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In the field of reinforcement learning, we propose a Correct Proximal Policy Optimization (CPPO) algorithm based on the modified penalty factor β and relative entropy in order to solve the robustness and stationarity of traditional algorithms. Firstly, In the process of reinforcement learning, this paper establishes a strategy evaluation mechanism through the policy distribution function. Secondly, the state space function is quantified by introducing entropy, whereby the approximation policy is used to approximate the real policy distribution, and the kernel function estimation and calculation of relative entropy is used to fit the reward function based on complex problem. Finally, through the comparative analysis on the classic test cases, we demonstrated that our proposed algorithm is effective, has a faster convergence speed and better performance than the traditional PPO algorithm, and the measure of the relative entropy can show the differences. In addition, it can more efficiently use the information of complex environment to learn policies. At the same time, not only can our paper explain the rationality of the policy distribution theory, the proposed framework can also balance between iteration steps, computational complexity and convergence speed, and we also introduced an effective measure of performance using the relative entropy concept. [ABSTRACT FROM AUTHOR]

Total variation (TV) is a one of the most popular regularizers for stabilizing the solution of ill-posed inverse problems. This paper proposes a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functionals. Unlike traditional methods that require nested iterations for computing the proximal step of TV, our algorithm approximates the latter with several simple proximals that have closed form solutions. We theoretically prove that the proposed parallel proximal method achieves the TV solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal-gradient methods. The results in this paper have the potential to enhance the applicability of TV for solving very large-scale imaging inverse problems. [ABSTRACT FROM AUTHOR]

JPEG compression based on the discrete cosine transform is a key building block in low-power multimedia applications. Approximate computation techniques are used to exploit the error tolerance of JPEG. An image-dependent framework is proposed in this paper to design optimized approximate hardware with variable approximate bit-widths for a user-specified error budget. The proposed method can dynamically adjust the extent of approximation in the system depending on the pixel values of the input image, thus leveraging the inherent sparsity of certain images. This novel technique not only improves the power-delay product by $3.4{\times }$ over the base case, i.e., where the JPEG hardware is accurate but also significantly outperforms the image-independent approximation case, which is solely based on the error tolerance of the JPEG algorithm. [ABSTRACT FROM AUTHOR]

Computation of Loss of Load Probability (LOLP) is a challenge in Generation Expansion Planning (GEP) problem. This paper presents a dynamic GEP model considering LOLP as a reliability criterion. The objective function of the proposed dynamic GEP model includes the discounted total costs of investment cost, operation cost, and maintenance cost. The proposed LOLP constrained GEP problem is formulated as a mixed integer nonlinear programming (MINLP) problem. The MINLP formulation of GEP problem is then converted to a mixed integer linear programming (MIP) problem by applying several approximations to LOLP constraint. The utilized approximations are divided into two clusters for low and high order outages. A test case containing 12 types of installed and 5 types of candidate plants with a 14-year planning horizon is used to validate the efficiency of the proposed dynamic GEP problem. The developed MIP-based GEP model is solved using CPLEX solver and the obtained results are compared with the conventional LOLP-constrained GEP model. [ABSTRACT FROM AUTHOR]

Recently, by taking advantage of evolutionary multiobjective optimization techniques in diversity preservation, the means of multiobjectivization has attracted increasing interest in the studies of multimodal optimization (MMO). While most existing work of multiobjectivization aims to find all optimal solutions simultaneously, in this paper, we propose to approximate multimodal fitness landscapes via multiobjectivization, thus providing an estimation of potential optimal areas. To begin with, an MMO problem is transformed into a multiobjective optimization problem (MOP) by adding an adaptive diversity indicator as the second optimization objective, and an approximate fitness landscape is obtained via optimization of the transformed MOP using a multiobjective evolutionary algorithm. Then, on the basis of the approximate fitness landscape, an adaptive peak detection method is proposed to find peaks where optimal solutions may exist. Finally, local search is performed inside the detected peaks on the approximate fitness landscape. To assess the performance of the proposed algorithm, extensive experiments are conducted on 20 multimodal test functions, in comparison with three state-of-the-art algorithms for MMO. Experimental results demonstrate that the proposed algorithm not only shows promising performance in benchmark comparisons, but also has good potential in assisting preference-based decision-making in MMO. [ABSTRACT FROM AUTHOR]

Mobile edge computing is a new computing paradigm, which pushes cloud computing capabilities away from the centralized cloud to the network edge. However, with the sinking of computing capabilities, the new challenge incurred by user mobility arises: since end users typically move erratically, the services should be dynamically migrated among multiple edges to maintain the service performance, i.e., user-perceived latency. Tackling this problem is non-trivial since frequent service migration would greatly increase the operational cost. To address this challenge in terms of the performance-cost tradeoff, in this paper, we study the mobile edge service performance optimization problem under long-term cost budget constraint. To address user mobility which is typically unpredictable, we apply Lyapunov optimization to decompose the long-term optimization problem into a series of real-time optimization problems which do not requirea prioriknowledge such as user mobility. As the decomposed problem is NP-hard, we first design an approximation algorithm based on Markov approximation to seek a near-optimal solution. To make our solution scalable and amenable to future fifth-generation application scenario with large-scale user devices, we further propose a distributed approximation scheme with greatly reduced time complexity, based on the technique of the best response update. Rigorous theoretical analysis and extensive evaluations demonstrate the efficacy of the proposed centralized and distributed schemes. [ABSTRACT FROM AUTHOR]

