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As well known, low rank representation method (LRR) has obtained promising performance for subspace clustering, and many LRR variants have been developed, which mainly solve the three problems existing in LRR: 1) Problem of mean calculation; 2) Problem of deviating from the real low rank solution; 3) Problem of high computation cost on the large-scale data. In this paper, we first propose a universal LRR method referring to the first two problems. More specifically, we introduce the ability of removing the optimal mean automatically into LRR and extend it to a Schatten p-norm minimization problem. Then, referring to the third problem, we reformulate the universal LRR version as an equivalent fast optimization version by removing the null space of data. More importantly, the effective theory proof is proposed to guarantee that the fast optimization method can dramatically improve the algorithmic computation efficiency on the large-scale data but without any loss of information. Finally, experimental results demonstrate the effectiveness and efficiency of the proposed method.

In this paper, we present an optimization model for the management of the green area in order to find the optimal green surface to absorb CO2 emissions of industrialized cities. We obtain a minimization problem and the related variational inequality. We study the Lagrange theory to better understand the process that regulates the possible increase in green space. Then, we propose a computational procedure, based on the Euler method, to find the optimal solution to the variational inequality associated with our minimization problem and, finally, some numerical examples based on real scenarios.

3D mesh segmentation is a challenging problem in computer graphics, computer vision, and multimedia. In this paper, we cast mesh segmentation as a L0 minimization problem using random walks and L0 norm. In random walks method, the probabilities of random walks change smoothly over the whole model, which may lead to inaccurate segmentation boundaries. To attain a perception-aware result, the changes of probabilities should comply with mesh geometry. That is, the changes of probabilities near region boundaries should be more drastic than those inside the regions. Therefore, we introduce a L0 constraint to reflect the sparsity of probability changes, and identify region boundaries more precisely. Experimental results show that the proposed algorithm is effective, robust, and outperforms the state-of-the-art methods on various 3D meshes.

The ability to obtain the accurate location of nodes in wireless sensor networks is crucial for practical applications. The sensed data is meaningless if it is not accompanied by its location. Range-free localization techniques are favored to overcome the hardware limitations of sensor nodes and to avoid the costly range-based techniques. DV-Hop is a range-free localization algorithm that is well-known for its simplicity. However, it suffers from low accuracy and poor stability. In this paper, an enhanced variant of the DV-Hop algorithm is used to estimate the distance between the unknown nodes and anchor nodes, then the position estimation phase is formulated as a minimization problem solved by means of the recently developed squirrel search algorithm (SSA). The SSA is utilized to find the locations of the unknown sensor nodes. Our proposed algorithm is thus called SSIDV-Hop algorithm. The performance of our proposed algorithm is compared to that of existing localization algorithms including the DV-Hop, PSODV-Hop, GADV-Hop, and DEIDV-Hop algorithms. Extensive simulations showed that our proposed algorithm is superior to other existing algorithms as it achieved higher localization accuracy, better stability and faster convergence rate.

The cutwidth minimization problem (CMP) consists in determining a linear layout (i.e., a one-dimensional arrangement), of the vertices of a graph that minimizes the maximum number of edges crossing any consecutive pair of vertices. This problem has applications, for instance, in design of very large-scale integration circuits, graph drawing, and compiler design. The CMP is an NP -Hard problem and presents a challenge to exact methods and heuristics. In this study, the metaheuristic adaptive large neighborhood search is applied to the CMP. The computational experiments include 11,786 benchmark instances from four sets in the literature, and the obtained results are compared with state-of-the-art methods. The proposed method was demonstrated to be competitive, as it matched most optimal and best known results, improved some of the (not proved optimal) best known solutions, and provided the first upper bounds for unsolved instances.

Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2–4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.

Wavelet tight frames have been actively investigated for various image restoration problems. In this paper, we introduce an analysis-sparsity model via $\ell _2$ -relaxed truncated $\ell _0$ regularization and nonlocal estimation, and the resulted nonconvex minimization problem is tackled by a proximal alternating minimization strategy. Numerical experiments demonstrate that the proposed algorithm is superior to many popular methods in both objective and perceptual quality.

