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During the process of cloud manufacturing, various uncertainties in the real world could have a significant impact on the smooth execution of task, and could render the planned composite manufacturing service (CMS) inefficient or even ineffective. Therefore, this paper proposes an optimal selection method to enhance the robustness of CMS during the planning stage. Firstly, the structure of robust CMS is proposed by arranging the preferred and alternative services for each subtask, and a robust service composition and optimal selection (rSCOS) model of cloud manufacturing is constructed by defining the expected Quality of Service. Then, the gABC-GWO (guiding artificial bee colony – grey wolf optimisation) algorithm is proposed to solve the rSCOS model efficiently, in which three improvement strategies for ABC algorithm are designed according to the characteristics of GWO. Finally, two experiments are implemented and the results show that QoS of the preferred scheme of robust CMS is approximately 1.29% lower than that of CMS on average, while its robustness is improved by 1.81% and 13.14% depending on the two robustness indexes. Compared with other commonly-used intelligence optimisation algorithms, gABC-GWO algorithm possesses better search performance without significantly increasing time consumption, which makes it more suitable for solving rSOCS problems. [ABSTRACT FROM AUTHOR]

Optimization of set-valued mappings has become an important subbranch of optimization. In set optimization, one of the main tools to compare sets is given by set relations, which are binary relations among sets. The main two set relations known in the literature are the upper and lower set relation, which are somewhat counterparts of each other and are used to model robust and optimistic solutions in uncertain (vector) programming, respectively. In this paper, we consider the convex case and propose a new set relation which is able to act as a weighting function between these two important set relations and therefore balances out possible gaps that can occur in modeling set optimization problems. [ABSTRACT FROM AUTHOR]

Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems. [ABSTRACT FROM AUTHOR]

Highlights • A robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a base matrix with fast implementation. • Designed a robust structured sparse sensing matrix by minimizing the mutual coherence and a surrogate function for the sparse representation error. • Proposed an alternating minimization algorithm for solving the corresponding optimization problem. • Provided global sequence convergence analysis for the proposed algorithm. Abstract We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently. We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence. Moreover, a regularization is added to enforce the robustness of the optimized structured sparse sensing matrix to the sparse representation error (SRE) of signals of interests. An alternating minimization algorithm with global sequence convergence is proposed for solving the corresponding optimization problem. Numerical experiments on synthetic data and natural images show that the obtained structured sensing matrix results in a higher signal reconstruction than a random dense sensing matrix. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel fault detection method is developed based on robust characteristic dimensionality reduction (RCDR). The time-constrained sparse representation (TCSR) method is firstly introduced by considering the space and time characteristics of industrial process monitoring data simultaneously. It can remove space-related outliers, time-related outliers and noises by solving an optimization problem. Then, a new RCDR method is proposed, which fully utilizes the constructed robust adjacency graph and considers the data characteristics. Its scatter matrices are specially designed by consideration of the data characteristics of fault detection. The within-class scatter matrix only characterizes normal data set with a classic covariance matrix, while the inter-class scatter matrix characterizes the separability between normal data and fault data through a pre-defined scatter matrix. It is worth mentioning that our method does not make Gaussian assumptions about the distribution of the fault data, and the number of projection directions is not limited as well. The TCSR is also embedded into our proposed dimensionality reduction method, enabling it to handle the fault detection problem under strong disturbances. Simulations on Tennessee Eastman process (TEP) and a case study of electric multiple unit (EMU) braking system of high-speed trains fully demonstrate the effectiveness and applicability of our proposed fault detection method. Highlights • New time-constrained sparse representation method is put forward. • Novel robust characteristic dimensionality reduction method is proposed. • Online fault detection algorithm is developed and fault detectability is analyzed. • Experimental studies on TEP and EMU braking system validate the proposed methods. [ABSTRACT FROM AUTHOR]

Harmonic retrieval (HR) is a problem of significance with numerous applications. Many existing algorithms are explicitly or implicitly developed under Gaussian noise assumption, which, however, are not robust against non-Gaussian noise such as impulsive noise or outliers. In this paper, by employing the $\ell _p$ -fitting criterion and block successive upper-bound minimization (BSUM) technique, a variant of the classical RELAX algorithm named as BSUM-RELAX is devised for robust HR. It is revealed that the BSUM-RELAX successively performs alternating optimization along coordinate directions, i.e., it updates one harmonic by fixing the other $(K-1)$ components, such that the whole problem is split into $K$ single-tone HR problems, which are then solved by creating a surrogate function that majorizes the objective function of each subproblem. To further refine the frequency component, the Newton's method that takes linear complexity $\mathcal {O}(N)$ is derived for updating the frequency estimates. We prove that under the single-tone case, BSUM-RELAX converges to a Karush-Kuhn-Tucker point. Furthermore, the BSUM-RELAX is extended to the multidimensional HR case. Numerical results show that the proposed algorithm outperforms the state-of-the-art methods in heavy-tailed noise scenarios. [ABSTRACT FROM AUTHOR]

