On properties of one functional used in software constructions for solving differential games

Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.

Mechanism of band gaps in self-similar triangular lattice with Koch fractal

Fractal lattice is a kind of lattices with multifunctional physical characteristics and superior mechanical properties. The wave propagation of the triangular lattice with Koch fractal is calculated by the finite element method and Bloch theorem. The effects of the iteration number on the band gaps and the band edge modes are studied. The finite element software was used to simulate the dynamic response of the triangular lattice with Koch fractal for verifying the vibration suppression performance. The results show that the triangular lattice with Koch fractal can produce multiple and low-frequency band gaps. As an increase of the iteration number, the band gap gradually shifts to a lower frequency. By comparing and analyzing the band edge modes and the eigenmodes of Koch fractal, the mechanisms of the band gaps within the low-frequency ranges are analyzed and discussed in detail. Additionally, the band edge modes exhibit similar vibration modes. Finally, the simulation results of the finite lattice verify the broadband vibration suppression performance of the triangular lattice with Koch fractal. This work provides insights into the lattice dynamic behavior adjusted by Koch fractal, which is beneficial to the periodic lattice for suppressing vibration in engineering applications.

The effect of maximum iteration using 3 dimensional limit equilibrium method in open pit mine

Nickel ore mines have a high potential of landslides due to their weak material base, which consists of soil. It is caused by the increase of soil density in rain conditions, leading to decreased soil shear strength (c) and internal friction angle (ϕ). This research aims to determine the optimum value of the maximum iteration number based on the Cuckoo Search and Particle Swarm Optimization search method. In this research, the slope is analyzed using the 3 Dimensional limit equilibrium method “Simplified Bishop,” a slope stability analysis method that uses the principle of static equilibrium. Alongside this method, the Cuckoo Search and Particle Swarm Optimization is adopted. The Cuckoo Search and Particle Swarm Optimization are metaheuristic optimization techniques used as the slipped surface search method. Series of 3-dimensional limit equilibrium computation is performed using different amounts of nests in the cuckoo search method and different particle values and maximum iteration number. Cuckoo Search method to achieve optimal nest 100 and iteration of 80 with the fastest compute time of 3 minutes 49 seconds. While the Particle Swarm Optimization to achieve optimal on particles 60, iteration as much as 480 with a compute time of 6 minutes 46 second, with a factor of safety value of 1,12.

A Cuckoo Search Algorithm Using Improved Beta Distributing and Its Application in the Process of EDM

Lévy flights random walk is one of key parts in the cuckoo search (CS) algorithm to update individuals. The standard CS algorithm adopts the constant scale factor for this random walk. This paper proposed an improved beta distribution cuckoo search (IBCS) for this factor in the CS algorithm. In terms of local characteristics, the proposed algorithm makes the scale factor of the step size in Lévy flights showing beta distribution in the evolutionary process. In terms of the overall situation, the scale factor shows the exponential decay trend in the process. The proposed algorithm makes full use of the advantages of the two improvement strategies. The test results show that the proposed strategy is better than the standard CS algorithm or others improved by a single improvement strategy, such as improved CS (ICS) and beta distribution CS (BCS). For the six benchmark test functions of 30 dimensions, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 3.67, 2.67, 1.5, and 1.17, respectively. For the six benchmark test functions of 50 dimensions, moreover, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 2.83, 2.5, 1.67, and 1.0, respectively. Confirmed by our case study, the performance of the ABCS algorithm was better than that of standard CS, ICS or BCS algorithms in the process of EDM. For example, under the single-objective optimization convergence of MRR, the iteration number (13 iterations) of the CS algorithm for the input process parameters, such as discharge current, pulse-on time, pulse-off time, and servo voltage, was twice that (6 iterations) of the IBCS algorithm. Similar, the iteration number (17 iterations) of BCS algorithm for these parameters was twice that (8 iterations) of the IBCS algorithm under the single-objective optimization convergence of Ra. Therefore, it strengthens the CS algorithm’s accuracy and convergence speed.

MANAGEMENT OF THE OPTIMIZATION ALGORITHM ON THE BASIS OF MODELING ARTIFICIAL IMMUNE SYSTEM

The efficiency improvement of the known optimization algorithm based on modeling of the artificial immune system due to the adaptive population compression operator is proposed. The radius of similarity of individuals, which is responsible for whether they can be represented in the next generation, is proposed to be proportional to the radius of mutation of cells - search agents. In this case, the radius of the mutation, and accordingly the radius of similarity proportional to it, should gradually decrease during the operation of the algorithm, in accordance with the optimal solution achievement and proportionally to the iteration number. The proposed approach was tested on a number of problems in real and binary space. The results of solving the test problems showed the high efficiency of the proposed algorithmic approach.

Development of a Numerical Model for Vibration Analysis of Low Folded Shells under Dynamic Actions

In this work a numerical model is developed for vibration analysis of low folded shells under dynamic actions. At first it is done to describe the used finite element discrete model based on Lagrange variational principles. To solve the eigen value problem of these structures a numerical algorithm is proposed using Householder's QR-iteration transformations. This method provides a tridiagonal matrix whose eigen values coincide with those of the initial matrix and significantly reduces the iteration number compared to the Lanczos method. Implementation of the method is carried out on seven folded shell mathematical models. Obtained results show that accuracy can be improved and computational time can be significantly reduced compared to the methods available in the technical literature for this class of problems.

Analyzing Decomposition Procedures in LP and Unraveling for the Two Person Zero Sum Game and Transportation Problems

This paper studies some decomposition methods, including Dantzig-Wolfe decomposition (DWD), decomposition-based pricing (DBP), Benders decomposition (BD), and a recently proposed improved decomposition (ID) method for solving linear programs (LPs). The authors then develop a new decomposition algorithm for solving LPs in a general form, allowing authors to combine the concept of Benders decomposition and decomposition-based pricing methods. The authors generate conditions for solving problems that have either infeasible or unbounded solutions. As an illustration, the authors give the corresponding models and numerical results for two standard mathematical programs: the two-person zero-sum game and the transportation problem. The authors compare several procedures and identify which one produces the best solution by giving the authors the smallest iteration number. This study reveals that the algorithm along with Benders decomposition produce the most efficient computational solutions of LPs.