This research is focused on Unconstrained Optimization problems. Among a number of methods that can be used to solve Unconstrained Optimization problems we have worked on Gradient and Coordinate Descent methods. Step size plays an important role for optimization. Here we have performed numerical experiment with Gradient and Coordinate Descent method for several step size choices. Comparison between different variants of Gradient and Coordinate Descent methods and their efficiency are demonstrated by implementing in loss functions minimization problem.

In this work, we introduce a useful and efficient calculation method for solving linear fractional pantograph delay equations (FPDEs). The proposed method is primarily dependent on the least-squares approximation technique. After embedding the problem into a minimization problem, it solves the Lagrange multiplier method. The convergence analysis is theoretically proved. Finally, some numerical examples singled out to show the usefulness and capability of the suggested approach.

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.

Due to the complexities of collected data that may contain outliers and noises, many variants of LDA and 2DLDA have been proposed to address this problem and have shown that the improved methods produce much better performance than classical LDA and 2DLDA. In this paper we propose a novel two-dimensional linear discriminant analysis method via information divergence. The proposed method applies the weighted L21 norm to learn a robust projection matrix in the image space. In the proposed model, we introduce the weights into the within-class scatter and the total scatter simultaneously, and learn the weights by imposing information divergence on the objective functions. To handle the proposed model, we resort to Dinkelbach’s extended algorithm to solve the proposed ratio minimization problem. Considering the characteristics of the subproblems, we exploit an equivalent representation of subproblems which can be solved by alternating optimization techniques where each block of variables has good optimization properties. The proposed model not only overcomes the small-sample-size problem, but also suppresses outliers by an adaptively weighted scheme with the guidance of information divergences. The experiments on several image data sets demonstrate that the classification performance of the proposed method is superior to that of some existing methods in the presence of outliers.

In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the entropy and minimizes the sparsity. In this extended formulation, the parameter estimation minimization problem can be understood as a multiple criteria problem, with three different and conflicting criteria: The generalized collage error, the entropy associated with the unknown parameters, and the sparsity of the set of unknown parameters. We implement a scalarization technique to reduce the multiple criteria program to a single criterion one, by combining all objective functions with different trade-off weights. Numerical examples confirm that the collage method produces good, but sub-optimal, results. A relatively low-weighted entropy term allows for better approximations while the sparsity term decreases the complexity of the solution in terms of the number of elements in the basis.

The penetration of multi-carrier energy systems in distribution system gains more and more concerns. In this paper, a bi-level transactive energy trading framework is proposed to improve the energy scheduling and operation efficiency for multi-carrier energy systems which are modeled as energy hubs (EHs). In the upper level, each EH in the distribution system not only makes energy scheduling decisions considering supplies and demands of local energy, but also trades energy with each other to further maximize their social welfare. The associated trading payment among EHs is made in a fair manner by applying Nash bargaining theory. We solve the bargaining problem by decomposing it into two subproblems: operation cost minimization problem and payment bargaining problem. Then, based on the trading decision, the nodal equivalent loads of EHs are sent to the distribution system operator (DSO) without publishing trading details. By applying the second-order cone programming (SOCP), DSO reconfigures the network to reduce the transmission loss of the system in the lower level. The network reconfiguration and the trading behavior of EHs interact and iterate until the convergence. Numerical studies on modified IEEE 33-bus distribution system demonstrate the effectiveness of the proposed framework.

It is widely known that the classic total variation(TV) model has been proven to be very effective in preserving sharp edges. However, the TV model suffers from the staircase effects which produce blocking artifacts in the restored images. In this paper, we propose a new hybrid regularization model by combining non-convex second order total variation with wavelet transform to restrain staircase effects and protect some details of the images. To compute the new model effectively, we propose an alternating minimization method for recovering images from the blurry and noisy observations. The new model is first transformed into several sub-problems, and the generalized iterated shrinkage algorithm, the Fourier transform method and projection method are used to solve these sub-problems, respectively. Numerical experiments show that the proposed model can restrain blocking artifacts while projecting sharp edges, and the restoration quality outperforms several state-of-the-art methods.

