Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

西藏交通警察道路执法工作的风险与防范

西藏自治区自然、地理与气候环境复杂且特殊,道路交通环境相对恶劣,这导致当地交通警察道路执法工作面临诸多风险,包括警员人身安全和执法效能等风险。对此,文章对西藏交通警察道路执法工作风险进行了调查分析,从地区环境、警员安全意识与技能、执法装备、社会宣传和教育等角度探讨了相关风险的成因,针对性相关风险成因,提出从优化警力配置与道路信息推送、加强警员培训、完善警务装备、加强法治化宣传教育等工作来消除相关风险,以期保障警员安全并改善西藏交通环境。

Six-Element Yagi Array Designs Using Central Force Optimization with Pseudo Random Negative Gravity

A six-element Yagi-Uda array is optimally designed using Central Force Optimization (CFO) with a small amount of pseudo randomly injected negative gravity. CFO is a simple, deterministic metaheuristic analogizing gravitational kinematics (motion of masses under the influence of gravity). It has been very effective in addressing a wide range of antenna and other problems and normally employs only positive gravity. With positive gravity the six element CFO-designed Yagi array described here exhibits excellent performance with respect to the objectives of impedance bandwidth and forward gain. This paper addresses the question of what happens when a small amount of negative gravity is injected into the CFO algorithm. Does doing so have any effect, beneficial, negative or neutral? In this particular case negative gravity improves CFO’s exploration and creates a region of optimality containing many designs that perform about as well as or better than the array discovered with only positive gravity. Without some negative gravity these array configurations are overlooked. This Yagi-Uda array design example suggests that antennas optimized or designed using deterministic CFO may well benefit by including a small amount of negative gravity, and that the negative gravity approach merits further study.

Central Force Optimization with Gravity <0, Elitism, and Dynamic Threshold Optimization: An Antenna Application, 6-Element Yagi-Uda Arrays

This paper investigates the effect of adding three extensions to Central Force Optimization when it is used as the Global Search and Optimization method for the design and optimization of 6-elementYagi-Uda arrays. Those extensions are Negative Gravity, Elitism, and Dynamic Threshold Optimization. The basic CFO heuristic does not include any of these, but adding them substantially improves the algorithm’s performance. This paper extends the work reported in a previous paper that considered only negative gravity and which showed a significant performance improvement over a range of optimized arrays. Still better results are obtained by adding to the mix Elitism and DTO. An overall improvement in best fitness of 19.16% is achieved by doing so. While the work reported here was limited to the design/optimization of 6- element Yagis, the reasonable inference based on these data is that any antenna design/optimization problem, indeed any Global Search and Optimization problem, antenna or not, utilizing Central Force Optimization as the Global Search and Optimization engine will benefit by including all three extensions, probably substantially.

Grey Relational Analysis Coupled with Principal Component Analysis Method For Optimization Design of Novel Crash Box Structure

Crashworthiness and lightweight optimization design of the crash box are studied in this paper. For the initial model, a physical test was performed to verify the model. Then, a parametric model using mesh morphing technology is used to optimize and decrease the maximum collision force (MCF) and increase specific energy absorption (SEA) while ensure mass is not increased. Because MCF and SEA are two conflicting objectives, grey relational analysis (GRA) and principal component analysis (PCA) are employed for design optimization of the crash box. Furthermore, multi-objective analysis can convert to a single objective using the grey relational grade (GRG) simultaneously, hence, the proposed method can obtain the optimal combination of design parameters for the crash box. It can be concluded that the proposed method decreases the MCF and weight to 16.7% and 29.4% respectively, while increasing SEA to 16.4%. Meanwhile, the proposed method in comparison to the conventional NSGA-Ⅱ method, reduces the time cost by 103%. Hence, the proposed method can be properly applied to the optimization of the crash box.

