Solving the Generalized Traveling Salesman Problem Using Sequential Constructive Crossover Operator in Genetic Algorithm

The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is highly expensive,we will develop genetic algorithms(GAs)to obtain heuristic solutions to the problem.In GAs,as the crossover is a very important process,the crossovermethods proposed for the traditional TSP could be adapted for the GTSP.The sequential constructive crossover(SCX)and three other operators are adapted to use in GAs to solve the GTSP.The effectiveness of GA using SCX is verified on some GTSP Library(GTSPLIB)instances first and then compared against GAs using the other crossover methods.The computational results show the success of the GA using SCX for this problem.Our proposed GA using SCX,and swap mutation could find average solutions whose average percentage of excesses fromthe best-known solutions is between 0.00 and 14.07 for our investigated instances.

A fast direct point-by-point generating algorithm for B Spline curves and surfaces

Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix trans- formation from B Spline representation to Bézier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.

A PROJECTION-TYPE ALGORITHM FOR SOLVING GENERALIZED MIXED VARIATIONAL INEQUALITIES

We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.

Architectures and Algorithms of Generalized Congruence Neural Networks

In this paper a novel class of neural networks called generalized congruence neural networks (GCNN) is proposed. All neurons in the neural networks are activated in the form of congruence. The architectures, learning rules and two algorithms are presented. Simulation results indicate that such network has satisfactory generalization properties near the sample points. Since this kind of neural nets can be easily operated and implemented, it is appropriate to make further research concerning the theory and applications of GCNN.

A ROBUST PHASE-ONLY DIRECT DATA DOMAIN ALGORITHM BASED ON GENERALIZED RAYLEIGH QUOTIENT OPTIMIZATION USING HYBRID GENETIC ALGORITHM

A robust phase-only Direct Data Domain Least Squares (D3LS) algorithm based on gen- eralized Rayleigh quotient optimization using hybrid Genetic Algorithm (GA) is presented in this letter. The optimization efficiency and computational speed are improved via the hybrid GA com- posed of standard GA and Nelder-Mead simplex algorithms. First, the objective function, with a form of generalized Rayleigh quotient, is derived via the standard D3LS algorithm. It is then taken as a fitness function and the unknown phases of all adaptive weights are taken as decision variables. Then, the nonlinear optimization is performed via the hybrid GA to obtain the optimized solution of phase-only adaptive weights. As a phase-only adaptive algorithm, the proposed algorithm is sim- pler than conventional algorithms when it comes to hardware implementation. Moreover, it proc- esses only a single snapshot data as opposed to forming sample covariance matrix and operating matrix inversion. Simulation results show that the proposed algorithm has a good signal recovery and interferences nulling performance, which are superior to that of the phase-only D3LS algorithm based on standard GA.

PROXIMAL POINT ALGORITHM WITH ERRORS FOR GENERALIZED STRONGLY NONLINEARQUASIVARIATIONAL INCLUSIONS

In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.

An Approach to Carbon Emissions Prediction Using Generalized Regression Neural Network Improved by Genetic Algorithm

The study on scientific analysis and prediction of China’s future carbon emissions is conducive to balancing the relationship between economic development and carbon emissions in the new era,and actively responding to climate change policy.Through the analysis of the application of the generalized regression neural network(GRNN)in prediction,this paper improved the prediction method of GRNN.Genetic algorithm(GA)was adopted to search the optimal smooth factor as the only factor of GRNN,which was then used for prediction in GRNN.During the prediction of carbon dioxide emissions using the improved method,the increments of data were taken into account.The target values were obtained after the calculation of the predicted results.Finally,compared with the results of GRNN,the improved method realized higher prediction accuracy.It thus offers a new way of predicting total carbon dioxide emissions,and the prediction results can provide macroscopic guidance and decision-making reference for China’s environmental protection and trading of carbon emissions.

Design of a Proportional-Integral-Derivative Controller for an Automatic Generation Control of Multi-area Power Thermal Systems Using Firefly Algorithm

Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is measured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control,automatic generation control(AGC) plays a crucial role. In this paper, multi-area(Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with proportional-integral-derivative(PID) controller as a supplementary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired firefly algorithm(FFA). The experimental results demonstrated the comparison of the proposed system performance(FFA-PID)with optimized PID controller based genetic algorithm(GAPID) and particle swarm optimization(PSO) technique(PSOPID) for the same investigated power system. The results proved the efficiency of employing the integral time absolute error(ITAE) cost function with one percent step load perturbation(1 % SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller.

Risk-sensitive reinforcement learning algorithms with generalized average criterion

A new algorithm is proposed, which immolates the optimality of control policies potentially to obtain the robnsticity of solutions. The robnsticity of solutions maybe becomes a very important property for a learning system when there exists non-matching between theory models and practical physical system, or the practical system is not static, or the availability of a control action changes along with the variety of time. The main contribution is that a set of approximation algorithms and their convergence results are given. A generalized average operator instead of the general optimal operator max （or rain） is applied to study a class of important learning algorithms, dynamic prOgramming algorithms, and discuss their convergences from theoretic point of view. The purpose for this research is to improve the robnsticity of reinforcement learning algorithms theoretically.

Forecasting and Evaluating the Efficiency of Test Generation Algorithms by Genetic Algorithm

To generate a test set for a given circuit (including both combinational and sequential circuits), choice of an algorithm within a number of existing test generation algorithms to apply is bound to vary from circuit to circuit. In this paper, the genetic algorithms are used to construct the models of existing test generation algorithms in making such choice more easily. Therefore, we may forecast the testability parameters of a circuit before using the real test generation algorithm. The results also can be used to evaluate the efficiency of the existing test generation algorithms. Experimental results are given to convince the readers of the truth and the usefulness of this approach.

Generalized Self-Adaptive Genetic Algorithms

In order to solve the problem between searching performance and convergence of genetic algorithms, a fast genetic algorithm generalized self-adaptive genetic algorithm (GSAGA) is presented. (1) Evenly distributed initial population is generated. (2) Superior individuals are not broken because of crossover and mutation operation for they are sent to subgeneration directly. (3) High quality im- migrants are introduced according to the condition of the population schema. (4) Crossover and mutation are operated on self-adaptation. Therefore, GSAGA solves the coordination problem between convergence and searching performance. In GSAGA, the searching per- formance and global convergence are greatly improved compared with many existing genetic algorithms. Through simulation, the val- idity of this modified genetic algorithm is proved.

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

STUDY ON STREAM CIPHERS USING GENERATING FUNCTIONS

Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.

An Improved Algorithm for the Solution of Generalized Burger-Fishers Equation

In this paper, an improved algorithm for the solution of Generalized Burger-Fisher’s Equation is presented. A Maple code is generated for the algorithm and simulated. It was observed that the algorithm gives the solution with less computation. The solution gives a better result when compared with the numerical solutions in the existing literature.

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

On Finding the Smallest Generalized Eigenpair Using Markov Chain Monte Carlo Algorithm

This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.

ONLINE REGULARIZED GENERALIZED GRADIENT CLASSIFICATION ALGORITHMS

This paper considers online classification learning algorithms for regularized classification schemes with generalized gradient. A novel capacity independent approach is presented. It verifies the strong convergence of sizes and yields satisfactory convergence rates for polynomially decaying step sizes. Compared with the gradient schemes, this al- gorithm needs only less additional assumptions on the loss function and derives a stronger result with respect to the choice of step sizes and the regularization parameters.

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.

Smoothing Newton Algorithm for Solving Generalized Complementarity Problem

The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.