In this paper, robust efficient solutions of a vector optimization problem, whose image space is ordered by an arbitrary ordering cone, are defined. This is done from different points of view, including set based and norm based. The relationships between these solution concepts are established. Furthermore, it is shown that, for a general vector optimization problem, each norm-based robust efficient solution is a strictly efficient solution; each isolated efficient solution is a norm-based robust efficient solution; and, under appropriate assumptions, each norm-based robust efficient solution is a Henig properly efficient solution. Various necessary and sufficient conditions for characterizing norm-based robust solutions of a general vector optimization problem, in terms of the tangent and normal cones and the nonascent directions, are presented. An optimization problem for calculating a robustness radius is provided, and then, the largest robustness radius is determined. Moreover, some alterations of objective functions preserving weak/strict/Henig proper/robust efficiency are studied. [ABSTRACT FROM AUTHOR]

Herein, the sample complexity of general weighted $\ell _1$ minimization in terms of support recovery from noisy underdetermined measurements is analyzed. This analysis generalizes prior work on $\ell _1$ minimization by considering arbitrary weighting. The explicit relationship between the weights and the sample complexity is stated such that for random matrices with i.i.d. Gaussian entries, the weighted $\ell _1$ minimization recovers the support of the underlying signal with high probability as the problem dimension increases. This result provides a measure that is predictive of relative performance of different algorithms. Motivated by the analysis, a new iterative reweighted strategy is proposed for binary signal recovery. In the binary sparsity-Promoting Reweighted $\ell _1$ minimization (bPRL1) algorithm, a sequence of weighted $\ell _1$ minimization problems are solved where partial support recovery is used to prune the optimization; furthermore, the weights used for the next iteration are updated by the current estimate. bPRL1 is compared to other weighted algorithms through the proposed measure and numerical results are shown to provide superior performance for a spectrum occupancy estimation problem motivated by cognitive radio. [ABSTRACT FROM AUTHOR]

Summary: In an earlier work, the authors proposed a globalized bounded Nelder‐Mead algorithm with deterministic restarts and a linearly growing memory vector. It was shown that the algorithm was a favorable option for solving multimodal optimization problems like controller tuning because of the greater probability of finding the global minimum and lesser numerical cost. Therefore, the algorithm was successfully used for model‐based offline tuning of sliding mode controller parameters for a servo‐pneumatic position control application. However, such offline tuning requires a sufficiently adequate system model, which, in some applications, is difficult to attain. Moreover, it is not generally appreciated as an essential requirement for controller tuning by the end user like the industry. An improvement in performance of optimization algorithm for tuning is expected if it relies on measurements coming directly from an actual physical system and not just its mathematical model. Therefore, in this paper, we apply the aforementioned algorithm for model‐free online optimization of controller parameters. The application involves the programmatic control of a real‐time interface of a physical system by the algorithm for data flow and logical decisions for optimization. For comparison with the results of the model‐based offline tuning suggested in earlier work, the sliding mode controller parameters are tuned online for the same position control application. The experimental results reveal that the system performance with controller parameters tuned online using the algorithm compares favorably to the one with model‐based offline tuning especially at higher priority level for accuracy. The improvement in system performance amounts to 21%. [ABSTRACT FROM AUTHOR]

Motivated by weakly convex optimization and quadratic optimization problems, we first show that there is no duality gap between a difference of convex (DC) program over DC constraints and its associated dual problem. We then provide certificates of global optimality for a class of nonconvex optimization problems. As an application, we derive characterizations of robust solutions for uncertain general nonconvex quadratic optimization problems over nonconvex quadratic constraints. [ABSTRACT FROM PUBLISHER]

Topology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first-order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient-based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies. [ABSTRACT FROM AUTHOR]

