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In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

In order to improve performance robustness of control systems, the discrete variable structure control (VSC) design for uncertain systems and its application to a ship autopilot are to be discussed in this paper.

Discrete‐time variable structure control (DVSC) becomes worth investigating and various DVSC methods have been suggested by many papers. The approach that used the reaching law for controller design can describe how the switching function decreases toward zero and easier to obtain the control law, but this conventional method has some defects not to be ignored. First, due to the influence of the conventional discrete reaching law itself, the system trajectory oscillates in a neighborhood of the origin rather than converges to the origin. Second, this method requires that the uncertainty bound is known as a premise to assure robustness, so creates an over‐conservative controller and enlarges chattering.

It can be shown that the estimation error dynamics can be decoupled from sliding surface dynamics using the proposed scheme. Robust stability of the closed‐loop system can be ensured in the presence of uncertainties with bounded changing rate. No chattering occurs.

To supply useful references to controller design.

A new approach in the design of discrete VSC based on the reaching law approach is presented, a new discrete reaching law, which is stable at the origin, is proposed, and an algorithm for uncertainty estimation is developed in this paper. The proposed algorithm is applied to the control of a ship autopilot servo system. Simulation results show that the controller designed here can track a desired course well and exhibits very good performance robustness.

The purpose of this paper is to overcome the shortcoming that discrete variable structure control (VSC) system trajectory oscillates in a neighborhood of the origin.

Among all the proposed reaching laws, W. Gao's theory is most perfect. It makes great progress in revealing the motion mechanism of discrete‐time VSC systems. However, it has an obvious defect, i.e. the system trajectory oscillates in a neighborhood of the origin rather than converges to the origin. So, a new reaching law named variable rate reaching law to which the stability at the origin can be expected is proposed. The special feature of this new reaching law is that it is directly proportional to the norm of the state vector and can result in a sector‐shaped switching region. On the basis of analyzing the characteristic of the variable rate and the conventional reaching laws, a new combined control algorithm that discards the shortcomings of the two reaching laws and carries on their merits is formed, so satisfactory control performance can be achieved.

A new combined reaching law control algorithm, which uses the exponential rate reaching law in the reaching mode and in the front phase of the sliding mode, and uses the variable rate reaching law in the back phase of the sliding mode and in the steady‐state mode, is formed.

The paper is a very useful reference for control system designers.

The new control strategy is applied to the controller design for a brushless DC servomotor and good control performance is obtained.

Much work has been done on the optimization of the discrete variable structure design. In order to handle the optimization problem effectively, the related theories, methods, and other beneficial results were summarized. On the basis of analyzing the predecessors' research, the development direction was introduced. Then, some practical methods, including their improvements, for discrete structural optimization were analyzed. Finally, the Ant Colony Optimization algorithms were shown as promising methods. This work has significance in theory and practice for the development of structural optimization.

This paper aims to present the optimum two-plane discrete balancing procedure for rigid rotor. The discrete two-plane balancing in which rotor is balanced to minimize the residual effects or the reactions on the bearing supports using discrete parameters such as masses and their angular positions on two balancing planes.

Therefore as a multi-objective optimization problem is formulated by considering reaction forces on the bearing supports as a multi objective functions and discrete parameters on each balancing plane as design variables. These multi-objective functions are converted into a single-objective function using appropriate weighting factors. Further, this optimization problem is solved using discrete optimization algorithm, based on Jaya algorithm.

The performance of the discrete Jaya algorithm is compared to genetic algorithm (GA) algorithm. It is found that Jaya algorithm is computationally more efficient than GA algorithm. A number of masses per plane are used to balance the rotor. A comparison of reaction forces using number of masses per plane is investigated.

The effectiveness of the proposed methodology is tested by the balancing problem of rotor available in the literature. The influence of a number of balance masses on bearing forces and objective function are discussed. ADAMS software is used for validation of a developed balancing approach.

Layout optimization of structures aims to find the optimal topology and member sizes in an integrated manner. For this purpose, the most successful attempts have addressed the outstanding features of the genetic algorithms.

This paper utilizes a direct index coding (DIC) in a way that the optimization algorithm can simultaneously integrate topology and size in a minimal length chromosome in order to seek the true optimum in an efficient and reasonable manner. Proper genetic operators are adopted for this special kind of encoding together with some modifications in the topological mutation aiming to improve the convergence of the algorithm.

