Optimal Portfolio Selection with Delay under the Framework of Uncertainty Theory

This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.

Interface Design and Functional Optimization of Chinese Learning Apps Based on User Experience

This research paper investigates the interface design and functional optimization of Chinese learning apps through the lens of user experience.With the increasing popularity of Chinese language learning apps in the era of rapid mobile internet development,users'demands for enhanced interface design and interaction experience have grown significantly.The study aims to explore the influence of user feedback on the design and functionality of Chinese learning apps,proposing optimization strategies to improve user experience and learning outcomes.By conducting a comprehensive literature review,utilizing methods such as surveys and user interviews for data collection,and analyzing user feedback,this research identifies existing issues in the interface design and interaction experience of Chinese learning apps.The results present user opinions,feedback analysis,identified problems,improvement directions,and specific optimization strategies.The study discusses the potential impact of these optimization strategies on enhancing user experience and learning outcomes,compares findings with previous research,addresses limitations,and suggests future research directions.In conclusion,this research contributes to enriching the design theory of Chinese learning apps,offering practical optimization recommendations for developers,and supporting the continuous advancement of Chinese language learning apps.

An Improved Harris Hawk Optimization Algorithm

Aiming at the problems that the original Harris Hawk optimization algorithm is easy to fall into local optimum and slow in finding the optimum,this paper proposes an improved Harris Hawk optimization algorithm(GHHO).Firstly,we used a Gaussian chaotic mapping strategy to initialize the positions of individuals in the population,which enriches the initial individual species characteristics.Secondly,by optimizing the energy parameter and introducing the cosine strategy,the algorithm's ability to jump out of the local optimum is enhanced,which improves the performance of the algorithm.Finally,comparison experiments with other intelligent algorithms were conducted on 13 classical test function sets.The results show that GHHO has better performance in all aspects compared to other optimization algorithms.The improved algorithm is more suitable for generalization to real optimization problems.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

THEOREMS OF PEANO'S TYPE FOR BIVARIATE FUNCTIONS AND OPTIMAL RECOVERY OF LINEAR FUNCTIONALS

The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

Hybrid Power Bank Deployment Model for Energy Supply Coverage Optimization in Industrial Wireless Sensor Network

Energy supply is one of the most critical challenges of wireless sensor networks(WSNs)and industrial wireless sensor networks(IWSNs).While research on coverage optimization problem(COP)centers on the network’s monitoring coverage,this research focuses on the power banks’energy supply coverage.The study of 2-D and 3-D spaces is typical in IWSN,with the realistic environment being more complex with obstacles(i.e.,machines).A 3-D surface is the field of interest(FOI)in this work with the established hybrid power bank deployment model for the energy supply COP optimization of IWSN.The hybrid power bank deployment model is highly adaptive and flexible for new or existing plants already using the IWSN system.The model improves the power supply to a more considerable extent with the least number of power bank deployments.The main innovation in this work is the utilization of a more practical surface model with obstacles and training while improving the convergence speed and quality of the heuristic algorithm.An overall probabilistic coverage rate analysis of every point on the FOI is provided,not limiting the scope to target points or areas.Bresenham’s algorithm is extended from 2-D to 3-D surface to enhance the probabilistic covering model for coverage measurement.A dynamic search strategy(DSS)is proposed to modify the artificial bee colony(ABC)and balance the exploration and exploitation ability for better convergence toward eliminating NP-hard deployment problems.Further,the cellular automata(CA)is utilized to enhance the convergence speed.The case study based on two typical FOI in the IWSN shows that the CA scheme effectively speeds up the optimization process.Comparative experiments are conducted on four benchmark functions to validate the effectiveness of the proposed method.The experimental results show that the proposed algorithm outperforms the ABC and gbest-guided ABC(GABC)algorithms.The results show that the proposed energy coverage optimization method based on the hybrid power bank deployment model generates more accurate results than the results obtained by similar algorithms(i.e.,ABC,GABC).The proposed model is,therefore,effective and efficient for optimization in the IWSN.

A New Evolutionary Algorithm for Function Optimization

A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.

Ant colony optimization algorithm and its application to Neuro-Fuzzy controller design

An adaptive ant colony algorithm is proposed based on dynamically adjusting the strategy of updating trail information. The algorithm can keep good balance between accelerating convergence and averting precocity and stagnation. The results of function optimization show that the algorithm has good searching ability and high convergence speed. The algorithm is employed to design a neuro-fuzzy controller for real-time control of an inverted pendulum. In order to avoid the combinatorial explosion of fuzzy rules due tσ multivariable inputs, a state variable synthesis scheme is employed to reduce the number of fuzzy rules greatly. The simulation results show that the designed controller can control the inverted pendulum successfully.

Adaptive immune-genetic algorithm for global optimization to multivariable function

An adaptive immune-genetic algorithm （AIGA） is proposed to avoid premature convergence and guarantee the diversity of the population. Rapid immune response （secondary response）, adaptive mutation and density operators in the AIGA are emphatically designed to improve the searching ability, greatly increase the converging speed, and decrease locating the local maxima due to the premature convergence. The simulation results obtained from the global optimization to four multivariable and multi-extreme functions show that AIGA converges rapidly, guarantees the diversity, stability and good searching ability.

Two-Phase Genetic Algorithm Applied in the Optimization of Multi-Modal Function

This paper presents a two-phase genetic algorithm (TPGA) based on the multi- parent genetic algorithm (MPGA). Through analysis we find MPGA will lead the population' s evol vement to diversity or convergence according to the population size and the crossover size, so we make it run in different forms during the global and local optimization phases and then forms TPGA. The experiment results show that TPGA is very efficient for the optimization of low-dimension multi-modal functions, usually we can obtain all the global optimal solutions.