This paper investigates an optimal small satellite orbit design problem subject to the atmospheric drag uncertainty, and the small satellite is assumed to have no orbital control systems due to volume and mass constraints. The optimization objective of maximum target observation time is considered, which is constrained by the priority and minimum observation duration of each target site. Given the adverse impacts of atmospheric drag uncertainty on the designed orbit, the optimal solution is expected to maximize observation duration for given target sites while being less sensitive to substantial variations of atmospheric coefficients involved in atmospheric drag modeling. As a result, a robust orbit design approach is proposed by combining the robust optimization model with multi-objective optimization algorithm. Finally, the Monte Carlo simulation results are provided to demonstrate that the robust orbit solutions are more reliable compared to the nominal orbit solution designed from the traditional single-objective stochastic optimization algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel absolute value inequalities discriminant analysis (AVIDA) criterion for supervised dimensionality reduction. Compared with the conventional linear discriminant analysis (LDA), the main characteristics of our AVIDA are robustness and sparseness. By reformulating the generalized eigenvalue problem in LDA to a related SVM-type “concave-convex” problem based on absolute value inequalities loss, our AVIDA is not only more robust to outliers and noises, but also avoids the SSS problem. Moreover, the additional L1-norm regularization term in the objective makes sure sparse discriminant vectors are obtained. A successive linear algorithm is employed to solve the proposed optimization problem, where a series of linear programs are solved. The superiority of our AVIDA is supported by experimental results on artificial examples as well as benchmark image databases. [ABSTRACT FROM AUTHOR]

Robust design optimization (RDO) is a field of optimization in which certain measure of robustness is sought against uncertainty. Unlike conventional optimization, the number of function evaluations in RDO is significantly more which often renders it time consuming and computationally cumbersome. This paper presents two new methods for solving the RDO problems. The proposed methods couple differential evolution algorithm (DEA) with polynomial correlated function expansion (PCFE). While DEA is utilized for solving the optimization problem, PCFE is utilized for calculating the statistical moments. Three examples have been presented to illustrate the performance of the proposed approaches. Results obtained indicate that the proposed approaches provide accurate and computationally efficient estimates of the RDO problems. Moreover, the proposed approaches outperforms popular RDO techniques such as tensor product quadrature, Taylor’s series and Kriging. Finally, the proposed approaches have been utilized for robust hydroelectric flow optimization, demonstrating its capability in solving large scale problems. [ABSTRACT FROM AUTHOR]

Point cloud registration is a fundamental building block of many robotic applications. In this paper we describe a system to solve the registration problem, that builds on top of our previous work (Serafin and Grisetti (2015)), and that represents an extension to the well known Iterative Closest Point (ICP) algorithm. Our approach combines recent achievements on optimization by using an extended point representation (Serafin and Grisetti (2014)) that captures the surface characteristics around the points. Thanks to an effective strategy to search for correspondences, our method can operate on-line and cope with measurements gathered with an heterogeneous set of range and depth sensors. By using an efficient map-merging procedure our approach can quickly update the tracked scene and handle dynamic aspects. We also introduce an approximated variant of our method that runs at twice the speed of our full implementation. Experiments performed on a large publicly available benchmarking dataset show that our approach performs better with respect to other state-of-the art methods. In most of the tests considered, our algorithm has been able to obtain a translational and rotational relative error of respectively ∼ 1 cm and ∼ 1 ° . [ABSTRACT FROM AUTHOR]

In this paper, following the framework of robust optimization, we consider robust optimal solutions for a fractional optimization problem in the face of data uncertainty both in the objective and constraints. To this end, by using the properties of the subdifferential sum formulae, we first introduce some robust basic subdifferential constraint qualifications, and then obtain some completely characterizations of the robust optimal solutions of this uncertain fractional optimization problem. We show that our results encompass as special cases some optimization problems considered in the recent literature. Moreover, as applications, the proposed approach is applied to investigate weakly robust effcient solutions for multi-objective fractional optimization problems in the face of data uncertainty both in the objective and constraints. [ABSTRACT FROM AUTHOR]

The problem of simultaneous localisation and mapping (SLAM) has been addressed in numerous ways with different approaches aiming to produce faster, more robust solutions that yield consistent maps. This focus, however, has resulted in a number of solutions that perform poorly in challenging real life scenarios. In order to achieve improved performance and map quality this article proposes a novel method to construct informative Bayesian mapping priors through a multi-objective optimisation of prior map design variables defined using a source of prior information. This concept is explored for 2D occupancy grid SLAM, constructing such priors by extracting structural information from architectural drawings and identifying optimised prior values to assign to detected walls and empty space. Using the proposed method a contextual optimised prior can be constructed. This prior is found to yield better quantitative and qualitative performance than the commonly used non-informative prior, yielding an increase of over 20% in the F 2 metric. This is achieved without adding to the computational complexity of the SLAM algorithm, making it a good fit for time critical real life applications such as search and rescue missions. [ABSTRACT FROM AUTHOR]

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets . In contrast to standard constrained robust optimal control problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a finite prediction horizon and a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of the uncertainty sets, while simultaneously ensuring the existence of a control policy that will keep the system within its constraints for all possible disturbance realizations inside the adjusted uncertainty set. Since our problem subsumes the classical constrained robust optimal control design problem, it is computationally intractable in general. Nevertheless, we demonstrate that by restricting the families of admissible uncertainty sets and control policies, the problem can be formulated as a tractable convex optimization problem. We show that our framework captures several families of (convex) uncertainty sets of practical interest, and illustrate our approach on a demand response problem of providing control reserves for a power system. [ABSTRACT FROM AUTHOR]