With the increasing penetration of electric vehicles (EVs) and various user preferences, charging stations often provide several different charging modes to satisfy the various requirements of EVs. How to effectively utilize the charging capacity to minimize the service dropping rate is a pressing and open issue for charging stations. Given that EV owners are price-sensitive to the charging modes, we intend to design an optimal pricing scheme to minimize the service dropping rate of the charging station. First, we formulate the operation of a dual-mode charging station as a queuing network with multiple servers and heterogeneous service rates, and analyze the relationship between the service dropping rate of the charging station and the selections of EVs. Then, we formulate a customer attrition minimization problem to minimize the number of EVs that leave the charging station without being charged and propose an optimal pricing approach to guide and coordinate the charging processes of EVs in the charging station. The simulation has been conducted to evaluate the performance of the proposed charging scheduling scheme and show the efficiency of the proposed pricing scheme.

Inspired by the widespread and increasing usage of natural gas, we study the power consumption minimization problem associated with natural gas pipeline transmission in gunbarrel networks with nonidentical compressors. To accurately and flexibly model both gas flow dynamics and compressor working domains, we formulate the problem as a dynamic programming problem. Then we propose an approximate solution approach based on state dimension reduction. We analyze the problem properties and characterize conditions under which optimality is not compromised by the proposed solution approach. Next, we conduct numerical experiments using two data sets based on real networks in China and a data set from the public library GasLib. Numerical results demonstrate that the proposed solution approach significantly reduces computation time without compromising optimality in most cases. Specifically, the proposed solution approach obtains optimal solutions more than a 100 times faster than the exhaustive search when gas pressures are discretized at 0.01 MPa. Further, the optimality gaps do not exceed 0.4%.

We propose a new shape optimization formulation of the Bernoulli problem by tracking the Neumann data. The associated state problem is an equivalent formulation of the Bernoulli problem with a Robin condition. We devise an iterative procedure based on a Lagrangian-like approach to numerically solve the minimization problem. The proposed scheme involves the knowledge of the shape gradient which is established through the minimax formulation. We illustrate the feasibility of the proposed method and highlight its advantage over the classical setting of tracking the Neumann data through several numerical examples.

In the article we have obtained some estimates of the rate of convergence for the recently proposed by Yu. E.Nesterov method of minimization of a convex Lipschitz-continuous function of two variables on a square with a fixed side. The idea of the method is to divide the square into smaller parts and gradually remove them so that in the remaining sufficiently small part. The method consists in solving auxiliary problems of one-dimensional minimization along the separating segments and does not imply the calculation of the exact value of the gradient of the objective functional. The main result of the paper is proved in the class of smooth convex functions having a Lipschitz-continuous gradient. Moreover, it is noted that the property of Lipschitzcontinuity for gradient is sufficient to require not on the whole square, but only on some segments. It is shown that the method can work in the presence of errors in solving auxiliary one-dimensional problems, as well as in calculating the direction of gradients. Also we describe the situation when it is possible to neglect or reduce the time spent on solving auxiliary one-dimensional problems. For some examples, experiments have demonstrated that the method can work effectively on some classes of non-smooth functions. In this case, an example of a simple non-smooth function is constructed, for which, if the subgradient is chosen incorrectly, even if the auxiliary one-dimensional problem is exactly solved, the convergence property of the method may not hold. Experiments have shown that the method under consideration can achieve the desired accuracy of solving the problem in less time than the other methods (gradient descent and ellipsoid method) considered. Partially, it is noted that with an increase in the accuracy of the desired solution, the operating time for the Yu. E. Nesterovs method can grow slower than the time of the ellipsoid method.

