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Using historical traffic flow information to accurately and real-time predict future traffic flow information is particularly important for the management and control of traffic scenarios, and the guidance and planning of traffic travel. Short-term traffic flow prediction requires a large amount of forecast data and complex changes in traffic flow in space and time. However, the current prediction model cannot meet the requirements of real-time and accuracy of short-term traffic flow prediction. This paper proposes two traffic flow prediction models based on the changing trend and correlation of short-term traffic flow in time and space, combined with deep learning related theories. Firstly, this paper takes the traffic flow of the expressway as the research object, explores the basic parameters of traffic flow-flow, speed occupancy rate in time and space distribution law and change trend, and selects the speed as the research object, analyzes its temporal and spatial characteristics and correlation to provide data support for this study. Then, this paper introduces the related theories and frameworks of deep learning, mainly including neural network theory and hyperparameter optimization theory, as well as the deep learning model design framework. Pytorch and hyperparameter optimization framework Optuna, so as to provide theoretical foundation and technical support for this research. Finally, experiments of short-term traffic prediction based on single detection point and short-term traffic prediction based on multiple detection points are carried out on the PeMS dataset. Firstly, a multi-lane spatiotemporal convolutional network model (MSCTAN) based on traffic flow prediction at a single detection point is proposed to capture the spatiotemporal correlation of multi-lane traffic at a single detection point. Spatiotemporal Convolution and Spatiotemporal Attention Network Model (MSCSAN). For the two models proposed in this paper, comparative experiments were designed, and the mean absolute error (MAE), the root mean square error (RMSE) and the mean absolute percentage error (MAPE) were used as evaluation indicators to verify their performance at a single detection point and multiple detection points. The results show that, whether it is a single detection point experiment or a multi-detection point experiment, the two models achieve the best performance compared with the comparison model. [ABSTRACT FROM AUTHOR]

This article designs an $$ \overline{X}\&S $$ control chart system for monitoring process shifts in mean and standard deviation in a multistage manufacturing system. Each of the $$ \overline{X}\&S $$ chart combination in a chart system monitors one of the critical quality characteristics (dimensions) of a product. The design algorithm optimally allocates the detection power of the chart system among different stages as well as between the $$ \overline{X} $$ chart and S chart within each stage based on the values of certain parameters (e.g., process capability, magnitude of the process shift) that would affect the performance of the chart system. Meanwhile, the sample sizes, sampling intervals, and control limits of the $$ \overline{X}\&S $$ charts are also optimized. The optimization design is carried out using false alarm rate and inspection capacity as constraints. Consequently, the performance of the system as a whole is improved without requiring additional cost and effort for inspection. The results of the comparative studies show that from an overall viewpoint, the optimal $$ \overline{X}\&S $$ chart system is more effective (in terms of reduction in detection time) than the traditional 3-sigma $$ \overline{X}\&S $$ chart system as well as a suboptimal $$ \overline{X}\&S $$ chart system by about 53 and 26 %, respectively. Some useful guidelines have been brought forth to aid the users to adjust the sample sizes, sampling intervals, and control limits of the charts in a system. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the application of the particle swarm optimization in logistics distribution routing problems. Combining with the characteristics of logistics and distribution, it established a mathematical model of the distribution routing problem. Introducing three kinds of optimization strategies in the particle swarm optimization to optimize the particle swarm algorithm, constructing three different particle swarm algorithms of LinWPSO, SAPSO and RandWPSO, used respectively the standard of PSO, LinWPSO, SAPSO and RandWPSO to solve calculation cases of problems in logistics and route, the results showed that the performance of the LinWPSO, SAPSO and RandWPSO to solve vehicle routing problem is better than standard PSO. Performance of SAPSO is optimal, which can effectively solve vehicle routing problems of the logistics distribution, when the problem size increases, optimization advantages of the SAPSO will display fully, we can greatly shorten the delivery mileage by using the SAPSO to solve the logistics distribution routing problem. [ABSTRACT FROM AUTHOR]