Temporal Prediction of Aircraft Loss-of-Control: A Dynamic Optimization Approach

Loss of Control (LOC) is the primary factor responsible for the majority of fatal air accidents during past decade. LOC is characterized by the pilot’s inability to control the aircraft and is typically associated with unpredictable behavior, potentially leading to loss of the aircraft and life. In this work, the minimum time dynamic optimization problem to LOC is treated using Pontryagin’s Maximum Principle (PMP). The resulting two point boundary value problem is solved using stochastic shooting point methods via a differential evolution scheme (DE). The minimum time until LOC metric is computed for corresponding spatial control limits. Simulations are performed using a linearized longitudinal aircraft model to illustrate the concept.

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.

Application of several optimization techniques for estimating TBM advance rate in granitic rocks

This study aims to develop several optimization techniques for predicting advance rate of tunnel boring machine(TBM)in different weathered zones of granite.For this purpose,extensive field and laboratory studies have been conducted along the 12,649 m of the Pahang-Selangor raw water transfer tunnel in Malaysia.Rock properties consisting of uniaxial compressive strength(UCS),Brazilian tensile strength(BTS),rock mass rating(RMR),rock quality designation(RQD),quartz content(q)and weathered zone as well as machine specifications including thrust force and revolution per minute(RPM)were measured to establish comprehensive datasets for optimization.Accordingly,to estimate the advance rate of TBM,two new hybrid optimization techniques,i.e.an artificial neural network(ANN)combined with both imperialist competitive algorithm(ICA)and particle swarm optimization(PSO),were developed for mechanical tunneling in granitic rocks.Further,the new hybrid optimization techniques were compared and the best one was chosen among them to be used for practice.To evaluate the accuracy of the proposed models for both testing and training datasets,various statistical indices including coefficient of determination(R^2),root mean square error(RMSE)and variance account for(VAF)were utilized herein.The values of R^2,RMSE,and VAF ranged in 0.939-0.961,0.022-0.036,and 93.899-96.145,respectively,with the PSO-ANN hybrid technique demonstrating the best performance.It is concluded that both the optimization techniques,i.e.PSO-ANN and ICA-ANN,could be utilized for predicting the advance rate of TBMs;however,the PSO-ANN technique is superior.

Optimization of Fairhurst-Cook Model for 2-D Wing Cracks Using Ant Colony Optimization (ACO), Particle Swarm Intelligence (PSO), and Genetic Algorithm (GA)

The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.

An Overview of Recently Developed Coupled Simulation Optimization Approaches for Reliability Based Minimum Cost Design of Water Retaining Structures

This paper reviews several recently-developed techniques for the minimum-cost optimal design of water-retaining structures (WRSs), which integrate the effects of seepage. These include the incorporation of uncertainty in heterogeneous soil parameter estimates and quantification of reliability. This review is limited to methods based on coupled simulation-optimization (S-O) models. In this context, the design of WRSs is mainly affected by hydraulic design variables such as seepage quantities, which are difficult to determine from closed-form solutions or approximation theories. An S-O model is built by integrating numerical seepage modeling responses to an optimization algorithm based on efficient surrogate models. The surrogate models (meta-models) are trained on simulated data obtained from finite element numerical code solutions. The proposed methodology is applied using several machine learning techniques and optimization solvers to optimize the design of WRS by incorporating different design variables and boundary conditions. Additionally, the effects of several scenarios of flow domain hydraulic conductivity are integrated into the S-O model. Also, reliability based optimum design concepts are incorporated in the S-O model to quantify uncertainty in seepage quantities due to uncertainty in hydraulic conductivity estimates. We can conclude that the S-O model can efficiently optimize WRS designs. The ANN, SVM, and GPR machine learning technique-based surrogate models are efficiently and expeditiously incorporated into the S-O models to imitate the numerical responses of simulations of various problems.