The present DIC, has the following features: enforcing one‐to‐one correspondence between discrete genotype space and the problems' phenotype space; avoiding any out‐of‐bound parameter addressing and limiting the GA search only to necessary genotypes; reduction in the size of genotype search space to increase the algorithm convergence and the possibility of leading to the global optimum; dealing with direct genetic operators so that the GA parameters can be purely controlled to tune the desired balance between convergence and escaping from local optima.

Employing direct index chromosome makes it possible to eliminate the additional topological bits in treated examples.

The purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete‐time domain for robot manipulators.

First, a discrete linear sliding mode controller is designed to an n‐link robot based on Gao's reaching law. In the second step, a discrete terminal sliding mode controller is developed to design a finite time and high precision controller. The stability analysis of both controllers is presented in the presence of model uncertainties and external disturbances. Finally, sampling time effects on the continuous‐time system outputs and sliding surfaces are discussed.

Computer simulations on a three‐link SCARA robot show that the proposed controllers are robust against model uncertainties and external disturbance. It was also shown that the sampling time has important effects on the closed loop system stability and convergence.

The proposed controllers are low cost and easily implemented in practice in comparison with continuous‐time ones.

The novelty associated with this paper is the development of an approach to finite time and robust control of n‐link robot manipulators in discrete‐time domain. Also, obtaining an upper bound for the sampling time is another contribution of this work.

This paper aims to present a new hybrid algorithm of Particle Swarm Optimization and the Genetic Algorithm (PSOGA) to optimize the space trusses with continuous design variables. The PSOGA is an efficient hybridized algorithm to solve optimization problems.

These algorithms have shown outstanding performance in solving optimization problems with continuous variables. The PSO conceptually models the social behavior of birds, in which individual birds exchange information about their position, velocity and fitness. The behavior of a flock is influencing the probability of migration to other regions with high fitness. The GAs procedure is based on the mechanism of natural selection. The present study uses mutation, random selection and reproduction to reach the best genetic algorithm by the operators of natural genetics. Thus, only identical chromosomes or particles can be converged.

In this research, using the idea of hybridization PSO and GA algorithms are hybridized and a new meta-heuristic algorithm is developed to minimize the space trusses with continuous design variables. To showing the efficiency and robustness of the new algorithm, several benchmark problems are solved and compared with other researchers.

The results indicate that the hybrid PSO algorithm improved in both exploration and exploitation. The PSO algorithm can be used to minimize the weight of structural problems under stress and displacement constraints.

The purpose of this paper is to investigate the mechanical properties’ behaviors of woven composite cut-out structures with specific parameters. Because of the complexity of micro-scale and meso-scale structure, it is difficult to accurately predict the mechanical material behavior of woven composites. Numerical simulations are increasingly necessary for the design and optimization of test procedures for composite structures made by the woven composite. The results of the proposed method are well satisfied with the results obtained from the experiment and other studies. Moreover, parametric studies on different plates based on the stacking sequences are investigated.

A multi-scale modeling approach is suggested. Back-propagation neural networks (BPNN), radial basis function (RBF) and least square support vector regression are integrated with efficient global optimization (EGO) to reduce the weight of assigned structure. Optimization results are verified by finite element analysis.

Compared with other similar studies, the advantage of the suggested strategy uses homogenized properties behaviors with more complex analysis of woven composite structures. According to investigation results, it can be found that 450/−450 ply-orientation is the best buckling load value for all the cut-out shape requirements. According to the optimal results, the BPNN-EGO is the best candidate for the EGO to optimize the woven composite structures.

A multi-scale approach is used to investigate the mechanical properties of a complex woven composite material architecture. Buckling of different cut-out shapes with the same area is surveyed. According to investigation, 45°/−45° ply-orientation is the best for all cut-out shapes. Different surrogate models are integrated in EGO for optimization. The BPNN surrogate model is the best choice for EGO to optimization difficult problems of woven composite materials.

The paper deals with robustness to plant parameter perturbations and sensitivity to disturbances of two‐loop control structures containing a model of the controlled plant and two PID controllers. Special attention is paid to high robustness of considered structure to perturbations of the controlled plant in relation to its nominal model and to good reduction of disturbances. On the basis of presented simulation results one can compare properties of the proposed structure with properties of the Smith predictor and classic control system structure with single feedback loop. The proposed model following control structures may find wide application to robust control of parameter‐varying plants.