration it adaptively creates and processes a hierarchy of lower-dimensional problems employing well-known iterated shrinkage methods. Analytical observations suggest, and numerical results confirm, that this new approach may significantly enhance the performance of existing iterative shrinkage algorithms in cases where the matrix is given explicitly. [ABSTRACT FROM PUBLISHER]

Autonomous agents deployed or moving on land for the purpose of carrying out coordinated tasks need to have good knowledge of their absolute or relative position. For large formations, it is often impractical to equip each agent with an absolute sensor such as GPS, whereas relative range sensors measuring interagent distances are cheap and commonly available. In this setting, this paper considers the problem of autonomous distributed estimation of the position of each agent in a networked formation using noisy measurements of interagent distances. The underlying geometrical problem has been studied quite extensively in various fields, ranging from molecular biology to robotics, and it is known to lead to a hard nonconvex optimization problem. Centralized algorithms do exist that work reasonably well in finding local or global minimizers for this problem (e.g., semidefinite programming relaxations). Here, we explore a fully decentralized approach for localization from range measurements, and we propose a computational scheme based on a distributed gradient algorithm with Barzilai–Borwein stepsizes. The advantage of this distributed approach is that each agent may autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station and without needing complete knowledge of the network structure. [ABSTRACT FROM PUBLISHER]

Differential evolution (DE) is one of the most powerful stochastic real parameter optimizers of current interest. In this paper, we propose a new mutation strategy, a fitness-induced parent selection scheme for the binomial crossover of DE, and a simple but effective scheme of adapting two of its most important control parameters with an objective of achieving improved performance. The new mutation operator, which we call DE/current-to-gr_best/1, is a variant of the classical DE/current-to-best/1 scheme. It uses the best of a group (whose size is q\% of the population size) of randomly selected solutions from current generation to perturb the parent (target) vector, unlike DE/current-to-best/1 that always picks the best vector of the entire population to perturb the target vector. In our modified framework of recombination, a biased parent selection scheme has been incorporated by letting each mutant undergo the usual binomial crossover with one of the p top-ranked individuals from the current population and not with the target vector with the same index as used in all variants of DE. A DE variant obtained by integrating the proposed mutation, crossover, and parameter adaptation strategies with the classical DE framework (developed in 1995) is compared with two classical and four state-of-the-art adaptive DE variants over 25 standard numerical benchmarks taken from the IEEE Congress on Evolutionary Computation 2005 competition and special session on real parameter optimization. Our comparative study indicates that the proposed schemes improve the performance of DE by a large magnitude such that it becomes capable of enjoying statistical superiority over the state-of-the-art DE variants for a wide variety of test problems. Finally, we experimentally demonstrate that, if one or more of our proposed strategies are integrated with existing powerful DE variants such as jDE and JADE, their performances can also be enhanced. [ABSTRACT FROM AUTHOR]

Although there are a variety of approaches to solve multiobjective optimization problems, few of them makes systematic use of the neighborhood relationship between the candidate solutions observed during the search process to improve the final results. In this paper, a new evolutionary algorithm, referred to as the neighborhood knowledge-based evolutionary algorithm (NKEA), is proposed to solve the multiobjective optimization problem. NKEA not only takes into account the advantages of NSGA-II, and JGGA, such as the fast nondominated sorting algorithm and horizontal transmission of information in a candidate solution, but also exploits systematically the neighborhood knowledge acquired during the search process. Specifically, NKEA consists of three major stages: the direction learning stage, the mutual adaptation stage, and the self adaptation stage. NKEA not only uses the fast nondominated sorting algorithm to find the Pareto optimal solutions, but also adopts the elitist strategy to maintain the best individuals for the next generation based on this strategy. Two adaptive control functions in the mutual adaptation stage and the self adaptation stage are designed to adjust the respective contributions of coarse local search and fine local search, which allows NKEA to perform a more thorough local search. Finally, we introduce a new notion, known as the measure space, which integrates multiple measures, such as the convergence metric and the diversity metric, to evaluate the performance of the algorithm. The results of our experiments show that NKEA not only achieves good performance in a large number of multiobjective optimization problems, but also outperforms most of the state-of-the-art approaches in these problems. [ABSTRACT FROM AUTHOR]

The alternating direction multipliers method (ADMM) has been recently proposed as a practical and efficient algorithm for distributed computing. We discuss its applicability to the average consensus problem in this paper. By carefully relaxing ADMM augmentation coefficients we are able to analytically investigate its properties, and to propose simple and strict analytical bounds. These provide a clear indication on how to choose system parameters for optimized performance. We prove both analytically and via simulations that the proposed approach exhibits convergence speed between the best in the literature (classical and optimized solutions), while providing the most powerful resilience to noise. [ABSTRACT FROM AUTHOR]

In this paper, we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of differential evolution (DE) is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points toward which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard DE on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima. [ABSTRACT FROM AUTHOR]

Recent applications of model-based iterative reconstruction (MBIR) algorithms to multislice helical CT reconstructions have shown that MBIR can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of MBIR in practical applications. Among the various iterative methods that have been studied for MBIR, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 1-D optimization algorithm that uses a quadratic substitute function to upper bound the local 1-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. We examine the performance of the proposed algorithm using several clinical data sets of various anatomy. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries. [ABSTRACT FROM AUTHOR]