The increasing popularity of location-based applications creates new opportunities for users to travel together. In this paper, we study a novel spatio-social optimization problem, i.e., Optimal Group Route, for multi-user itinerary planning. With our problem formulation, users can individually specify sources and destinations, preferences on the Point-of-interest (POI) categories, as well as the distance constraints. The goal is to find a itinerary that can be traversed by all the users while maximizing the group’s preference of POI categories in the itinerary. Our work advances existing group trip planning studies by maximizing the group’s social experience. To this end, individual preferences of POI categories are aggregated by considering the agreement and disagreement among group members. Furthermore, planning a multi-user itinerary on large road networks is computationally challenging. We propose two efficient greedy algorithms with bounded approximation ratio, one exact solution which computes the optimal itinerary by exploring a limited number of paths in the road network, and a scaled approximation algorithm to speed up the dynamic programming employed by the exact solution. We conduct extensive empirical evaluations on two real-world road network/POI datasets and our results confirm the effectiveness and efficiency of our solutions. [ABSTRACT FROM AUTHOR]

Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed in the proposed OPF formulation combines an exact ac power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on the IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate ac model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties. [ABSTRACT FROM AUTHOR]

The magnetic nanoparticles (MNPs) in ac alternating magnetic fields will produce a sufficient amount of heats owing to the Néel and Brown relaxations. Magnetic fluid hyperthermia (MFH), based on this mechanism, is a new promising approach for tumor treatments. The temperature field distribution in the cancer and its neighbor regions have a significant effect on the therapeutic effect of MFH. As a result, it is generally required to maintain the temperature in the cancer in the range of 42 °C–90 °C while guaranteeing a sharp temperature gradient in the neighbor regions of the cancer and healthy tissues. This paper provides an automated shape and MNP volume fraction solid design optimization methodology with finite element analysis, coupled field analysis, and an enhanced multiobjective quantum particle swarm optimization, to realize the aforementioned two ultimate goals. Moreover, an optimal radial basis function approximation technique is proposed to approximate the distribution of the optimized nanoparticles volume fraction solids to give a smooth and implementable nanoparticles distribution. [ABSTRACT FROM PUBLISHER]

Singleton interval type-2 fuzzy logic systems (FLSs) have been widely applied in several real-world applications, where it was shown that the singleton interval type-2 FLSs outperform their singleton type-1 counterparts in applications with high uncertainty levels. However, one of the main criticisms of singleton interval type-2 FLSs is the fact that they outperform singleton type-1 FLSs solely based on their use of extra degrees of freedom (extra parameters) and that type-1 FLSs with a sufficiently large number of parameters may provide the same performance as interval type-2 FLSs. In addition, most works on type-2 FLSs only compare their results with singleton type-1 FLSs but fail to consider nonsingleton type-1 systems. In this paper, we aim to directly address and investigate this criticism. In order to do so, we will perform a comparative study between optimized singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs under the presence of noise. We will also present a multiobjective evolutionary algorithm (MOEA) for the optimization of singleton type-1, nonsingleton type-1, and singleton interval type-2 fuzzy systems for function approximation problems. The MOEA will aim to satisfy two objectives to maximize the accuracy of the FLS and minimize the number of rules in the FLS, thus improving its interpretability. Furthermore, we will present a methodology to obtain “optimal” consequents for the FLSs. Hence, this paper has two main contributions: First, it provides a common methodology to learn the three types of FLSs (i.e., singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs) from data samples. The second contribution is the creation of a common framework for the comparison of type-1 and type-2 FLSs that allows us to address the aforementioned criticism. We provide details of a series of experiments and include statistical analysis showing that the type-2 FLS is able to handle higher levels of noise than its nonsingleton and singleton type-1 counterparts. [ABSTRACT FROM AUTHOR]

In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [ABSTRACT FROM AUTHOR]

Worldwide interoperability for microwave access (WiMAX) is a promising technology for last-mile Internet access, particularly in the areas where wired infrastructures are not available. In a WiMAX network, call admission control (CAC) is deployed to effectively control different traffic loads and prevent the network from being overloaded. In this paper, we propose a framework of a 2-D CAC to accommodate various features of WiMAX networks. Specifically, we decompose the 2-D uplink and downlink WiMAX CAC problem into two independent 1-D CAC problems and formulate the 1-D CAC optimization, in which the demands of service providers and subscribers are jointly taken into account. To solve the optimization problem, we develop a utility- and fairness-constrained optimal revenue policy, as well as its corresponding approximation algorithm. Simulation results are presented to demonstrate the effectiveness of the proposed WiMAX CAC approach. [ABSTRACT FROM AUTHOR]