This second part of the paper presents and discuss results from the implementation of the MILP model presented in Part I. This comprehensive model is intended for the expansion planning of power distribution systems. The results were obtained using the programming language OPL and the minimization problem was solved using the CPLEX solver. We applied the model to three known systems, with 23, 54 and 69 buses, and also to a system with 276 buses containing real data, to illustrate potential uses and advantages of the proposed formulation. For the sake of validation, a comparison was carried out between the results obtained with the linearized model and the results obtained through a conventional load flow, showing the accuracy and efficiency of the model. Furthermore, the results obtained for the 54-bus system were compared with equivalent results obtained with another MILP model.

The output stabilization for a class of distributed semilinear system is obtained with stabilizing controls that depend on the output operator. Then, we give sufficient conditions for expo...

Unmanned aerial vehicle (UAV)-relaying can forward files for user devices, but also faces the challenge of the traffic blockage of wireless backhaul. In this paper, we propose a novel caching strategy to pre-cache some popular files at both UAV and user devices to reduce duplicate transmissions in device-to-device (D2D)-enabled UAV-relaying networks. Considering the quality of experience (QoE) of the requesting users, we formulate a file access delay minimization problem by optimizing the cache placement. Due to the dynamics of the environment and the complexity of the formulated problem, we propose a deep deterministic policy gradient (DDPG)-based cache placement optimizing algorithm to decide which files to be cached and where to be cached. In addition, we also analyze theoretically the complexity of the proposed algorithm. Numerical results show our proposed scheme outperforms other baselines.

We formally define the Formal-Language-Constrained Graph Minimization problem. The goal is to minimize the amount of data associated to the edges of a graph database, while preserving its utility, defined as a conjunctive path query. We show that the problem is NP-hard. A solution to this problem contributes to balancing the trade-off between privacy protection and utility when publishing a graph database.

The greater the number of devices on a network, the higher load in the network, the more chance of a collision occurring, and the longer it takes to transmit a message. The size of load can be identified by measuring the network occupancy, hence it is desirable to minimize the latter. In this paper, we present an approach for network occupancy minimization by optimizing the packing process while satisfying multiple constraints. We formulate the minimization problem as a bin packing problem and we implement a modification of the Best-Fit Decreasing algorithm to find the optimal solution. The approach considers grouping signals that are sent to different destinations in the same package. The analysis is done on a medium-sized plant model, and different topologies are tested. The results show that the proposed solution lowers the network occupancy compared to a reference case.

In this paper, a new self-adaptive step size algorithm to approximate the solution of the split minimization problem and the fixed point problem of nonexpansive mappings was constructed, which combined the proximal algorithm and a modified Mann’s iterative method with the inertial extrapolation. The strong convergence theorem was provided in the framework of Hilbert spaces and then proven under some suitable conditions. Our result improved related results in the literature. Moreover, some numerical experiments were also provided to show our algorithm’s consistency, accuracy, and performance compared to the existing algorithms in the literature.

The proliferation of Industrial Internet of Things (IIoT) applications has significantly boosted the need for fresh information to guarantee good real-time performance. To characterize the freshness of information in time-critical systems, the concept of the age of information (AoI) has been proposed. Based on minimizing AoI, most research has designed information update policies from the perspective of the source to keep data fresh. In this work, we find that actively discarding some packets at the receiver can reduce AoI as well, which motivates us to develop this idea. By introducing a packet dropping threshold at the receiver, we formulate an AoI minimization problem. Then, we propose a heuristic algorithm to solve this problem. Finally, simulation results demonstrate that the proposed approach has priority on decreasing the average AoI.

