Earticle

In this paper, a hybrid method is proposed to design an air-core superconducting solenoid system for 6 T axial uniform magnetic field using Niobium Titanium (NbTi) superconducting wire. In order to minimize the volume of conductor, the hybrid optimization method including a linear programming and a nonlinear programming was adopted. The feasible space of solenoid is divided by several grids and the magnetic field at target point is approximated by the sum of magnetic field generated by an ideal current loop at the center of each grid. Using the linear programming, a global optimal current distribution in the feasible space can be indicated by non-zero current grids. Furthermore the clusters of the non-zero current grids also give the information of probable solenoids in the feasible space, such as the number, the shape, and so on. Applying these probable solenoids as the initial model, the final practical configuration of solenoids with integer layers can be obtained by the nonlinear programming. The design result illustrates the efficiency and the flexibility of the hybrid method. And this method can also be used for the magnet design which is required the high homogeneity within several ppm (parts per million).

This article is based on the mixture of tabu search algorithm and interior search algorithm(ISA) to address the reliability redundancy assignment problem. Iinterior search algorithm is immersed in a tabu search algorithm. TS is used to search solution space and ISA is applied to generate neighborhood solutions. The merit of two algorithms is considered at the same time. And a mixed TS-ISA method is proposed to deal with three benchmark reliability redundancy optimization problem. The experimental results show that a the method is effective and efficient for RRAP by comparing with other results in the previous literaturs.

The bat algorithm is a recently proposed meta-heuristic algorithm. Usually in solving the problem of optimization, the position of virtual bats is updated by flying speed, which decreases efficiency of the algorithm and accuracy of the solution. This paper has improved the location update strategy and individual selection strategy of bat algorithm, then puts forward an improved bat algorithm. The algorithm is used to solve three typical reliability-redundancy allocation problems, and the simulation experiment results show that the presented algorithm greatly enhances the computation efficiency, convergence speed and precision of the optimal solution in addressing the problem of reliability redundancy optimization. When compared with the best results reported in the previous literatures, the algorithm achieves a better or equally good optimal solution. It is demonstrated that the proposed algorithm is effective in solving reliability-redundancy allocation problems.

In this paper, a differential evolution (DE) algorithm combined with Lévy flight is proposed to solve the reliability redundancy allocation problems. The Lévy flight is incorporated to enhance the ability of global search of differential evolution algorithm. DE is used for local search mainly. The method considers the trade-off of the diversification and the intensification simultaneously. Experimental results for three benchmark problems demonstrate that the proposed algorithm is more effective for solving the reliability redundancy allocation problems.

A new algorithm combined Eagle Strategy with PSO is proposed. The new algorithm performs by two phases: First Eagle Strategy is used to do global search; Second PSO algorithm is used to do fast local search around a promising solution. The balance of global search and local search is considered simultaneously. It is not only help to jump out of local optimum but also accelerate local convergence. Experimental results on three benchmark problems illustrate that the presented approach is effective, efficient and accurate for solving reliability redundancy optimization problems.

Localization is used in location-aware applications such as navigation, autonomous robotic movement, and asset tracking to position a moving object on a coordinate system. In this paper, a Nonlinear Programming algorithm is proposed based on RSSI and improved DV-Hop algorithm, called NPRDV-Hop. The algorithm makes four major contributions to the localization problem in the wireless sensor networks (WSNs). Firstly, a hop distance is improved, called Hop Distance. This scheme could assure that the most nodes receive the Hop Distance from beacon node who has the least hops between them. This practical localization scheme is relatively high accuracy and low cost for WSNs. Secondly, Heron's formula is introduced as objective function. Thirdly, Gauss distribution is introduced to select RSSI so that the error of distance is little. Lastly, the general problem is considered by the nonlinear programming to solve for the locations of the sensors. Simulation results show that the proposed method can improve location accuracy and coverage without increasing hardware cost of sensor node. The performance of this algorithm is superior to the original DV-Hop algorithm.