In this paper we utilize a generalized weakly contractive mapping to establish some best proximity point results which are global optimization results for finding the minimum distances between two sets. Amongst many approaches to this problem, we adopt the approach where the problem is treated as that of finding global optimal approximate solution of the fixed point equation for the generalized weak contraction mapping. We use three control functions to define such mappings. The results are obtained in metric spaces with a partial ordering defined therein. There is a blending of analytic and order theoretic approaches in the proofs. The uniqueness is obtained by imposing some order theoretic conditions additionally. There are several corollaries. An illustration of the main theorem through an example is given which also shows that the corollaries are properly contained in the main theorem. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to propose a local approximation-based search method to optimize any function. For this purpose, an approximation method is combined with an estimation filter, and a new local search mechanism is constituted. Design/methodology/approach – Radial basis function (RBF) network is very efficient interpolation method especially if we have sufficient reference data. Here, reference data refer to the exact value of the objective function at some points. Using this capability of RBFs, we can approximately inspect the vicinity each point in search space. Meanwhile, in order to obtain a smooth, rapid and better trajectory toward the global optimum, the alpha-beta filter can be integrated to this mechanism. For better description and visualization, the operations are defined in two-dimensional search space; but the outlined procedure can be extended to higher dimensions without loss of generality. Findings – When compared with the previous studies using conventional heuristic methods, approximation-based curvilinear local search mechanism provide better minimization performance for almost all benchmark functions. Moreover computational cost of this method too less than heuristics. The number of iteration down to at least 1/10 compared to conventional heuristic algorithm. Additionally, the solution accuracy is very improved for majority of the test cases. Originality/value – This paper proposes a new search approach to solve optimization problems with less cost. For this purpose, a new local curvilinear search mechanism is built using RBF-based approximation technique and alpha-beta estimation filter. [ABSTRACT FROM AUTHOR]

Over the past decade, several approximate adders have been proposed in the literature based on the design concept of Equal Segment Adder (ESA). In this approach, an $N$ -bit adder is segmented into several smaller and independent equally sized accurate sub-adders. An $N$ -bit ESA has two primary design parameters: (i) Segment size ($k$ ), which represents the maximum length of carry propagation; and (ii) Overlapping bits ($l$ ), which represents the minimum number of bits used in carry prediction, where $1 \leq k < N$ and $0 \leq l < k$ . Based on the combinations of $k$ and $l$ , an $N$ -bit ESA has $N(N-1)/2$ possible configurations. In this paper, we analyse ESAs and propose analytical models to estimate accuracy, delay, power and area of ESAs. The key features of the proposed analytical models are that: (i) They are generalized, i.e., work for all possible configurations of an $N$ -bit ESA; and (ii) They are superior (i.e., estimate more accurately) or at par to the existing analytical models. From the proposed analytical models, we observe that in an $N$ -bit ESA, there exist multiple (more than one) configurations which exhibit similar accuracy. However, these configurations exhibit different delay, power and area. Therefore, for a given accuracy, the configurations which provide minimal delay, power and/or area need to be known apriori for efficient, intelligent and goal oriented implementations of ESAs. In this regard, we present an optimization framework that exploits the proposed analytical models to find the optimal configurations of an $N$ -bit ESA. Further, we know that accuracy of an ESA does not depend on the adder architecture used to implement it, however, its delay, power and area depend significantly. Consequently, the optimal configurations vary with adder architectures used to implement the ESA. In order to cover a wide range of adders, we consider three types of adder architecture in our analysis: (i) Architectures having smaller area ($O(N)$ ); (ii) Architectures having smaller delay ($O(log_2N)$ ); and (iii) Architectures having in-between delay ($O(N/4)$ ) and area ($O(2N)$ ). [ABSTRACT FROM AUTHOR]

Despite the surrogate-based two-level algorithms that have been proposed for accelerating the optimization procedures, it may be still expensive for large problems. Therefore, this paper proposes the exploration of the approximation characteristics of the wavelet functions to define a coarse subspace for this kind of approach with relatively few float point operations. The wavelet transform is used to create the coarse model in a two-level genetic algorithm (GA), which is applied to a set of benchmark test problems. Although the coarse model is simpler and less accurate than the fine model, it behaves similarly to this last one and the original function. Moreover, the approach prevented the convergence to local minima whenever the GA presented such behavior and it is faster than the use of principal components analysis. [ABSTRACT FROM PUBLISHER]

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover optical properties, denoted as absorption and the scattering coefficient of the media, through source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but it lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two of which encode the information of the two coefficients, respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit. [ABSTRACT FROM AUTHOR]