In this paper, we propose a new method to solve the minimization problem in a simultaneous reconstruction and segmentation (SRS) model for X-ray computed tomography (CT). The SRS model uses Bayes' rule and the maximum a posteriori (MAP) estimate on the hidden Markov measure field model (HMMFM). The original method [Romanov M, Dahl AB, Dong Y, Hansen PC. Simultaneous tomographic reconstruction and segmentation with class priors. Inverse Problems Sci Eng. 2016;24(8):1432–1453] includes a subproblem with logarithmic-summation (log-sum) term, which is non-separable to the classification index. This subproblem was solved by Frank–Wolfe algorithm, which is very time consuming especially when dealing with large-scale CT problems. The starting point of this paper is the commutativity of log-sum operations, where the log-sum problem could be transformed into a sum-log problem by introducing an auxiliary variable. The corresponding sum-log problem for the SRS model is separable. By applying the primal-dual algorithm, the sum-log problem turns into several easy-to-solve convex subproblems. In addition, we introduce an improved model by adding Tikhonov regularization on the SRS model, and give some convergence results for the proposed methods. Experimental results demonstrate that the proposed methods produce comparable results compared with the original SRS method with much less CPU time.

Test-suite minimization problem is an essential problem in software engineering as its application helps to improve the software quality. This paper proposes a quantum algorithm to solve the test-suite minimization problem with high probability in $$O\left({\sqrt {{2^n}} } \right)$$, where $$n$$ is the number of test cases. It generates an incomplete superposition to find the best solution. It also handles the non-uniform amplitudes’ distribution case for the system with multisolutions. The proposed algorithm uses amplitude amplification techniques to search for the minimum number of test cases required to test all the requirements. The proposed algorithm employs two quantum search algorithms, Younes et al. algorithm for quantum searching via entanglement and partial diffusion to prepare incomplete superpositions that represent different search spaces such that the number of test cases is incremented in each search space, and updated Arima’s algorithm to handle the multisolutions case. The updated Arima’s algorithm searches for a quantum state that satisfies an oracle that represent the instance of the test-suite minimization problem.

In this paper, the problem of load uncertainty in compliance problems is addressed where the uncertainty is described in the form of a set of finitely many loading scenarios. Computationally, more efficient methods are proposed to exactly evaluate and differentiate: (1) the mean compliance or (2) any scalar-valued function of the individual load compliances such as the weighted sum of the mean and standard deviation. The computational time complexities of all the proposed algorithms are analyzed, compared with the naive approaches and then experimentally verified. Finally, a mean compliance minimization problem, a risk-averse compliance minimization problem, and a maximum compliance-constrained problem are solved to showcase the efficacy of the proposed algorithms. The maximum compliance-constrained problem is solved using the augmented Lagrangian method and the method proposed for handling scalar-valued functions of the load compliances, where the scalar-valued function is the augmented Lagrangian function.

Although wearable robotic systems are designed to reduce the risk of low-back injury, it is unclear how effective assistance is, compared to improvements in lifting technique. We use a two-factor block study design to simulate how effective exoskeleton assistance and technical improvements are at reducing the risk of low-back injury when compared to a typical adult lifting a box. The effects of assistance are examined by simulating two different models: a model of just the human participant, and a model of the human participant wearing the SPEXOR exoskeleton. The effects of lifting technique are investigated by formulating two different types of optimal control problems: a least-squares problem which tracks the human participant’s lifting technique, and a minimization problem where the model is free to use a different movement. Different lifting techniques are considered using three different cost functions related to risk factors for low-back injury: cumulative low-back load (CLBL), peak low-back load (PLBL), and a combination of both CLBL and PLBL (HYB). The results of our simulations indicate that an exoskeleton alone can make modest reductions in both CLBL and PLBL. In contrast, technical improvements alone are effective at reducing CLBL, but not PLBL. The largest reductions in both CLBL and PLBL occur when both an exoskeleton and technical improvements are used. While all three of the lifting technique cost functions reduce both CLBL and PLBL, the HYB cost function offers the most balanced reduction in both CLBL and PLBL.