In this paper, we present the synthesis of a robust controller for uncertain discrete systems. The synthesis method of such a robust controller is the generalization of the Loop Shaping Design Procedure (LSDP) approach of McFarlane and Glover in the discrete case based on the work of Gu et al. We exploit the bilinear transform known as Tustin’s method in order to formulate the discrete loop shaping technique. A discrete weighting filter and a shaped discrete plant result from this technique. By taking into account the coprime factor uncertainty representation for the resulting shaped plant and by applying the small gain theorem, we define the concept of the robust stabilization of the discrete LSDP approach. This concept is based on the resolution of an optimization problem characterized by the maximum stability margin for the synthesis of the robust controller. To calculate the robust controller we transform this problem to a standard robust H ∞ controller design based on the resolution of the Riccati equations. Also, we present the gap metric theory to characterize the controller’s robustness. We note that the resulting final controller is the combination of the discrete weighting filter and the robust controller. We propose then to exploit the recent work of Bouzrara et al. in order to develop a reduced robust controller by expanding the final controller on two independent Laguerre orthonormal bases. The discrete LSDP and the reduced controller approaches were validated on a Continuous Stirred Tank Reactor chemical reactor for a set of different equilibrium points in order to take into account the nonlinearities. [ABSTRACT FROM AUTHOR]

To solve optimization problems with matrix uncertainty, a novel optimization approach is proposed based on chance-constrained and robust optimization, which focuses on constraints with continuous uncertainty, especially with matrix uncertainty. In chance-constrained approach, constraints with matrix uncertainty are always regarded as joint chance constraints, which can be simplified into individual chance constraints and can be further reformulated into algebraic constraints by robust methods. Motivated by reformulation of chance constraints with right-hand side uncertainty, a novel formulation of constraints with left-hand side uncertainty is proposed, where the uncertainty is described as intervals related to the confidence level of chance constraints. Through using kernel density estimation, confidence sets of uncertain parameters are built to approximate unknown true probability density functions. The approach is illustrated with a motivating and process industry scheduling example with energy consumption uncertainties. [ABSTRACT FROM AUTHOR]

We formulate the supplier selection and allocation problem in outsourcing under an uncertain environment as a stochastic programming problem. Both the decision-maker's attitude towards risk and the penalty parameters for demand deviation are considered in the objective function. A service level agreement, upper bound for each selected supplier's allocation and the number of selected suppliers are considered as constraints. A novel robust optimisation approach is employed to solve this problem under different economic situations. Illustrative examples are presented with managerial implications highlighted to support decision-making. [ABSTRACT FROM PUBLISHER]

The relaxation factor is a key parameter in gradient-based inversion and optimization methods, as well as in solving nonlinear equations using iterative techniques. In gradient-based inversion methods, the relaxation factor directly affects the inversion efficiency and the convergence stability. In general, the bigger the relaxation factor is, the faster the inversion process is. However, divergences may occur if the relaxation factor is too big. Therefore, there should be an optimal value of the relaxation factor at each iteration, guaranteeing a high inversion efficiency and a good convergence stability. In the present work, an optimization technique is proposed, using which the relaxation factor is adaptively updated at each iteration, rather than a constant during the whole iteration process. Based on this, a new inverse analysis method is developed for solving multi-dimensional transient nonlinear inverse heat conduction problems. One- and two-dimensional transient nonlinear inverse heat conduction problems are involved, and the instability issues occurred in the previous works are reconsidered. The results show that the new inverse analysis method in the present work has the same high accuracy, the same good robustness, and a higher inversion efficiency, compared with the previous least-squares method. Most importantly, the new method is more stable by innovatively optimizing and adaptively updating the relaxation factor at each iteration. [ABSTRACT FROM AUTHOR]

Two new approximate formulations to joint chance-constrained optimization problems are proposed in this paper. The relationships of CVaR (conditional-value-at-risk), chance constrains and robust optimization are reviewed. Firstly, two new upper bounds on E((·) + ) are proposed, where E stands for the expectation and x + = max(0, x ), based on which two approximate formulations for individual chance-constrained problems are derived. The approximations are proved to be the robust optimization with the corresponding uncertain sets. Then the approximations are extrapolated to joint chance-constrained problem. Finally numerical studies are performed to compare the solutions of individual and joint chance constraints approximations and the results demonstrate the validity of our method. [ABSTRACT FROM AUTHOR]