Shortest path query is one of the most fundamental and classic problems in graph analytics, which returns the complete shortest path between any two vertices. However, in many real-life scenarios, only critical vertices on the shortest path are desirable and it is unnecessary to search for the complete path. This paper investigates the shortest path sketch by defining a top- $k$ critical vertices ($k$ CV) query on the shortest path. Given a source vertex $s$ and target vertex $t$ in a graph, $k$ CV query can return the top- $k$ significant vertices on the shortest path $SP(s,t)$ . The significance of the vertices can be predefined. The key strategy for seeking the sketch is to apply off-line preprocessed distance oracle to accelerate on-line real-time queries. This allows us to omit unnecessary vertices and obtain the most representative sketch of the shortest path directly. We further explore a series of methods and optimizations to answer $k$ CV query on both centralized and distributed platforms, using exact and approximate approaches, respectively. We evaluate our methods in terms of time, space complexity and approximation quality. Experiments on large-scale real-world networks validate that our algorithms are of high efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Multithreshold Entropy Linear Classifier (MELC) is a density based model which searches for a linear projection maximizing the Cauchy-Schwarz Divergence of dataset kernel density estimation. Despite its good empirical results, one of its drawbacks is the optimization speed. In this paper we analyze how one can speed it up through solving an approximate problem. We analyze two methods, both similar to the approximate solutions of the Kernel Density Estimation querying and provide adaptive schemes for selecting a crucial parameters based on user-specified acceptable error. Furthermore we show how one can exploit well known conjugate gradients and L-BFGS optimizers despite the fact that the original optimization problem should be solved on the sphere. All above methods and modifications are tested on 10 real life datasets from UCI repository to confirm their practical usability. [ABSTRACT FROM AUTHOR]

This paper presents a method to analyze thin-walled beams with quadrilateral cross sections reinforced with diaphragms using a one-dimensional higher-order beam theory. The effect of a diaphragm is reflected focusing on the increase of static stiffness. The deformations on the beam-interfacing boundary of a thin diaphragm are described by using deformation modes of the beam cross section while the deformations inside the diaphragm are approximated in the form of complete cubic polynomials. By using the principle of minimum potential energy, its stiffness that significantly affects distortional deformation of a thin-walled beam can be considered in the one-dimensional beam analysis. It is shown that the accuracy of the resulting one-dimensional analysis is comparable with that by a shell element based analysis. As a means to demonstrate the usefulness of the present approach for design, position optimization problems of diaphragms for stiffness reinforcement of an automotive side frame are solved. [ABSTRACT FROM AUTHOR]

This paper describes two approaches to optimization of the key design parameters, the support region threshold and the number of magnitude representation levels, of product polar companded quantizer (PPCQ) for Gaussian source of unit variance. The first approach is based on the exact performance analysis of PPCQ and on distortion optimization with respect to the key design parameters. Due to the optimization problem complexity we encountered with the first approach, some suitable approximations are introduced with the second one. As a result, much simpler asymptotic closed-form formula for distortion of PPCQ is derived as a function of the support region threshold. Although with this approach the closed-form formula for the support region threshold cannot be derived, the results of this approach indicate the useful support region threshold form. By combining the results of both approaches we propose, the worthy closed-form formulas for the support region threshold and signal to quantization noise ratio of a nearly optimal PPCQ are provided. Moreover, from the results of both analyses the lower and upper bound expressions for the number of magnitude representation levels are provided. The analysis presented in the paper is useful for designing PPCQ and is of great theoretical and practical importance. [ABSTRACT FROM AUTHOR]

In this work, we study a geometric structure called disjoint convex shell or simply DC-shell. A DC-shell of a polyhedron is a set of pairwise interior disjoint convex objects that collectively approximate the given polyhedron. Preventing convex objects from overlapping enables faster and robust collision response and more realistic fracturing simulation. Without the disjointness constraint, a physical realization of the approximation becomes impossible. This paper investigates multiple approaches that construct DC-shells from shapes that are either composed of overlapping components or segmented into parts. We show theoretically that, even under this rather simplified setting, constructing DC-shell is difficult. To demonstrate the power of DC-shell, we studied how DC-shell can be used in mesh unfolding, an important computational method in manufacturing 3D shape from the 2D material. Approximating a given polyhedron model by DC-shells provides two major benefits. First, they are much easier to unfold using the existing unfolding methods. Second, they can be folded easily by both human folder or self-folding machines. Consequently, DC-shell makes paper craft creation and design more accessible to younger children and provides chances to enrich their education experiences. [ABSTRACT FROM AUTHOR]

Computing the centroid and performing type-reduction for type-2 fuzzy sets and systems are operations that must be taken into consideration. Karnik–Mendel (KM) algorithms are the standard ways to do these operations; however, because these algorithms are iterative, much research has been conducted during the past decade about centroid and type-reduction computations. This tutorial paper focuses on the research that has been conducted to 1) improve the KM algorithms; 2) understand the KM algorithms, leading to further improved algorithms; 3) eliminate the need for KM algorithms; 4) use the KM algorithms to solve other (nonfuzzy logic system) problems; and 5) use (or not use) KM algorithms for general type-2 fuzzy sets and fuzzy logic systems. [ABSTRACT FROM AUTHOR]

Wireless sensor networks are constrained by limited battery energy. Thus, finite network lifetime is widely regarded as a fundamental performance bottleneck. Recent breakthrough in the area of wireless power transfer offers the potential of removing this performance bottleneck, i.e., allowing a sensor network to remain operational forever. In this paper, we investigate the operation of a sensor network under this new enabling energy transfer technology. We consider the scenario of a mobile charging vehicle periodically traveling inside the sensor network and charging each sensor node's battery wirelessly. We introduce the concept of renewable energy cycle and offer both necessary and sufficient conditions. We study an optimization problem, with the objective of maximizing the ratio of the wireless charging vehicle (WCV)'s vacation time over the cycle time. For this problem, we prove that the optimal traveling path for the WCV is the shortest Hamiltonian cycle and provide a number of important properties. Subsequently, we develop a near-optimal solution by a piecewise linear approximation technique and prove its performance guarantee. [ABSTRACT FROM AUTHOR]