Detection and treatment of diseases might be one of the most promising fields of application of flow-guided nanocommunication networks. This type of networks can enable new medical developments for health monitoring, vital sign information gathering, and data transmission inside the human body. As these nano-networks might require the introduction of nano-devices in the human circulatory system, it is crucial to investigate feasible network setups that meet the requirements of custom medical applications. Reducing body invasiveness by minimizing the number of nano-devices needed is also an important factor. This paper contributes by formulating and solving a nano-node minimization problem for some medical applications, thus demonstrating the feasibility of this technology.

This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate optimization problems and design robotic strategies. First, by analyzing multiple random walks on a common graph as a single random walk on the Kronecker product graph, we provide the first closed-form expression for the expected meeting time in terms of the transition matrices of the moving agents. This novel expression leads to necessary and sufficient conditions for the meeting time to be finite and to insightful graph-theoretic interpretations. Second, based on the closed-form expression, we setup and study the minimization problem for the expected capture time for a pursuer/evader pair. We report theoretical and numerical results on basic case studies to show the effectiveness of the design., Comment: arXiv admin note: substantial text overlap with arXiv:1806.08843

Feature selection method is used for generating an optimal number of features to be used for a certain task like classification. Particle Swarm Optimization (PSO) is an algorithm influenced by the habit of bird flocking or fish schooling. The main goal of this paper is designing and evaluating a viable wrapper-based feature selection algorithm. Feature selection can also be viewed as a minimization problem for which PSO can be applied. In this paper, we attempt to introduce a PSO based feature selection method using mutual information (MI). Feature-class MI has been used to select a subset of features based on its relevancy. A wrapper-based method is used to find the productiveness of the method by evaluating with different classifiers in different datasets. The classification performances have been found promising when compared with classifications performed using normal classifiers and PSO method without using mutual information.

This article aims a melting pool of complex vectors, that is, the aggregation and the minimization problem of sufficiency spectra. A mixture of this blended standard and image decline issue works admirably to reduce and deteriorate the example of concussion which occurs when old pictures are filtered with granular surfaces. In most cases, the appealing appropriation of regular photos easily reduces from low repetition to the high repetition band, while the episode of concussion is scarcely circulating. We agree along these lines that a picture viewed includes an idle image and an example clamor, describing them separately by using the full range and capacity work. This enables the two parts to decompose sensibly. In contrast to the comparative strategies of deterioration, for instance, robust PCA, our technique is decent, less computer expenditure, and moreover less time suited for any image organization

We propose a novel projected gradient-like method to solve a minimization problem with simple constraints. The new search direction is consistent with the first-order optimality condition for the simple constrained optimization problem, and makes the search step-size easier to determine. Convergence properties of the method are analyzed. Numerical experiments are presented to illustrate the performance and application of the proposed method.

While Wi-Fi is of great potential for indoor localization, the access points (APs) deployment in realistic indoor environments is particularly challenging due to the impact of various obstacles, e.g., walls, pillars or bookcases. The diverse obstacles create the troublesome non-line-of-sight and the multipath effect, which deteriorate the localization accuracy. In this paper, we study the effect of obstacles on the localization error and formulate the AP planning problem as a AP selection problem. This problem is decomposed into two subproblems, i.e., AP selection problem and error minimization problem. The AP selection problem aims to choose the minimum number of APs to satisfy the preset accuracy requirement. Furthermore, the error minimization problem improves the localization performance through optimizing the AP positions and array orientations. Extensive simulations show that our proposed method is adaptive to the obstacles and it achieves higher localization accuracy compared with the existing deployment method.

This paper studies the Containership Stowage Stack Minimization Problem(CSSMP) under a circular route so as to obtain the containership stowage plan for each port. This paper analyzes the process of multi-port containership stowage problem under the circular route, taking into consideration the sequence of port of call and container information of each port. A greedy algorithm is designed to solve the problem. The efficiency of the algorithm is verified by analyzing the results of the instances and therefore some rules can be obtained to provide reference for subsequent research.