Solving optimization problems under hybrid uncertainty bears a heavy computational burden. In this study, we propose a unified structured optimization approach, termed robust granular optimization (RGO), to tackle the optimization problems under hybrid manifold uncertainties in a computationally tractable manner. Essentially, the RGO can be regarded as a complementary fusion of granular computing and robust optimization techniques. The paradigm of RGO consists of three core phases: 1) uncertainty identification, 2) information granulation in which basic granular units (BGUs) are formed, and 3) robust optimization realized over the BGUs. Following the proposed paradigm, we develop two classes of RGO models for general single-stage and two-stage optimization problems with separable and higher order hybrid uncertainties, respectively. It is shown that both types RGO models can be equivalently transformed into linear programs or mixed integer linear programs that can be handled efficiently by off-the-shelf solvers. Furthermore, a target-based tradeoff model is developed to enhance the flexibility of the RGO models in balancing the granularity level (or robustness level) and the solution conservativeness. The tradeoff model can also be efficiently solved by a binary search algorithm. Finally, sufficient computational studies are presented, and comparisons with the existing approaches show that the RGO models can bring much higher computational efficiency and scalability without losing much optimality, and the RGO solutions exhibit a stronger resistance to the uncertainty. [ABSTRACT FROM PUBLISHER]

This work deals with a facility location problem in which location and allocation (transportation) policy is defined in two stages such that a first-stage solution should be robust against the possible realizations (scenarios) of the input data that can only be revealed in a second stage. This solution should be robust enough so that it can be recovered promptly and at low cost in the second stage. In contrast to some related modeling approaches from the literature, this new recoverable robust model is more general in terms of the considered data uncertainty; it can address situations in which uncertainty may be present in any of the following four categories: provider-side uncertainty, receiver-side uncertainty, uncertainty in-between , and uncertainty with respect to the cost parameters. For this novel problem, a sophisticated branch-and-cut framework based on Benders decomposition is designed and complemented by several non-trivial enhancements, including scenario sorting, dual lifting, branching priorities, matheuristics and zero-half cuts. Two large sets of instances that incorporate spatial and demographic information of countries such as Germany and US (transportation) and Bangladesh and the Philippines (disaster management) are introduced. They are used to analyze in detail the characteristics of the proposed model and the obtained solutions as well as the effectiveness, behavior and limitations of the designed algorithm. [ABSTRACT FROM AUTHOR]

Automatic facial landmark localization is a challenging problem for real world images because of face pose variations and occlusions. This paper proposes a unified framework to robustly locate facial landmarks under different poses and occlusions. Instead of explicitly modeling the statistical point distribution, we use a sparse linear combination to approximate the observed shape, and hence alleviate the multi-pose problem. In addition, we use the sparsity constraint to handle outliers caused by occlusions. We also model the initial misalignment and use convex optimization techniques to solve them simultaneously and efficiently. We evaluated the proposed method extensively on both synthetic and real data. The experimental results are promising on handling pose variations and occlusions. [ABSTRACT FROM AUTHOR]

This paper proposes a new metaheuristic, the runner-root algorithm (RRA), inspired by the function of runners and roots of some plants in nature. The plants which are propagated through runners look for water resources and minerals by developing runners and roots (as well as root hairs). The first tool helps the plant for search around with random big steps while the second one is appropriate for search around with small steps. Moreover, the plant which is placed at a very good location by chance spreads in a larger area through its longer runners and roots. Similarly, the proposed algorithm is equipped with two tools for exploration: random jumps with big steps, which model the function of runners in nature, and a re-initialization strategy in case of trapping in local optima, which redistributes the computational agents randomly in the domain of problem and models the propagation of plant in a larger area in case of being located in a good position. Exploitation in RRA is performed by the so-called roots and root hairs which respectively apply random large and small changes to the variables of the best computational agent separately (in case of stagnation). Performance of the proposed algorithm is examined by applying it to the standard CEC’ 2005 benchmark problems and then comparing the results with 9 state-of-the-art algorithms using nonparametric methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a new relaxed nonmonotone trust region method with adaptive radius for solving unconstrained optimization problems. The proposed method combines a relaxed nonmonotone technique with a modified version of the adaptive trust region strategy proposed by Shi and Guo (J Comput Appl Math 213:509-520, ). Under some suitable and standard assumptions, we establish the global convergence property as well as the superlinear convergence rate for the new method. Numerical results on some test problems show the efficiency and effectiveness of the new proposed method in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose an L1-norm two-dimensional linear discriminant analysis (L1-2DLDA) with robust performance. Different from the conventional two-dimensional linear discriminant analysis with L2-norm (L2-2DLDA), where the optimization problem is transferred to a generalized eigenvalue problem, the optimization problem in our L1-2DLDA is solved by a simple justifiable iterative technique, and its convergence is guaranteed. Compared with L2-2DLDA, our L1-2DLDA is more robust to outliers and noises since the L1-norm is used. This is supported by our preliminary experiments on toy example and face datasets, which show the improvement of our L1-2DLDA over L2-2DLDA. [ABSTRACT FROM AUTHOR]