Contribution to Development of Reliability and Optimization Methods Applied to Mechanical Structures

In order to take into account the uncertainties linked to the variables in the evaluation of the statistical properties of structural response, a reliability approach with probabilistic aspect was considered. This is called the Probabilistic Transformation Method (PTM). This method is readily applicable when the function between the input and the output of the system is explicit. However, the situation is much more involved when it is necessary to perform the evaluation of implicit function between the input and the output of the system through numerical models. In this work, we propose a technique that combines Finite Element Analysis (FEA) and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the function between the input and the output of the system is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) using an interface between Finite Element software and Matlab. Some problems of structures are treated in order to prove the applicability of the proposed technique. Moreover, the obtained results are compared to those obtained by the reference method of Monte Carlo. A second aim of this work is to develop an algorithm of global optimization using the local method SQP, because of its effectiveness and its rapidity of convergence. For this reason, we have combined the method SQP with the Multi start method. This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO). In order to test the applicability of the proposed approach, a structure is optimized under reliability constraints.

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

Minimizing the impact of the mixed uncertainties(i.e.,the aleatory uncertainty and the epistemic uncertainty) for a complex product of compliant mechanism(CPCM) quality improvement signifies a fascinating research topic to enhance the robustness.However, most of the existing works in the CPCM robust design optimization neglect the mixed uncertainties, which might result in an unstable design or even an infeasible design. To solve this issue, a response surface methodology-based hybrid robust design optimization(RSM-based HRDO) approach is proposed to improve the robustness of the quality characteristic for the CPCM via considering the mixed uncertainties in the robust design optimization. A bridge-type amplification mechanism is used to manifest the effectiveness of the proposed approach. The comparison results prove that the proposed approach can not only keep its superiority in the robustness, but also provide a robust scheme for optimizing the design parameters.

Applying Network Flow Optimization Techniques to Improve Relief Goods Transport Strategies under Emergency Situation

Given the seriously damaged emergency situation occurring after a large-scale natural disaster, a critical and important problem that needs to be solved urgently is how to distribute the necessary relief goods, such as drinking water, food, and medicine, to the damaged area and how to transport them corresponding to the actual supply and demand situation as quickly as possible. The existing infrastructure, such as traffic roads, bridges, buildings, and other facilities, may suffer from severe damage. Assuming uncertainty related with each road segment’s availability, we formulate a transshipment network flow optimization problem under various types of uncertain situations. In order to express the uncertainty regarding the availability of each road segment, we apply the Monte Carlo simulation technique to generate random networks following certain probability distribution conditions. Then, we solve the model to obtain an optimal transport strategy for the relief goods. Thus, we try to implement a necessary and desirable response strategy for managing emergency cases caused by, for example, various natural disasters. Our modeling approach was then applied to the actual road network in Sumatra Island in Indonesia in 2009, when a disastrous earthquake occurred to develop effective and efficient public policies for emergency situations.

Parameter Optimization of Interval Type-2 Fuzzy Neural Networks Based on PSO and BBBC Methods

Interval type-2 fuzzy neural networks(IT2FNNs)can be seen as the hybridization of interval type-2 fuzzy systems(IT2FSs) and neural networks(NNs). Thus, they naturally inherit the merits of both IT2 FSs and NNs. Although IT2 FNNs have more advantages in processing uncertain, incomplete, or imprecise information compared to their type-1 counterparts, a large number of parameters need to be tuned in the IT2 FNNs,which increases the difficulties of their design. In this paper,big bang-big crunch(BBBC) optimization and particle swarm optimization(PSO) are applied in the parameter optimization for Takagi-Sugeno-Kang(TSK) type IT2 FNNs. The employment of the BBBC and PSO strategies can eliminate the need of backpropagation computation. The computing problem is converted to a simple feed-forward IT2 FNNs learning. The adoption of the BBBC or the PSO will not only simplify the design of the IT2 FNNs, but will also increase identification accuracy when compared with present methods. The proposed optimization based strategies are tested with three types of interval type-2 fuzzy membership functions(IT2FMFs) and deployed on three typical identification models. Simulation results certify the effectiveness of the proposed parameter optimization methods for the IT2 FNNs.