In this paper a new approach to the Reliability-based Robust Design Optimization (RBRDO) of angle-ply composite laminate structures is presented. The problem is defined as a bi-objective Robust Design Optimization (RDO) problem, with deterministic and probabilistic constraints . Design optimization is considered as the minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix of the response functionals of the system (robustness). Reliability assessment is executed by the Reliability Index Approach (RIA), as an inner cycle. The key concept of this methodology is the exclusive use of evolutionary algorithms with elitist strategy, allowing for global convergence in the two optimization cycles. The RIA problem was reformulated and a set of new evolutionary operators were developed. A numerical example is presented and the results compared with other RBRDO and RDO formulations. Results show that deterministic and probabilistic structural integrity measures are quite sensitive to uncertainty, for multi-component composite structures.

International audience; Falsification has garnered much interest recently as a way to validate complex CPS designs with respect to a specification expressed via temporal logics. Using their quantitative semantics, the falsification problem can be formulated as robustness minimization problem. To make this infinite-dimensional problem tractable, a common approach is to restrict to classes of signals that can be defined using a finite number of parameters, such as piecewise-constant or piecewise-linear signals with fixed time intervals). A major drawback of this approach is that when the input signals must satisfy non-trivial temporal constraints, encoding these constraints into bounded domains for parameters can be difficult. In this work, to better capture temporal constraints on the input signal space, we use timed automata (TA) and make use of a transformation that allows sampling TA traces by sampling points in the unit box. We exploit this transformation to efficiently encode constrained CPS signals in the robustness minimization problem. This transformation also allows us to define an effective coverage measure of the constrained signal space so as to provide quantitative guarantees when no falsifying behaviour is found. In addition, this coverage is used to improve the black-box optimisation performance by detecting situations where the search is stuck near a local optimum. The approach is demonstrated on a ∆Σ modulator and a model of car automatic transmission subject to constraints describing usual driving patterns.

This paper considers the planning problem of an object’s optimal path that passes through a random search region. The problem specifics consist in that the search region is a priori unknown but the algorithmic and technical characteristics of search means are known. Two variational statements of the integral risk minimization problem with and without path length constraints are suggested. Program modules for their numerical solution are also developed.

This paper investigates permutation flowshop manufacturing cell scheduling problems with deteriorating jobs and sequence dependent setup times under dominant machines. In the proposed models, we need to make joint decisions on part families sequencing and jobs sequencing within each family. To solve the makespan minimization problem, the structural properties of the optimal solutions are derived, based on which an optimization algorithm is developed. Then, we consider the total completion time minimization problem and propose a useful lemma for the optimal solutions. Finally, we discuss two special cases of the problem and propose optimization algorithms to solve them respectively.

The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

This paper analyzes the limited range, spatial load balancing problem for agents deployed in non-convex environments and subject to differential constraints which restricts how the agents can move. First, the (unlimited range) spatial load balancing problem is introduced and the minimization problem with area constraints is defined. Then, to extend the problem for limited ranges, two cost functions and a sub-partition are defined. The problems are then analyzed and the results prove the existence of a partition that satisfies the area constraints. The non-convex environment makes the problem difficult to solve in continuous-space. Therefore, a probabilistic roadmap is used to approximate agents’ cells via a graph. A distributed algorithm is proven to converge to an approximate solution. Finally, the convergence of the algorithm is shown in simulation.

The Densest $k$-Subgraph (D$k$S) problem, and its corresponding minimization problem Smallest $p$-Edge Subgraph (S$p$ES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed that they do not an admit a subpolynomial approximation ratio (although the best known hardness results do not rule this out). In this paper we generalize both D$k$S and S$p$ES from graphs to hypergraphs. We consider the Densest $k$-Subhypergraph problem (given a hypergraph $(V, E)$, find a subset $W\subseteq V$ of $k$ vertices so as to maximize the number of hyperedges contained in $W$) and define the Minimum $p$-Union problem (given a hypergraph, choose $p$ of the hyperedges so as to minimize the number of vertices in their union). We focus in particular on the case where all hyperedges have size 3, as this is the simplest non-graph setting. For this case we provide an $O(n^{4(4-\sqrt{3})/13 + \epsilon}) \leq O(n^{0.697831+\epsilon})$-approximation (for arbitrary constant $\epsilon > 0$) for Densest $k$-Subhypergraph and an $\tilde O(n^{2/5})$-approximation for Minimum $p$-Union. We also give an $O(\sqrt{m})$-approximation for Minimum $p$-Union in general hypergraphs. Finally, we examine the interesting special case of interval hypergraphs (instances where the vertices are a subset of the natural numbers and the hyperedges are intervals of the line) and prove that both problems admit an exact polynomial time solution on these instances., Comment: 21 pages