It has been deemed as an effective tool of forecasting performance improvement to combine different component forecasting models. However, current nonlinear combining models are not able to meet the requirement of high forecasting accuracy in practice. To tackle this challenge, this paper constructs a hybrid, named genetic programming and least squared estimation based nonlinear combining method (GPLSE-NC), of a standard genetic programming (GP) algorithm and the least square estimation (LSE) method, based on which a new nonlinear combined forecasting model is proposed. To verify the feasibility of the proposed model, based on the container throughput data of Shanghai Port from January 2004 to November 2015, 4 different forecasting models are constructed and compared with the proposed GPLSE-NC combining model in terms of three forecasting performance evaluation criteria. The empirical results show significant superiority of the GPLSE-NC model over its rivals, which reveals that the proposed model has a great potential to be a powerful nonlinearly combine forecasting approach.

The concept of criterion function is proposed as a framework for comparing the geometric and computational characteristics of various nonlinear programming approaches to linear programming such as the method of centers, Karmakar's algorithm and the gravitational method. Also, we discuss various computational issues involved in obtaining an efficient parallel implementation of these methods. Clearly, the most time consuming part in solving a linear programming problem is the direction finding procedure, where we obtain an improving direction. In most cases, finding an improving direction is equivalent to solving a simple optimization problem defined at the current feasible solution. Again, this simple optimization problem can be seen as a least squares problem, and the computational effort in solving the least squares problem is, in fact, same as the effort as in solving a system of linear equations. Hence, getting a solution to a system of linear equations fast is very important in solving a linear programming problem efficiently. For solving system of linear equations on parallel computing machines, an iterative method seems more adequate than direct methods. Therefore, we propose one possible strategy for getting an efficient parallel implementation of an iterative method for solving a system of equations and present the summary of computational experiment performed on transputer based parallel computing board installed on IBM PC.

In this paper, we establish a nonlinear Lagrangian algorithm for nonlinear programming problems with inequality constraints. Under some assumptions, it is proved that the sequence of points, generated by solving an unconstrained programming, convergents locally to a Kuhn-Tucker point of the primal nonlinear programming problem.

When a Sequential Quadratic Programming (SQP) method is used to solve the nonlinear programming problems, one of the main difficulties is that the Quadratic Programming (QP) subproblem may be incompatible. In this paper, an SQP algorithm is given by modifying the traditional QP subproblem and applying a class of $l_{\infty}$ penalty function whose penalty parameters can be adjusted automatically. The new QP subproblem is compatible. Under the extended Mangasarian-Fromovitz constraint qualification condition and the boundedness of the iterates, the algorithm is showed to be globally convergent to a KKT point of the non-linear programming problem.

In this paper, a new nonlinear programming approach is suggested to solve biaffine matrix inequality (BMI) problems in multiobjective and structured controls. It is shown that these BMI problems are reduced to nonlinear minimization problems. An algorithm that is easily implemented with existing convex optimization codes is presented for the nonlinear minimization problem. The efficiency of the proposed algorithm is illustrated by numerical examples.

We formulated the multi-robot trajectory problem into a series of NLP problem, each of which is that of finding the optimal tip positions of the robots for the next time step. The NLP problem is composed of an objective function and three constraints, namely: a) Joint position limits, b) Joint velocity limits, and c) Collision-avoidance constraints. By solving a series of NLP problem, optimally coordinated trajectories can be determined without requiring any prior path information. This is a novel departure from the previous approach in which either all paths or at least one path is assumed to be given. Practical application of the developed method is for optimal synthesis of multiple robot trajectories in off-line. To test the validity and effectiveness of the method, numerical examples are illustrated.

We show how some probability nonreplacement sampling designs can be implemented using nonlinear programming, The efficiency of the proposed approach is compared with selected probability sampling schemes in the literature. The approach is simple to use and appears to have reasonable variance.

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

A dual algorithm based on the smooth function proposed by Polyak (1988) is constructed for solving nonlinear programming problems with inequality constraints. It generates a sequence of points converging locally to a Kuhn-Tucker point by solving an unconstrained minimizer of a smooth potential function with a parameter. We study the relationship between eigenvalues of the Hessian of this smooth potential function and the parameter, which is useful for analyzing the effectiveness of the dual algorithm.

This paper deals with an algorithm for solving nonlinear programming problems with equality constraints. Nonlinear programming problems are transformed into a square sums of nonlinear functions by the Lagrangian multiplier method. And an iteration method minimizing this square sums is suggested and then an algorithm is proposed. Also theoretical basis of the algorithm is presented.