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。

Global Optimization of Norris Derivative Filtering with Application for Near-Infrared Analysis of Serum Urea Nitrogen

Near-infrared (NIR) spectroscopy combined with chemometrics methods was applied to the rapid and reagent-free analysis of serum urea nitrogen (SUN). The mul-partitions modeling was performed to achieve parameter stability. A large-scale parameter cyclic and global optimization platform for Norris derivative filter (NDF) of three parameters (the derivative order: d, the number of smoothing points: s and the number of differential gaps: g) was developed with PLS regression. Meantime, the parameters’ adaptive analysis of NDF algorithm was also given, and achieved a significantly better modeling effect than one without spectral pre-processing. After eliminating the interference wavebands of saturated absorption, the modeling performance was further improved. In validation, the root mean square error (SEP), correlation coefficient (RP) for prediction and the ratio of performance to deviation (RPD) were 1.66 mmol?L-1, 0.966 and 4.7, respectively. The results showed that the high-precision analysis of SUN was feasibility based on NIR spectroscopy and Norris-PLS. The global optimization method of NDF is also expected to be applied to other analysis objects.

Recent Advances in Global Optimization for Combinatorial Discrete Problems

The optimization of discrete problems is largely encountered in engineering and information domains. Solving these problems with continuous-variables approach then convert the continuous variables to discrete ones does not guarantee the optimal global solution. Evolutionary Algorithms (EAs) have been applied successfully in combinatorial discrete optimization. Here, the mathematical basics of real-coding Genetic Algorithm are presented in addition to three other Evolutionary Algorithms: Particle Swarm Optimization (PSO), Ant Colony Algorithms (ACOA) and Harmony Search (HS). The EAs are presented in as unifying notations as possible in order to facilitate understanding and comparison. Our combinatorial discrete problem example is the famous benchmark case of New-York Water Supply System WSS network. The mathematical construction in addition to the obtained results of Real-coding GA applied to this case study (authors), are compared with those of the three other algorithms available in literature. The real representation of GA, with its two operators: mutation and crossover, functions significantly faster than binary and other coding and illustrates its potential as a substitute to the traditional optimization methods for water systems design and planning. The real (actual) representation is very effective and provides two near-optimal feasible solutions to the New York tunnels problem. We found that the four EAs are capable to afford hydraulically-feasible solutions with reasonable cost but our real-coding GA takes more evaluations to reach the optimal or near-optimal solutions compared to other EAs namely the HS. HS approach discovers efficiently the research space because of the random generation of solutions in every iteration, and the ability of choosing neighbor values of solution elements “changing the diameter of the pipe to the next greater or smaller commercial diameter” beside keeping good current solutions. Our proposed promising point to improve the performance of GA is by introducing completely new individuals in every generation in GA using a new “immigration” operator beside “mutation” and “crossover”.

A New Filled Function with One Parameter to Solve Global Optimization

In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.

A global optimization algorithm based on multi-loop neural network control

This paper proposes an optimization algorithm based on a multi-loop control system with a neural network controller,in which the objective function that is used is the control plant of each sub-control system.To obtain the global optimization solution from a control plant that has many local minimum points,a transformation function is presented.On the one hand,this approach changes a complex objective function into a simple function under the condition of an unchanged globally optimal solution,to find the global optimization solution more easily by using a multi-loop control system.On the other hand,a special neural network(in which the node function can be simply positioned locally)that is composed of multiple transformation functions is used as the controller,which reduces the possibility of falling into local minimum points.At the same time,a filled function is presented as a control law;it can jump out of a local minimum point and move to another local minimum point that has a smaller value of the objective function.Finally,18 simulation examples are provided to show the effectiveness of the proposed method.

AN INTERVAL ALGORITHM FOR CONSTRAINED GLOBAL OPTIMIZATION

In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient.

Green’s Function Technique and Global Optimization in Reconstruction of Elliptic Objects in the Regular Triangle

The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.