We demonstrate the fabrication of metallic nanomesh with hexagonal array of circular holes by nanosphere lithography and measure the optical transmission spectrum of the nanomesh. The optical property of metallic nanomesh is theoretically investigated by the finite-difference time-domain method. The numerical simulation results indicate that the transmission properties of metallic nanomesh can be tuned by changing the hole diameter, period and film thickness. The optimized aluminum nanomesh shows enhanced broadband optical transmission of about 80%. This research provides a significant guidance for the design and fabrication of transparent metallic electrodes in optoelectronic devices. [ABSTRACT FROM AUTHOR]

The quadratic knapsack problem ( QKP) maximizes a quadratic objective function subject to a binary and linear capacity constraint. Due to its simple structure and challenging difficulty, it has been studied intensively during the last two decades. This paper first presents some global optimality conditions for ( QKP), which include necessary conditions and sufficient conditions. Then a local optimization method for ( QKP) is developed using the necessary global optimality condition. Finally a global optimization method for ( QKP) is proposed based on the sufficient global optimality condition, the local optimization method and an auxiliary function. Several numerical examples are given to illustrate the efficiency of the presented optimization methods. [ABSTRACT FROM AUTHOR]

In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable. [ABSTRACT FROM AUTHOR]

We propose in this paper novel global descent methods for unconstrained global optimization problems to attain the global optimality by carrying out a series of local minimization. More specifically, the solution framework consists of a two-phase cycle of local minimization: the first phase implements local search of the original objective function, while the second phase assures a global descent of the original objective function in the steepest descent direction of a (quasi) global descent function. The key element of global descent methods is the construction of the (quasi) global descent functions which possess prominent features in guaranteeing a global descent. [ABSTRACT FROM AUTHOR]

We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract convexity. [ABSTRACT FROM AUTHOR]

In this paper we derive necessary and sufficient conditions for some problems of global minimization. Our approach is based on methods of abstract convexity: we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions. We discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities. [ABSTRACT FROM AUTHOR]

The increase of within-die variations and the design margin growth are creating a need for statistical design methodologies. This paper proposes a simple statistical timing analysis method considering the lot to lot process shifts that occur during production. This method is validated for 90~nm and 65~nm process. Finally, this statistical timing analysis is applied to evaluate, on basic ring oscillators and combinational paths, the timing margins introduced at the design level by the traditional corner based approach. [ABSTRACT FROM AUTHOR]

In this article, we first introduce a definition of a local minimizer for the quadratic programs with {-1, 1} constraints and show that the existing necessary condition of global optimality in some recent literature is in fact the necessary and sufficient condition of local optimality under the present definition. A filled function and the corresponding filled function algorithm then are proposed to get the global minimizer of the concerned minimization problem. The existing sufficient condition of global optimality is employed to form one of the termination rules of the algorithm. Several numerical examples are reported to show the efficiency of the present method for solving quadratic programs with binary constraints. [ABSTRACT FROM AUTHOR]

In this article, we present some global optimality conditions for mixed quadratic programming problems. Our approach is based on a L-subdifferential and an associated L-normal cone. Unlike most subdifferentials, the L-subdifferential is formed by functions that are not necessarily linear functions. We derive some sufficient and necessary global optimality conditions for mixed quadratic programs with box constraints and binary constraints. [ABSTRACT FROM AUTHOR]

A vibration-based approach to detect crack damage for large structural systems by using the Hilbert-Huang transform (HHT) has been proposed. The proposed method has been numerically implemented on a composite wingbox. In the implementation process, the following steps have been identified as being important: (a) An optimization procedure is developed by genetic algorithm (GA) in order to determine the location of piezoelectric sensor for damage detection in a composite wingbox: (b) To solve the end effect problem of empirical mode decomposition (EMD), axis-symmetry signal extension method is introduced; (c) Finally, a damage detection method by using HHT is developed. Furthermore, the effect of noise is considered. Examination of the results confirms that the identification method is very robust. [ABSTRACT FROM AUTHOR]