A novel optimization framework for resource allocation in wireless networks and radar systems is proposed, which merges the methods of maximum block improvement (MBI) and of sequential optimization. A detailed convergence proof is provided, showing that the proposed algorithm is able to monotonically increase the objective value while ensuring that every limit point of the generated variable sequence fulfills the problem first-order optimality conditions under very mild hypothesis. These results extend available convergence results on MBI and sequential optimization, significantly widening the range of applications that can be handled by the proposed framework compared to available approaches. This point is illustrated in detail presenting relevant applications from both the cellular and radar context, which fall under the umbrella of the developed optimization method. [ABSTRACT FROM AUTHOR]

We consider derivative-free algorithms for stochastic and nonstochastic convex optimization problems that use only function values rather than gradients. Focusing on nonasymptotic bounds on convergence rates, we show that if pairs of function values are available, algorithms for d -dimensional optimization that use gradient estimates based on random perturbations suffer a factor of at most \sqrt {d} in convergence rate over traditional stochastic gradient methods. We establish such results for both smooth and nonsmooth cases, sharpening previous analyses that suggested a worse dimension dependence, and extend our results to the case of multiple ( {m}\ge 2$ ) evaluations. We complement our algorithmic development with information-theoretic lower bounds on the minimax convergence rate of such problems, establishing the sharpness of our achievable results up to constant (sometimes logarithmic) factors. [ABSTRACT FROM AUTHOR]

The multiplicative update (MU) algorithm has been extensively used to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizers. However, theoretical convergence guarantees have only been derived for a few special divergences without regularization. In this work, we provide a conceptually simple, self-contained, and unified proof for the convergence of the MU algorithm applied on NMF with a wide range of divergences and regularizers. Our main result shows the sequence of iterates (i.e., pairs of basis and coefficient matrices) produced by the MU algorithm converges to the set of stationary points of the nonconvex NMF optimization problem. Our proof strategy has the potential to open up new avenues for analyzing similar problems in machine learning and signal processing. [ABSTRACT FROM PUBLISHER]

We propose a self-contained, flat, quadratic global placer that is simpler than existing placers and easier to integrate into timing-closure flows. It maintains lower-bound and upper-bound placements that converge to a final solution. The upper-bound placement is produced by a novel look-ahead legalization algorithm. Our placer SimPL outperforms mPL6, FastPlace3, NTUPlace3, APlace2, and Capo simultaneously in runtime and solution quality, running 7.10 times faster than mPL6 (when using a single thread) and reducing wirelength by 3% on the ISPD 2005 benchmark suite. More significant improvements are achieved on larger benchmarks. The new algorithm is amenable to parallelism, and we report empirical studies with SSE2 instructions and up to eight parallel threads. [ABSTRACT FROM PUBLISHER]

We investigate weighted sum-rate maximization and rate-balancing problems for spectrum-sharing multiple-input–multiple-output orthogonal frequency-division-multiplexing (MIMO OFDM) based broadcast channels. The problem is solved by converting the MIMO OFDM channel into a block-diagonal form and applying the principle of multiple-access channel–broadcast channel (MAC-BC) duality. The algorithm in its dual form is solved using subgradient methods. The simulation results demonstrate the convergence of the algorithms. [ABSTRACT FROM PUBLISHER]

A globally convergent optimization algorithm for solving large nonlinear optimal power flow (OPF) problems is presented. As power systems become heavily loaded, there is an increasing need for globally convergent OPF algorithms. By global convergence, one means the optimization algorithm being able to converge to an OPF solution, if at least one exists, for any choice of initial point. The globally convergent OPF presented is based on an infinity-norm trust region approach, using interior-point methods to solve the trust region subproblems. The performance of the proposed trust region interior-point OPF algorithm, when applied to the IEEE 30-, 57-, 118-, and 300-bus systems, and to an actual 1211-bus system, is compared with that of two widely used nonlinear interior-point methods, namely, a pure primal-dual and its predictor-corrector variant. [ABSTRACT FROM PUBLISHER]

Modifications in the velocity calculation of the particle swarm optimization (PSO) algorithm are proposed. The suggested modifications aim to arrive at a faster, more straightforward and still robust search procedure as compared to the conventional method. Two main factors, i.e., personal best influence and initial velocity values, are evaluated. It is shown that in problems with wide-range parameters, the effect of personal best locations is intrinsically encompassed by that of global best locations, thereby allowing for further simplification of the PSO algorithm by eliminating the factor which accounts for the personal best solutions in the velocity calculation. This simplification expedites the convergence procedure in real PSO. It is also shown that the initial velocity values can be modified to enhance the performance in terms of achieving better solution when compared with the existing algorithms, particularly in binary PSO. In order to validate the viability of the proposed procedure, the performances of the real-number and binary PSO algorithms with different velocity calculations are assessed in 1000-run sets, and pros and cons are studied. In particular, the performance of the proposed algorithm, when used to design software defined thinned array antennas, is shown to be superior to those of the existing algorithms. [ABSTRACT FROM AUTHOR]

We introduce the decentralized Broyden–Fletcher–Goldfarb–Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. Decentralized quasi-Newton methods are of interest in problems that are not well conditioned, making first-order decentralized methods ineffective, and in which second-order information is not readily available, making second-order decentralized methods impossible. D-BFGS is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition. We additionally provide a formulation of the algorithm in asynchronous settings. Convergence of D-BFGS is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to existing methods are shown numerically. [ABSTRACT FROM PUBLISHER]