An Algorithm for Global Optimization Using Formula Manupulation

Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively;this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.

A Multi-Strategy-Improved Northern Goshawk Optimization Algorithm for Global Optimization and Engineering Design

Optimization algorithms play a pivotal role in enhancing the performance and efficiency of systems across various scientific and engineering disciplines.To enhance the performance and alleviate the limitations of the Northern Goshawk Optimization(NGO)algorithm,particularly its tendency towards premature convergence and entrapment in local optima during function optimization processes,this study introduces an advanced Improved Northern Goshawk Optimization(INGO)algorithm.This algorithm incorporates a multifaceted enhancement strategy to boost operational efficiency.Initially,a tent chaotic map is employed in the initialization phase to generate a diverse initial population,providing high-quality feasible solutions.Subsequently,after the first phase of the NGO’s iterative process,a whale fall strategy is introduced to prevent premature convergence into local optima.This is followed by the integration of T-distributionmutation strategies and the State Transition Algorithm(STA)after the second phase of the NGO,achieving a balanced synergy between the algorithm’s exploitation and exploration.This research evaluates the performance of INGO using 23 benchmark functions alongside the IEEE CEC 2017 benchmark functions,accompanied by a statistical analysis of the results.The experimental outcomes demonstrate INGO’s superior achievements in function optimization tasks.Furthermore,its applicability in solving engineering design problems was verified through simulations on Unmanned Aerial Vehicle(UAV)trajectory planning issues,establishing INGO’s capability in addressing complex optimization challenges.

Multi-objective global optimization approach predicted quasi-layered ternary TiOS crystals with promising photocatalytic properties

Titanium dioxide(TiO_(2))has attracted considerable research attentions for its promising applications in solar cells and photocatalytic devices.However,the intrinsic challenge lies in the relatively low energy conversion efficiency of TiO_(2),primarily attributed to the substantial band gaps(exceeding 3.0 eV)associated with its rutile and anatase phases.Leveraging multi-objective global optimization,we have identified two quasi-layered ternary Ti-O-S crystals,composed of titanium,oxygen,and sulfur.The calculations of formation energy,phonon dispersions,and thermal stability confirm the chemical,dynamical and thermal stability of these newly discovered phases.Employing the state-of-art hybrid density functional approach and many-body perturbation theory(quasiparticle GW approach and Bethe-Salpeter equation),we calculate the optical properties of both the TiOS phases.Significantly,both phases show favorable photocatalytic characteristics,featuring band gaps suitable for visible optical absorption and appropriate band alignments with water for effective charge carrier separation.Therefore,ternary compound TiOS holds the potential for achieving high-efficiency photochemical conversion,showing our multi-objective global optimization provides a new approach for novel environmental and energy materials design with multicomponent compounds.

Swarm-Based Extreme Learning Machine Models for Global Optimization

Extreme Learning Machine(ELM)is popular in batch learning,sequential learning,and progressive learning,due to its speed,easy integration,and generalization ability.While,Traditional ELM cannot train massive data rapidly and efficiently due to its memory residence,high time and space complexity.In ELM,the hidden layer typically necessitates a huge number of nodes.Furthermore,there is no certainty that the arrangement of weights and biases within the hidden layer is optimal.To solve this problem,the traditional ELM has been hybridized with swarm intelligence optimization techniques.This paper displays five proposed hybrid Algorithms“Salp Swarm Algorithm(SSA-ELM),Grasshopper Algorithm(GOA-ELM),Grey Wolf Algorithm(GWO-ELM),Whale optimizationAlgorithm(WOA-ELM)andMoth Flame Optimization(MFO-ELM)”.These five optimizers are hybridized with standard ELM methodology for resolving the tumor type classification using gene expression data.The proposed models applied to the predication of electricity loading data,that describes the energy use of a single residence over a fouryear period.In the hidden layer,Swarm algorithms are used to pick a smaller number of nodes to speed up the execution of ELM.The best weights and preferences were calculated by these algorithms for the hidden layer.Experimental results demonstrated that the proposed MFO-ELM achieved 98.13%accuracy and this is the highest model in accuracy in tumor type classification gene expression data.While in predication,the proposed GOA-ELM achieved 0.397which is least RMSE compared to the other models.