In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least squares with ellipsoidal constraints, and quadratic minimization with binary constraints. We discuss examples which demonstrate that our optimality conditions can effectively be used for identifying global minimizers of certain multi-extremal non-convex quadratic optimization problems. [ABSTRACT FROM AUTHOR]

Convexity is, without a doubt, one of the most desirable features in optimization. Many optimization problems that are nonconvex in their original settings may become convex after performing certain equivalent transformations. This paper studies the conditions for such hidden convexity. More specifically, some transformation-independent sufficient conditions have been derived for identifying hidden convexity. The derived sufficient conditions axe readily verifiable for quadratic optimization problems. The global minimizer of a hidden convex programming problem can be identified using a local search algorithm. [ABSTRACT FROM AUTHOR]

We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions. [ABSTRACT FROM AUTHOR]

This paper gives a new definition of a filled function, which eliminates certain drawbacks of the traditional definitions. Moreover, this paper proposes a quasi-filled function to improve the efficiency of numerical computation and overcomes some drawbacks of filled functions. Then, a new filled function method and a quasi-filled function method are presented for solving a class of global optimization problems. The global optimization approaches proposed in this paper will find a global minimum of original problem by implementing a local search scheme to the proposed filled function or quasi-filled function. Illustrative examples are provided to demonstrate the efficiency and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

A class of convexification and concavification methods are proposed for solving some classes of non-monotone optimization problems. It is shown that some classes of non-monotone optimization problems can be converted into better structured optimization problems, such as, concave minimization problems, reverse convex programming problems, and canonical D.C. programming problems by the proposed convexification and concavification methods. The equivalence between the original problem and the converted better structured optimization problem is established. [ABSTRACT FROM AUTHOR]

Optimal design and rehabilitation of a water distribution system is a constrained nonlinear optimization problem. A penalty function is often employed to transform a constrained into a nonconstrained optimization problem within the framework of a genetic algorithm search. A penalty factor is used for defining the penalty function and calculating the penalty cost for the solutions with constraint violation. Effective penalty factors vary from one optimization model to another. This paper introduces a self-adaptive penalty approach to artificially evolve both the penalty factor and the design solutions. Solution robustness is proposed and quantified, along with solution fitness, for representing the boundary between the infeasible and feasible solutions of a high-dimension optimization problem. The solution space of multiple dimensions is mapped onto a 2D space, providing significant insight into the self-adaptive penalty approach, which is compared with other constraint-handling techniques tested on a benchmark example. The results show that this approach is more effective than other penalty methods used for searching for optimal and near-optimal solutions. The self-adaptive penalty approach relieves modelers from tuning the penalty function and facilitates a practical optimization modeling for water distribution design. [ABSTRACT FROM AUTHOR]

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved. [ABSTRACT FROM AUTHOR]

A new hybrid genetic algorithm with the significant improvement of convergence performance is proposed in this study. This algorithm comes from the incorporation of a modified microgenetic algorithm with a local optimizer based on the heuristic pattern move. The hybridization process is implemented by replacing the two worst individuals in the offspring obtained from the conventional genetic operations with two new individuals generated from the local optimizer in each generation. Some implementation-related problems such as the selection of control parameters in the local optimizer are addressed in detail. This new algorithm has been examined using six benchmarking functions, and is compared with the conventional genetic algorithms without the local optimizer incorporated, as well as the hybrid algorithms incorporated with the hill-climbing method in terms of convergence performance. The results show that the proposed hybrid algorithm is more effective and efficient to obtain the global optimum. It takes about 6.4%-74.4% of the number of generations normally required by the conventional genetic algorithms to obtain the global optimum, while the computation cost for reproducing each new generation has hardly increased compared to the conventional genetic algorithms. Another advantage of this new algorithm is the implementation process is very simple and straightforward. There are no extra function evaluations and other complex calculations involved in the added local optimizer as well as in the hybridization process. This makes the new algorithm easy to be incorporated with the existing software packages of genetic algorithms so as to further improve their performance. As an engineering example, this new algorithm is applied for the detection of a crack in a composite plate, which demonstrates its effectiveness in solving engineering practical problems. [ABSTRACT FROM AUTHOR]