In this paper, we consider the basic makespan minimization problem on identical parallel machines. The aim of this study is to solve, to optimality the hard instances of the literature. We present an integer linear program based on an innovative arc-flow model inspired from the duality between the bin packing problem and the parallel-machine scheduling problem. The proposed mathematical model is tested on a large set of hard instances. The results of computational experiments attest the efficiency of the new approach and prove that it outperforms the existing ones. In addition to its efficiency, the proposed method is simple and easy to use.

At many instances, information on the state of a multistate system executing a mission is obtained via the costly inspections performed at discrete instants of time. Therefore, the corresponding cost-wise optimal mission abort policy that takes into account the state of a system should be designed accordingly. In this paper, we introduce an optimal mission abort policy that minimizes the expected costs due to inspections, mission failure and loss of a system. A system operates in a random environment modeled by a renewal process of shocks. With each shock, its state can deteriorate with certain probabilities that can eventually result in the total failure. The decision to abort or to continue operation depends on the number of experienced shocks and on the state of a system that is revealed only at inspections. The corresponding cost minimization problem is formulated and the necessary relationships for solving it are derived. Detailed numerical illustrations and discussions are presented.

First-order program schemata represent one of the most simple models of sequential imperative programs intended for solving verification and optimization problems. We consider the decidable relation of logical-thermal equivalence on these schemata and the problem of their size minimization while preserving logical-thermal equivalence. We prove that this problem is decidable. Further we show that the first-order program schemata supplied with logical-thermal equivalence and finite-state deterministic transducers operating over substitutions are mutually translated into each other. This relationship makes it possible to adapt equivalence checking and minimization algorithms developed in one of these models of computation to the solution of the same problems for the other model of computation. In addition, on the basis of the discovered relationship, we describe a subclass of first-order program schemata such that minimization of the program schemata from this class can be performed in polynomial time by means of known techniques for minimization of finite-state transducers operating over semigroups. Finally, we demonstrate that in the general case the minimization problem for finite state transducers over semigroups may have several non-isomorphic solutions.

A study to evaluate the effects of different sources of uncertainty in the Reliability-based Robust Design (RBRDO) of composite laminate structures is performed. The goal is to understand how the set of Pareto-optimal solutions will change and the interaction between the design search and the reliability constraint. The RBRDO is executed by a newly proposed methodology exclusively based on Genetic Algorithms (GA), to guarantee higher levels of accuracy in the optimization procedure, avoiding local minima, common to gradient methods. Design optimization is considered as the bi-objective minimization problem of the weight (optimality) and the determinant of the variance–covariance matrix (robustness). Reliability assessment is made by a mathematical reformulation of the Performance Measure Approach, suitable for GA’s, as an inner-cycle of the design optimization. A numerical example of a fuselage-like composite laminate structure is presented. In the reliability assessment, the uncertainty of the system is considered only through the group of mechanical parameters. It is plausible that there exists an implicit functional relationship between feasibility robustness and the reliability constraint, on which the latter constrains the former, at least for the evaluated numerical example. Optimized weights vary between the same values. Tsai numbers and reliability indexes have similar distributions, for different sources of uncertainty. Only the thickness variables and the ply-angle seem to be affected by the structural feasibility robustness assessment. The distribution the Tsai numbers is affected by the reliability constraint, to respect the imposed reliability level.