A Filled Function with Adjustable Parameters for Unconstrained Global Optimization

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.

Electromagnetic Radiation Causes Weight Loss and Weight Destabilization of Objects with Presumed Elevated Levels of KELEA (Kinetic Energy Limiting Electrostatic Attraction), Relevance to Human Health and to Global Warming

A natural force has been proposed, which is required to prevent the fusion and disappearance of the discrete electrical charges that are present on electrostatically attached opposing electrical charges. This force may also explain the repulsion between objects with either matching positive or negative electrical charges. The energy of this force is referred to as KELEA (kinetic energy limiting electrostatic attraction). KELEA is especially attracted to dipolar compounds and to other materials with spatially separated opposite electrical charges. These compounds can be used to increase the level of KELEA in water. KELEA activated water can become an added source of KELEA for objects that are placed in close proximity to the water. It is generally held that the weight of an object is solely determined by its mass in relation to that of the earth. Yet, it was previously reported that the measured weight of certain KELEA attracting objects can undergo considerable variability over time. This observation is consistent with the concept that KELEA can contribute to the measured weight of certain objects. The present study strengthens this concept by demonstrating that the weight of cellulose containing materials, including paper, cotton fabrics, and wood, is increased if the materials are placed close to containers of KELEA activated water. It is further shown that electromagnetic radiation can significantly reduce the added weight of the KELEA exposed cellulose containing materials. Moreover, the previously added weight of the materials can be regained by replacing the materials back into the KELEA enhanced environment. It is proposed that the electrical charges that accompany electromagnetic radiation are able to competitively withdraw some of the KELEA from certain KELEA-enhanced objects. This effect can be reliably demonstrated using single sheets of writing paper, which are primarily composed of mechanically-bonded, branched cellulose fibers. There can be considerable fluctuations of the weight of the materials exposed to electromagnetic radiation after having been placed nearby to KELEA activated water. The weight instability is interpreted as being due to the electromagnetic radiation also triggering a dynamic process of rapid additions and removals of significant quantities of KELEA to and from objects. These observations are relevant to the further understanding of KELEA and to the potential health and climate consequences of manmade electromagnetic radiation causing a reduction in the environmental levels of KELEA.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization

In this paper, an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed algorithm is based on the Bernstein polynomial approach. Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point, modified rules for the selection of the subdivision direction, and a new acceleration device to avoid some unnecessary subdivisions. The performance of the proposed algorithm is numerically tested on a collection of 16 test problems. The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.

A new hybrid algorithm for global optimization and slope stability evaluation

A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

Global optimization of protein-peptide docking by a filling function method

Molecular docking programs play a crucial role in drug design and development. In recent years, much attention has been devoted to the protein-peptide docking problem in which docking of a flexible peptide with a known protein is sought. In this work we present a new docking algorithm which is based on the use of a filling function method for continuos constrained global optimization. Indeed, the protein-peptide docking position is sought by minimizing the conformational potential energy subject to constraints necessary to maintain the primary sequence of the given peptide. The resulting global optimization problem is difficult mainly for two reasons. First, the problem is large scale in constrained global optimization;second, the energy function is multivariate non-convex so that it has many local minima. The method is based on the device of modifying the original objective function once a local minimum has been attained by adding to it a filling term. This allows the overall algorithm to escape from local minima thus, ultimately, giving the algorithm ability to explore large regions in the peptide conformational space. We present numerical results on a set of benchmark docking pairs and comparison with the well-known software package for molecular docking PacthDock.

ANew Theoretical Framework forAnalyzing Stochastic Global Optimization Algorithms

In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.