High Dimensional Model Representation (HDMR) based methods are used to generate an approximation for a given multivariate function in terms of less variate functions. This paper focuses on Hybrid HDMR which is composed of Plain HDMR and Logarithmic HDMR. The Plain HDMR method works well for representing multivariate functions having additive nature. If the function under consideration has a multiplicative nature, then the Logarithmic HDMR method produces better approximation. Hybrid HDMR method aims to successfully represent a multivariate function having neither purely additive nor purely multiplicative nature under a hybridity parameter. The performance of the Hybrid HDMR method strongly depends on the value of this hybridity parameter because this parameter manages the contribution level of Plain and Logarithmic HDMR expansions. The main purpose of this work is to optimize the hybridity parameter to get the best approximations. Fluctuationlessness Approximation Theorem is used in this optimization process and in evaluating the multiple integrals appearing in HDMR based methods. A number of numerical implementations are given at the end of the paper to show the performance of our proposed method. [ABSTRACT FROM AUTHOR]

Policy improvement in discrete event dynamic systems is usually based on simulation, which is time-consuming and provides only noisy performance evaluation. For a given system state, it is of great practical interest to understand how to allocate the computing budget among action candidates so that the best action is correctly selected with high probability. Despite the abundant studies on simulation-based policy optimization, few consider this important allocation problem, which is considered in this paper. We develop the method of optimal computing budget allocation for policy improvement (OCBAPI) which is shown to asymptotically maximize a lower bound of the probability of correctly selecting the best action. OCBAPI can also be used when there are multiple base policies available. This allocation procedure is compared with equal allocation and proportional-to-variance on an academic toy example and an engine maintenance policy optimization problem. The numerical results show that even when there are only finite computing budget to allocate, OCBAPI performs well. We hope this work brings insight to computing budget allocation for simulation-based policy improvement in more general situations. [ABSTRACT FROM PUBLISHER]

This correspondence investigates the least squares and minimax design problems for allpass variable fractional delay (VFD) filters. A two stage optimization approach is proposed to solve the resulting minimax optimization problem. This approach includes a combination of a one-dimensional global search method and an adaptive scheme to refine the discretization points. In addition, the paper investigates the design of allpass VFD filters which minimizes the weighted integral squared error subject to constraints on peak error deviation from the desired response. By using approximations, the design problem can be formulated as a quadratic optimization problem. Design examples show that a tradeoff between the weighted integral squared error and the peak error deviation can be achieved. In addition, the integral squared error can be reduced significantly from the minimax solution while maintaining approximately the same peak error deviation. Similarly, the peak error deviation can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. [ABSTRACT FROM AUTHOR]

In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix. [ABSTRACT FROM AUTHOR]

In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments. [ABSTRACT FROM AUTHOR]

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 addresses the problem of discretization of fractional differintegrators and fractional systems in general. Two new discretization schemes are proposed-optimal direct method, and computationally inexpensive indirect method. The proposed methods are highly flexible and suitable for obtaining both general purpose and specialized, application-specific approximations. Both proposed methods outperform recently proposed approximations, as it is shown in several illustrative examples. [ABSTRACT FROM AUTHOR]

This paper introduces an algorithm for direct search of control policies in continuous-state discrete-action Markov decision processes. The algorithm looks for the best closed-loop policy that can be represented using a given number of basis functions (BFs), where a discrete action is assigned to each BF. The type of the BFs and their number are specified in advance and determine the complexity of the representation. Considerable flexibility is achieved by optimizing the locations and shapes of the BFs, together with the action assignments. The optimization is carried out with the cross-entropy method and evaluates the policies by their empirical return from a representative set of initial states. The return for each representative state is estimated using Monte Carlo simulations. The resulting algorithm for cross-entropy policy search with adaptive BFs is extensively evaluated in problems with two to six state variables, for which it reliably obtains good policies with only a small number of BFs. In these experiments, cross-entropy policy search requires vastly fewer BFs than value-function techniques with equidistant BFs, and outperforms policy search with a competing optimization algorithm called DIRECT. [ABSTRACT FROM AUTHOR]

We consider the problem of extracting the source signals from an under-determined convolutive mixture assuming known mixing filters. State-of-the-art methods operate in the time–frequency domain and rely on narrowband approximation of the convolutive mixing process by complex-valued multiplication in each frequency bin. The source signals are then estimated by minimizing either a mixture fitting cost or a \ell1 source sparsity cost, under possible constraints on the number of active sources. In this paper, we define a wideband \ell2 mixture fitting cost circumventing the above approximation and investigate the use of a \ell1,2 mixed-norm cost promoting disjointness of the source time–frequency representations. We design a family of convex functionals combining these costs and derive suitable optimization algorithms. Experiments indicate that the proposed wideband methods result in a signal-to-distortion ratio improvement of 2 to 5 dB compared to the state-of-the-art on reverberant speech mixtures. [ABSTRACT FROM PUBLISHER]