In dynamic multiobjective optimization problems, the environmental parameters change over time, which makes the true pareto fronts shifted. So far, most works of research on dynamic multiobjective optimization methods have concentrated on detecting the changed environment and triggering the population based optimization methods so as to track the moving pareto fronts over time. Yet, in many real-world applications, it is not necessary to find the optimal nondominant solutions in each dynamic environment. To solve this weakness, a novel method called robust pareto-optimal solution over time is proposed. It is in fact to replace the optimal pareto front at each time-varying moment with the series of robust pareto-optimal solutions. This means that each robust solution can fit for more than one time-varying moment. Two metrics, including the average survival time and average robust generational distance, are present to measure the robustness of the robust pareto solution set. Another contribution is to construct the algorithm framework searching for robust pareto-optimal solutions over time based on the survival time. Experimental results indicate that this definition is a more practical and time-saving method of addressing dynamic multiobjective optimization problems changing over time. [ABSTRACT FROM AUTHOR]

Although the original particle swarm optimizer (PSO) method and its related variant methods show some effectiveness for solving optimization problems, it may easily get trapped into local optimum especially when solving complex multimodal problems. Aiming to solve this issue, this paper puts forward a novel method called parallel and cooperative particle swarm optimizer (PCPSO). In case that the interacting of the elements in D-dimensional function vector X=[x1,x2,…,xd,…,xD] is independent, cooperative particle swarm optimizer (CPSO) is used. Based on this, the PCPSO is presented to solve real problems. Since the dimension cannot be split into several lower dimensional search spaces in real problems because of the interacting of the elements, PCPSO exploits the cooperation of two parallel CPSO algorithms by orthogonal experimental design (OED) learning. Firstly, the CPSO algorithm is used to generate two locally optimal vectors separately; then the OED is used to learn the merits of these two vectors and creates a better combination of them to generate further search. Experimental studies on a set of test functions show that PCPSO exhibits better robustness and converges much closer to the global optimum than several other peer algorithms. [ABSTRACT FROM AUTHOR]

We formulated a solution procedure for vehicle routing problems with uncertainty (VRPU for short) with regard to future demand and transportation cost. Unlike E-SDROA (expectation semideviation robust optimisation approach) for solving the proposed problem, the formulation focuses on robust optimisation considering situations possibly related to bidding and capital budgets. Besides, numerical experiments showed significant increments in the robustness of the solutions without much loss in solution quality. The differences and similarities of the robust optimisation model and existing robust optimisation approaches were also compared. [ABSTRACT FROM AUTHOR]

The existing studies involving matrix or tensor completion problems are commonly under the nuclear norm penalization framework due to the computational efficiency of the resulting convex optimization problem. Folded-concave penalization methods have demonstrated surprising developments in sparse learning problems due to their nice practical and theoretical properties. To share the same light of folded-concave penalization methods, we propose a new tensor completion model via folded-concave penalty for estimating missing values in tensor data. Two typical folded-concave penalties, the minmax concave plus (MCP) penalty and the smoothly clipped absolute deviation (SCAD) penalty, are employed in the new model. To solve the resulting nonconvex optimization problem, we develop a local linear approximation augmented Lagrange multiplier (LLA-ALM) algorithm which combines a two-step LLA strategy to search a local optimum of the proposed model efficiently. Finally, we provide numerical experiments with phase transitions, synthetic data sets, real image and video data sets to exhibit the superiority of the proposed model over the nuclear norm penalization method in terms of the accuracy and robustness. [ABSTRACT FROM AUTHOR]

The Traveling Salesman Problem (TSP) is one of the typical NP-hard problems. Efficient algorithms for the TSP have been the focus on academic circles at all times. This article proposes a discrete invasive weed optimization (DIWO) to solve TSP. Firstly, weeds individuals encode positive integer, on the basis that the normal distribution of the IWO does not change, and then calculate the fitness value of the weeds individuals. Secondly, the 3-Opt local search operator is used. Finally, an improved complete 2-Opt (I2Opt) is selected as a second local search operator for solve TSP. A benchmarks problem selected from TSPLIB is used to test the algorithm, and the results show that the DIWO algorithm proposed in this article can achieve to results closed to the theoretical optimal values within a reasonable period of time, and has strong robustness. [ABSTRACT FROM AUTHOR]