Linking a Simulated Annealing Based Optimization Model with PHT3D Simulation Model for Chemically Reactive Transport Processes to Optimally Characterize Unknown Contaminant Sources in a Former Mine Site in Australia

Historical mining activities often lead to continuing wide spread contaminants in both groundwater and surface water in previously operational mine site areas. The contamination may continue for many years after closing down the mining activities. The essential first step for sustainable management of groundwater and development of remediation strategies is the unknown contaminant source characterization. In a mining site, there are multiple species of contaminants involving complex geochemical processes. It is difficult to identify the potential sources and pathways incorporating the chemically reactive multiple species of contaminants making the source characterization process more challenging. To address this issue, a reactive transport simulation model PHT3D is linked to a Simulated Annealing based the optimum decision model. The numerical simulation model PHT3D is utilized for numerically simulating the reactive transport process involving multiple species in the former mine site area. The simulation results from the calibrated PHT3D model are illustrated, with and without incorporating the chemical reactions. These comparisons show the utility of using a reactive, geochemical transport process’ simulation model. Performance evaluation of the linked simulation optimization methodology is evaluated for a contamination scenario in a former mine site in Queensland, Australia. These performance evaluation results illustrate the applicability of linked simulation optimization model to identify the source characteristics while using PHT3D as a numerical reactive chemical species’ transport simulation model for the hydro-geochemically complex aquifer study area.

MPSO Algorithm Based QoS Parameter Optimization for LTE Networks

QoS Optimization is an important part of LTE SON, but not yet defined in the specification. We discuss modeling the problem of QoS optimization, improve the fitness function, then provide an algorithm based on MPSO to search the optimal QoS parameter value set for LTE networks. Simulation results show that the algorithm converges more quickly and more accurately than the GA which can be applied in LTE SON.

Integrated design optimization of composite frames and materials for maximum fundamental frequency with continuous fiber winding angles

Fiber reinforced composite frame structure is an ideal lightweight and large-span structure in the fields of aerospace,satellite and wind turbine.Natural fundamental frequency is one of key indicators in the design requirement of the composite frame since structural resonance can be effectively avoided with the increase of the fundamental frequency.Inspired by the concept of integrated design optmization of composite frame structures and materials,the design optimization for the maximum structural fundamental frequency of fiber reinforced frame structures is proposed.An optimization model oriented at the maximum structural fundamental frequency under a composite material volume constraint is established.Two kinds of independent design variables are optimized,in which one is variables represented structural topology,the other is variables of continuous fiber winding angles.Sensitivity analysis of the frequency with respect to the two kinds of independent design variables is implemented with the semi-analytical sensitivity method.Some representative examples in the manuscript demonstrate that the integrated design optimization of composite structures can effectively explore coupled effects between structural configurations and material properties to increase the structural fundamental frequency.The proposed integrated optimization model has great potential to improve composite frames structural dynamic performance in aerospace industries.

An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT

Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.

Bi-Criteria Optimization Technique in Stochastic System Maintenance Allocation Problem

In this paper, the problem of optimum allocation of repairable and replaceable components in a system is formulated as a Bi-objective stochastic non linear programming problem. The system maintenance time and cost are random variable and has gamma and normal distribution respectively. A Bi-criteria optimization technique, weighted Tchebycheff is used to obtain the optimum allocation for a system. A numerical example is also presented to illustrate the computational details.

Data mining optimization of laidback fan-shaped hole to improve film cooling performance

To improve the cooling performance, shape optimization of a laidback fan-shaped film cooling hole was performed. Three geometric parameters, including hole length, lateral expansion angle and forward expansion angle, were selected as the design parameters. Numerical model of the film cooling system was established, validated, and used to generate 32 groups of training samples. Least square support vector machine(LS-SVM) was applied for surrogate model, and the optimal design parameters were determined by a kind of chaotic optimization algorithm. As hole length, lateral expansion angle and forward expansion angle are 90 mm, 20° and 5°, the area-averaged film cooling effectiveness can reach its maximum value in the design space. LS-SVM coupled with chaotic optimization algorithm is a promising scheme for the optimization of shaped film cooling holes.