The focus of this paper is on the synthesis of first-order filters which generate approximations for upper bounds of some signals needed in sliding mode control laws. The approximation is based on optimization methods which are applied to reduce the amplitude of the control signal. This paper also considers the application of these filters in output-feedback sliding mode controllers of linear systems in regular form with uncertain parameters and uncertain order. An experimental setup where the filters are applied to the model-reference control of an electromechanical system is presented to illustrate the design method. [ABSTRACT FROM AUTHOR]

Device-to-Device (D2D) networks impose a significant challenge on delay-sensitive crowdsourcing due to the highly non-deterministic and intermittent network connectivity. Under this setting, the paper investigates a participant recruitment problem in which an initial set of recruited nodes, which we call seeds, need to make an optimal decision on what other nodes to recruit to perform the crowdsourcing task. These seeds face the dilemma that recruiting more nodes increases their own payment but on the other hand also increases the risk of being excluded from the crowdsourcing task. As a first attack to this problem, we propose a dynamic programming algorithm. However, it is a centralized solution and hence the practicality is compromised. Therefore, we introduce two distributed alternatives. One is based on the divide-and-conquer paradigm by first partitioning a network into a set of opportunistic Voronoi cells and then running an optimization algorithm in each cell. The other is a task-splitting scheme which recursively delegates the recruitment task to newly joined nodes. We implemented our proposed solutions on an Android-based prototype and built a testbed using 25 Dell Streak tablets. Our experiments which lasted for 24 days demonstrate that the distributed schemes approximate the theoretical optimum with affordable complexity. Moreover, we conducted simulations with a much larger scale and more diverse settings. The simulation results corroborate the experimental data and confirm that our proposed distributed solutions closely approach the performance of the centralized solution while satisfying the optimization goal under different network configurations. [ABSTRACT FROM AUTHOR]

Stochastic dual dynamic programming (SDDP) is a widely used technique for operation optimization of large-scale hydropower systems in which reservoir inflow uncertainty is modeled with discrete scenarios produced by statistical time series models, such as the family of periodic auto-regressive (PAR) models. It is a common practice in statistical modeling of hydrologic time series to fit a well-known probability distribution (usually normal distribution) to the data by applying proper transformation. Box-Cox transformation is a commonly used transformation in the case of normal distribution fitting. The convexity requirement of SDDP means that nonlinearly transformed time series cannot be used for statistical inflow model calibration. In this paper, a linear approximation is proposed to estimate the expected value of the next stage inflow. In the proposed approach, next-stage inflows are estimated by a model that uses transformed time series. Furthermore, using the proposed linear approximation, it is shown that it is possible to utilize the time series transformed by Box-Cox transformation for scenario generation in SDDP. The Karoon multireservoir system in Iran has been used as a case study in order to show the effectiveness of the proposed method. Some concluding remarks have also been provided by comparing the results of the two SDDP models, with and without the proposed linear approximation. [ABSTRACT FROM AUTHOR]

The material in this paper has been divided into two main parts. In the first part we describe two optimization problems--one maximization and one minimization--related to a sharp trace inequality that was recently obtained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure. We prove the maximization to be solvable, whilst the minimization will turn out not to be solvable in general. We will also discuss the case of radial domains. In the second part of the paper, we study approximation and stability results regarding rearrangement optimization problems. First, we show that if a sequence of the generators of rearrangement classes converges, then the corresponding sequence of the optimal solutions will also converge. Second, a stability result regarding the Hausdorff distance between the weak closures of two rearrangement classes is presented. [ABSTRACT FROM AUTHOR]

In this paper, a generalized projection quasi-Newton method with inexact line search is proposed for the nonlinear optimization problem with linear constraints. The projection and quasi-Newton technique are used to determine the search direction at each iteration. It is proved that the method has properties of global convergence and superlinear convergence rate under some suitable assumptions. [ABSTRACT FROM AUTHOR]

The design of water distribution networks (WDNs) is a complex nonlinear problem that has been solved using optimization techniques attempting to find near-globally optimal solutions. This paper demonstrates that relying on engineering judgment, with very limited use of optimization, can generate reasonable quality approximations of the Pareto front of multiobjective WDN design problems without intensive computational requirements. First the results of the implementation of a previous implementation of the engineering judgment approach to the Battle of Background Leakage Assessment for Water Networks (BBLAWN) design competition is summarized. Additionally, a simplified version of the BBLAWN problem is solved using both the engineering judgment approach and a multiobjective optimization algorithm and the corresponding Pareto fronts are compared. Relative to other BBLAWN solutions, the engineering judgment solution produced a high-quality result with a very small computational budget and was able to identify a more realistic number of changes in the WDN (~10% of the network) compared with BBLAWN teams relying on global optimization algorithms. [ABSTRACT FROM AUTHOR]