We study coherent quantum control strategy that is robust with respect to coupling with an external environment. We model this interaction by appending an additional subsystem to the initial system and we choose the strength of the coupling to be proportional to the magnitude of the control pulses. Therefore, to minimize the interaction, we impose $$L_1$$ norm restrictions on the control pulses. In order to efficiently solve this optimization problem, we employ the BFGS algorithm. We use three different functions as the derivative of the $$L1$$ norm of control pulses: the signum function, a fractional derivative $$\frac{\mathrm {d}^\alpha |x|}{\mathrm {d}x^\alpha }$$ , where $$0<\alpha <1$$ , and the Fermi-Dirac distribution. We show that our method allows to efficiently obtain the control pulses which neglect the coupling with an external environment. [ABSTRACT FROM AUTHOR]

The USP monograph describes an HPLC method for seven impurities in the amiodarone drug substance using a L1 column, 4.6 mm × 150 mm, 5 μm packing (PF listed ODS2 GL-Science, Inertsil column) at 30 °C with detection at 240 nm. The standard contains 0.01 mg/mL of amiodarone, and USP specified impurities D and E with a resolution requirement of NLT 3.5 between peaks D and E. Impurities in a 5 mg/mL sample are quantitated against the standard. Impurity A peak elutes just before peak D. We observed two problems with the method; the column lot-to-lot variability resulted in unresolved A, D, and E peaks, and peak D in the sample preparation eluted much later than that in the standard solution. Therefore, optimization experiments were conducted on the USP method following the QbD approach with Fusion AE™ software (S-Matrix Corporation). The resulting optimized conditions were within the allowable changes per USP 〈621〉. Lot-to-lot variability was negligible with the Atlantis T3 (Waters Corporation) L1 column. Peak D retention time remained constant from standard to sample. The optimized method was validated in terms of accuracy, precision, linearity, range, LOQ/LOD, specificity, robustness, equivalency to the USP method, and solution stability. The QbD based development helped in generating a design space and operating space with knowledge of all method performance characteristics and limitations and successful method robustness within the operating space. [ABSTRACT FROM AUTHOR]

This article presents a new approach based on a hybrid algorithm consisting of biogeography based optimization (BBO) with an adaptive mutation scheme and the concept of predator-prey optimization technique for solving the multi-objective optimal power flow problems. The adaptive mutation scheme, based on distance-to-average point diversity measure, avoids the dominance of highly probable solutions through increasing the population diversity. The predators search around the best prey in a concentrated manner, while the preys explore the solution space so as to stay away from the predators. These mechanisms enhance the exploitation and exploration capabilities of the BBO search process, provide a mean of escaping from the suboptimal solutions and force the population to arrive at the global best solution. The proposed method is tested on IEEE 30 bus test system with different objectives that reflect fuel cost minimization, loss reduction, voltage profile improvement and voltage stability enhancement. The comparison of results with those of the existing approaches illustrates the effectiveness and robustness of the suggested method. [ABSTRACT FROM AUTHOR]

Conventional local preserving projection (LPP) is sensitive to outliers because its objective function is based on the L2-norm distance criterion and suffers from the small sample size (SSS) problem. To improve the robustness of LPP against outliers, LPP-L1 uses L1-norm distance metric. However, LPP-L1 does not work ideally when there are larger outliers. We propose a more robust version of LPP, called LPP-MCC, which formulates the objective problem based on maximum correntropy criterion (MCC). The objective problem is efficiently solved via a half-quadratic optimization procedure and the complicated non-linear optimization procedure can thereby be reduced to a simple quadratic optimization at each iteration. Moreover, LPP-MCC avoids the SSS problem because the generalized eigenvalues computation is not involved in the optimization procedure. The experimental results on both synthetic and real-world databases demonstrate that the proposed method can outperform LPP and LPP-L1 when there are large outliers in the training data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-facility Weber location problem (MFWP) with uncertain location of demand points and transportation cost parameters. Equivalent formulations of its robust counterparts for both the Euclidean and block norms and interval and ellipsoidal uncertainty sets are given as conic linear optimization problems. [ABSTRACT FROM AUTHOR]

Linear Fresnel collector arrays present some relevant advantages in the domain of concentrating solar power because of their simplicity, robustness and low capital cost. However, they also present important drawbacks and limitations, notably their average concentration ratio, which seems to limit significantly the performance of these systems. First, the paper addresses the problem of characterizing the mirror field configuration assuming hourly data of a typical year, in reference to a configuration similar to that of Fresdemo. For a proper comparative study, it is necessary to define a comparison criterion. In that sense, a new variable is defined, the useful energy efficiency, which only accounts for the radiation that impinges on the receiver with intensities above a reference value. As a second step, a comparative study between central linear Fresnel reflectors and compact linear Fresnel reflectors is carried out. This analysis shows that compact linear Fresnel reflectors minimize blocking and shading losses compared to a central configuration. However this minimization is not enough to overcome other negative effects of the compact Fresnel collectors, as the greater dispersion of the rays reaching the receiver, caused by the fact that mirrors must be located farther from the receiver, which yields to lower efficiencies. [ABSTRACT FROM AUTHOR]