Dipper Throated Optimization Algorithm for Unconstrained Function and Feature Selection

Dipper throated optimization(DTO)algorithm is a novel with a very efficient metaheuristic inspired by the dipper throated bird.DTO has its unique hunting technique by performing rapid bowing movements.To show the efficiency of the proposed algorithm,DTO is tested and compared to the algorithms of Particle Swarm Optimization(PSO),Whale Optimization Algorithm(WOA),Grey Wolf Optimizer(GWO),and Genetic Algorithm(GA)based on the seven unimodal benchmark functions.Then,ANOVA and Wilcoxon rank-sum tests are performed to confirm the effectiveness of the DTO compared to other optimization techniques.Additionally,to demonstrate the proposed algorithm’s suitability for solving complex realworld issues,DTO is used to solve the feature selection problem.The strategy of using DTOs as feature selection is evaluated using commonly used data sets from the University of California at Irvine(UCI)repository.The findings indicate that the DTO outperforms all other algorithms in addressing feature selection issues,demonstrating the proposed algorithm’s capabilities to solve complex real-world situations.

A Parallel Global-Local Mixed Evolutionary Algorithm for Multimodal Function Optimization Based on Domain Decomposition

This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.

Artificial bee colony algorithm with comprehensive search mechanism for numerical optimization

The artificial bee colony （ABC） algorithm is a sim- ple and effective global optimization algorithm which has been successfully applied in practical optimization problems of various fields. However, the algorithm is still insufficient in balancing ex- ploration and exploitation. To solve this problem, we put forward an improved algorithm with a comprehensive search mechanism. The search mechanism contains three main strategies. Firstly, the heuristic Gaussian search strategy composed of three different search equations is proposed for the employed bees, which fully utilizes and balances the exploration and exploitation of the three different search equations by introducing the selectivity probability P,. Secondly, in order to improve the search accuracy, we propose the Gbest-guided neighborhood search strategy for onlooker bees to improve the exploitation performance of ABC. Thirdly, the self- adaptive population perturbation strategy for the current colony is used by random perturbation or Gaussian perturbation to en- hance the diversity of the population. In addition, to improve the quality of the initial population, we introduce the chaotic opposition- based learning method for initialization. The experimental results and Wilcoxon signed ranks test based on 27 benchmark func- tions show that the proposed algorithm, especially for solving high dimensional and complex function optimization problems, has a higher convergence speed and search precision than ABC and three other current ABC-based algorithms.

MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.

Optimization of the Dressing Parameters in Cylindrical Grinding Based on a Generalized Utility Function

The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on the experience of the qualified staff or using data from reference books. The optimal dressing parameters, which are only valid for the particular methods and dressing and grinding conditions, are also used. The paper presents a methodology for optimization of the dressing parameters in cylindrical grinding. The generalized utility function has been chosen as an optimization parameter. It is a complex indicator determining the economic, dynamic and manufacturing characteristics of the grinding process. The developed methodology is implemented for the dressing of aluminium oxide grinding wheels by using experimental diamond roller dressers with different grit sizes made of medium- and high-strength synthetic diamonds type AC32 and AC80. To solve the optimization problem, a model of the generalized utility function is created which reflects the complex impact of dressing parameters. The model is built based on the results from the conducted complex study and modeling of the grinding wheel lifetime, cutting ability, production rate and cutting forces during grinding. They are closely related to the dressing conditions （dressing speed ratio, radial in-feed of the diamond roller dresser and dress-out time）, the diamond roller dresser grit size/grinding wheel grit size ratio, the type of synthetic diamonds and the direction of dressing. Some dressing parameters are determined for which the generalized utility fimction has a maximum and which guarantee an optimum combination of the following： the lifetime and cutting ability of the abrasive wheels, the tangential cutting force magnitude and the production rate of the grinding process. The results obtained prove the possibility of control and optimization of grinding by selecting particular dressing parameters.

Modified coupled map car-following model and its delayed feedback control scheme

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no traffic jam is derived. A new control scheme is presented to suppress the traffic jam in the modified coupled map car-following model under the open boundary. A control signal including the velocity differences between the following and the considering vehicles, and between the preceding and the considering vehicles is used. The condition under which the traffic jam can be well suppressed is analysed. The results are compared with that presented by t^onishi et al. （the KKH model）. The simulation results show that the temporal behaviour obtained in our model is better than that in the KKH model. The simulation results are in good agreement with the theoretical analysis.

Family genetic algorithms based on gene exchange and its application

Genetic Algorithms （GA） are a search techniques based on mechanics of nature selection and have already been successfully applied in many diverse areas. However, increasing samples show that GA＇s performance is not as good as it was expected to be. Criticism of this algorithm includes the slow speed and premature result during convergence procedure. In order to improve the performance, the population size and individuals＇ space is emphatically described. The influence of individuals＇ space and population size on the operators is analyzed. And a novel family genetic algorithm （FGA） is put forward based on this analysis. In this novel algorithm, the optimum solution families closed to quality individuals is constructed, which is exchanged found by a search in the world space. Search will be done in this microspace. The family that can search better genes in a limited period of time would win a new life. At the same time, the best gene of this micro space with the basic population in the world space is exchanged. Finally, the FGA is applied to the function optimization and image matching through several experiments. The results show that the FGA possessed high performance.