The approximation of a multivector by a decomposable one is a distance-optimization problem between the multivector and the Grassmann variety of lines in a projective space. When the multivector diverges from the Grassmann variety, then the approximate solution sought is the worst possible. In this paper, it is shown that the worst solution of this problem is achieved, when the eigenvalues of the matrix representation of a related two-vector are all equal. Then, all these pathological points form a projective variety. We derive the equation describing this projective variety, as well as its maximum distance from the corresponding Grassmann variety. Several geometric and algebraic properties of this extremal variety are examined, providing a new aspect for the Grassmann varieties and the respective projective spaces. [ABSTRACT FROM AUTHOR]

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of a few elements from a given system of elements. There is an increasing interest in building such sparse approximate solutions using different greedy-type algorithms. The problem of approximation of a given element of a Banach space by linear combinations of elements from a given system (dictionary) is well studied in nonlinear approximation theory. At first glance, the settings of approximation and optimization problems are very different. In the approximation problem, an element is given and our task is to find a sparse approximation of it. In optimization theory, an energy function is given and we should find an approximate sparse solution to the minimization problem. It turns out that the same technique can be used for solving both problems. We show how the technique developed in nonlinear approximation theory, in particular the greedy approximation technique, can be adjusted for finding a sparse solution of an optimization problem. [ABSTRACT FROM AUTHOR]

We consider the problem of gathering correlated sensor data by a single sink node in a wireless sensor network. We assume that the sensor nodes are energy constrained and design efficient distributed protocols to maximize the network lifetime. Many existing approaches focus on optimizing the routing layer only, but in fact the routing strategy is often coupled with power control in the physical layer and link access in the MAC layer. This paper represents a first effort on network lifetime maximization that jointly considers the three layers. We first assume that link access probabilities are known and consider the joint optimal design of power control and routing. We show that the formulated optimization problem is convex and propose a distributed algorithm, JRPA, for the solution. We also discuss the convergence of JRPA. When the optimal link access probabilities are unknown, as in many practical networks, we generalize the problem formulation to encompass all the three layers of routing, power control, and link-layer random access. In this case, the problem cannot be converted into a convex optimization problem, but there exists a duality gap when the Lagrangian dual method is employed. We propose an efficient heuristic algorithm, JRPRA, to solve the general problem, and show through numerical experiments that it can significantly narrow the gap between the computed and optimal solutions. Moreover, even without a priori knowledge of the best link access probabilities predetermined for JRPA, JRPRA achieves extremely competitive performance with JRPA. Beyond the metric of network lifetime, we also discuss how to solve the problem of correlated data gathering under general utility functions. Numerical results are provided to show the convergence of the algorithms and their advantages over existing solutions. [ABSTRACT FROM AUTHOR]

We formulate the following combinatorial multi-armed bandit (MAB) problem: There are N random variables with unknown mean that are each instantiated in an i.i.d. fashion over time. At each time multiple random variables can be selected, subject to an arbitrary constraint on weights associated with the selected variables. All of the selected individual random variables are observed at that time, and a linearly weighted combination of these selected variables is yielded as the reward. The goal is to find a policy that minimizes regret, defined as the difference between the reward obtained by a genie that knows the mean of each random variable, and that obtained by the given policy. This formulation is broadly applicable and useful for stochastic online versions of many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weighted matching, shortest path, and minimum spanning tree computations. Prior work on multi-armed bandits with multiple plays cannot be applied to this formulation because of the general nature of the constraint. On the other hand, the mapping of all feasible combinations to arms allows for the use of prior work on MAB with single-play, but results in regret, storage, and computation growing exponentially in the number of unknown variables. We present new efficient policies for this problem that are shown to achieve regret that grows logarithmically with time, and polynomially in the number of unknown variables. Furthermore, these policies only require storage that grows linearly in the number of unknown parameters. For problems where the underlying deterministic problem is tractable, these policies further require only polynomial computation. For computationally intractable problems, we also present results on a different notion of regret that is suitable when a polynomial-time approximation algorithm is used. [ABSTRACT FROM AUTHOR]

This paper considers linear precoder optimization problems for multiple-input multiple-output (MIMO) systems. In addition to the conventionally used sum-power constraint, maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations. A framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean-square error (MSE). It turns out that power allocations in such situations are piecewise linear in sum-power space. The piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints. A Homotopy-type algorithm is then proposed to obtain the solution for an arbitrary sum-power constraint. The number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas, so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency. Simulated experiments are performed to verify our theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers a parallel system with a random number of units according to a Poisson distribution. The fracture of an aircraft fuselage with multiple site damage serves as a real world application for this problem. The mean time to failure is obtained. Using this result, an optimal number of units and replacement time for the system which minimize the expected cost rates are derived analytically, and numerically, when the failure time has a Weibull distribution. It is of interest that these results also give good approximations to those of the system with a constant number of units. Further, similar discussions for a scheduling problem of a job with random working times are made, when a parallel system is provided. [ABSTRACT FROM AUTHOR]