Abstract: The robust shortest path problem is a network optimization problem that can be defined to deal with uncertainty of costs associated with the arcs of a network. Two models have been considered for the robust shortest path problem: interval data and discrete data sets. This work addresses the robust shortest path problem with a minmax regret objective function on a finite multi-scenario model. This problem consists in finding an optimal path in the sense that it has the minimum maximum deviation from the shortest one over all scenarios. With this goal some properties of the problem and of its optimal solutions are derived. These results allow to introduce three approaches, a labeling algorithm, an algorithm based on ranking loopless paths, and a hybrid algorithm which ranks loopless paths in a suitable way to apply the early elimination of useless solutions. The algorithms are tested on random networks and compared with a previous method for the same problem. The obtained computational results are reported and discussed. They show that the labeling and the hybrid approaches outperform the others. [Copyright &y& Elsevier]

In this paper we present new concepts of efficiency for uncertain multi-objective optimization problems. We analyze the connection between the concept of minmax robust efficiency presented by Ehrgott et al. (Eur J Oper Res, , doi:) and the upper set less order relation $$\preceq _s^u$$ introduced by Kuroiwa (, ). From this connection we derive new concepts of efficiency for uncertain multi-objective optimization problems by replacing the set ordering with other set orderings. Those are namely the lower set less ordering (see Kuroiwa , ), the set less ordering (see Nishnianidze in Soobshch Akad Nauk Gruzin SSR 114(3):489-491, ; Young in Math Ann 104(1):260-290, , doi:; Eichfelder and Jahn in Vector Optimization. Springer, Berlin, ), the certainly less ordering (see Eichfelder and Jahn in Vector Optimization. Springer, Berlin, ), and the alternative set less ordering (see Ide et al. in Fixed Point Theory Appl, , doi:; Köbis ). We analyze the resulting concepts of efficiency and present numerical results on the occurrence of the various concepts. We conclude the paper with a short comparison between the concepts, and an outlook to further work. [ABSTRACT FROM AUTHOR]

This paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider 'ambiguity neighborhoods' around this tree as alternative models which are close to the baseline model. Closeness is defined in terms of a distance for probability trees, called the nested distance. This distance is appropriate for scenario models of multistage stochastic optimization problems as was demonstrated in Pflug and Pichler (SIAM J Optim 22:1-23, ). The ambiguity model is formulated as a minimax problem, where the the optimal decision is to be found, which minimizes the maximal objective function within the ambiguity set. We give a setup for studying saddle point properties of the minimax problem. Moreover, we present solution algorithms for finding the minimax decisions at least asymptotically. As an example, we consider a multiperiod stochastic production/inventory control problem with weekly ordering. The stochastic scenario process is given by the random demands for two products. We determine the minimax solution and identify the worst trees within the ambiguity set. It turns out that the probability weights of the worst case trees are concentrated on few very bad scenarios. [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper presents TLBO and OTLBO to solve combined heat and power dispatch problem. [•] The proposed methods are implemented on three standard test systems. [•] The effectiveness of the proposed methods are compared with other reported algorithms. [•] Robustness of the proposed methods are checked through statistical analysis. [Copyright &y& Elsevier]

This letter examines the problem of robust subspace discovery from input data samples (instances) in the presence of overwhelming outliers and corruptions. A typical example is the case where we are given a set of images; each image contains, for example, a face at an unknown location of an unknown size; our goal is to identify or detect the face in the image and simultaneously learn its model. We employ a simple generative subspace model and propose a new formulation to simultaneously infer the label information and learn the model using low-rank optimization. Solving this problem enables us to simultaneously identify the ownership of instances to the subspace and learn the corresponding subspace model. We give an efficient and effective algorithm based on the alternating direction method of multipliers and provide extensive simulations and experiments to verify the effectiveness of our method. The proposed scheme can also be used to tackle many related high-dimensional combinatorial selection problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an evolutionary algorithm is employed to address the controller design problem based on μ analysis. Conventional solutions to μ synthesis problem such as D–K iteration method often lead to high order, impractical controllers. In the proposed approach, a constrained optimization problem based on μ analysis is defined and then an evolutionary approach is employed to solve the optimization problem. The goal is to achieve a more practical controller with lower order. A benchmark system named two-tank system is considered to evaluate performance of the proposed approach. Simulation results show that the proposed controller performs more effective than high order H ∞ controller and has close responses to the high order D–K iteration controller as the common solution to μ synthesis problem. [Copyright &y& Elsevier]