Algorithms that make use of the gradient, i.e., the direction of maximum improvement, to search for the optimum of a single-objective function have been around for decades. They are commonly accepted to be important and have been applied to tackle single-objective optimization problems in many fields. For multiobjective optimization problems, much less is known about the gradient and its algorithmic use. In this paper, we aim to contribute to the understanding of gradients for numerical, i.e., real-valued, multiobjective optimization. Specifically, we provide an analytical parametric description of the set of all nondominated, i.e., most promising, directions in which a solution can be moved such that the objective values either improve or remain the same. This result completes previous work where this set is described only for one particular case, namely when some of the nondominated directions have positive, i.e., nonimproving, components and the final set can be computed by taking the subset of directions that are all nonpositive. In addition we use our result to assess the utility of using gradient information for multiobjective optimization where the goal is to obtain a Pareto set of solutions that approximates the optimal Pareto set. To this end, we design and consider various multiobjective gradient-based optimization algorithms. One of these algorithms uses the description of the multiobjective gradient provided here. Also, we hybridize an existing multiobjective evolutionary algorithm (MOEA) with the various multiobjective gradient-based optimization algorithms. During optimization, the performance of the gradient-based optimization algorithms is monitored and the available computational resources are redistributed to allow the (currently) most effective algorithm to spend the most resources. We perform an experimental analysis using a few well-known benchmark problems to compare the performance of different optimization methods. The results underline that the use of a population of solutions that is characteristic of MOEAs is a powerful concept if the goal is to obtain a good Pareto set, i.e., instead of only a single solution. This makes it hard to increase convergence speed in the initial phase using gradient information to improve any single solution. However, in the longer run, the use of gradient information does ultimately allow for better fine-tuning of the results and thus better overall convergence. [ABSTRACT FROM PUBLISHER]

Location fingerprinting utilizing ultrawideband (UWB) radio frequency (RF) signals is an attractive alternative to conventional positioning concepts based on range, angle, or received signal strength estimates. Such a location fingerprinting method proves particularly beneficial in indoor environments with dense multipath propagation and nonline-of-sight situations where conventional approaches would fail. The ultrawide bandwidth allows for location fingerprints with many degrees of freedom and thus gives the important advantage that a single anchor suffices for good localization performance. The downside is that a large amount of training data is usually required, which makes the training phase time-consuming and tedious. In this paper, we propose and study a novel and efficient training method which is based on the idea of spatial signal prediction. We develop a regional channel model which supports spatial signal prediction in the vicinity of a reference point. We show that the parameters of this regional channel model can be estimated from very few measured received signals with known transmitter and receiver positions. The prediction accuracy and the location fingerprinting performance are evaluated with measured channel impulse responses obtained in an anechoic chamber and in a typical office environment. [ABSTRACT FROM AUTHOR]

Abstract: Extreme learning machine (ELM) is one of the most popular and important learning algorithms. It comes from single-hidden-layer feedforward neural networks. It has been proved that ELM can achieve better performance than support vector machine (SVM) in regression and classification. In this paper, mathematically, with regression problem, the step 3 of ELM is studied. First of all, the equation are reformulated as an optimal model. With the optimality, the necessary conditions of optimal solution are presented. The equation is replaced by . We can prove that the latter must have one solution at least. Second, optimal approximation solution is discussed in cases of is column full rank, row full rank, neither column nor row full rank. In the last case, the rank-1 and rank-2 methods are used to get optimal approximation solution. In theory, this paper present a better algorithm for ELM. [Copyright &y& Elsevier]

The application of nonlinear optimization to the estimation of fuzzy model parameters is well known. To do the reverse of this, the concept of stationary fuzzy Fokker–Planck learning (SFFPL) is introduced, i.e., SFFPL applies the fuzzy modeling technique in nonlinear optimization problems. SFFPL is based on the fuzzy approximation of the stationary cumulative distribution function of a stochastic search process associated with the nonlinear optimization problem. A carefully designed algorithm is suggested for SFFPL to locate the optimum point. This paper also considers the variational Bayes (VB)-based inference of a stochastic fuzzy filter whose consequents, as well as antecedents, are random variables. The problem of VB inference of stochastic antecedents, because of the nonlinearity of the likelihood function, is analytically intractable. The SFFPL algorithm for high-dimensional nonlinear optimization that does not require the derivative of the objective function can be used to numerically solve the stochastic fuzzy filtering problem. [ABSTRACT FROM AUTHOR]

Efficient segmentation of globally optimal surfaces in volumetric images is a central problem in many medical image analysis applications. Intraclass variance has been successfully utilized for object segmentation, for instance, in the Chan–Vese model, especially for images without prominent edges. In this paper, we study the optimization problem of detecting a region (volume) between two coupled smooth surfaces by minimizing the intraclass variance using an efficient polynomial-time algorithm. Our algorithm is based on the shape probing technique in computational geometry and computes a sequence of minimum-cost closed sets in a derived parametric graph. The method has been validated on computer-synthetic volumetric images and in X-ray CT-scanned datasets of plexiglas tubes of known sizes. Its applicability to clinical data sets was also demonstrated. In all cases, the approach yielded highly accurate results. We believe that the developed technique is of interest on its own. We expect that it can shed some light on solving other important optimization problems arising in medical imaging. Furthermore, we report an approximation algorithm which runs much faster than the exact algorithm while yielding highly comparable segmentation accuracy. [ABSTRACT FROM AUTHOR]