In this paper we present a general formalism for the establishment of the family of selective partial update affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU partial rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms are established by this general formalism. In these algorithms, the filter coefficients are partially updated rather than the entire filter coefficients at every iteration which is computationally efficient. Following this, the transient and steady-state performance analysis of this family of adaptive filter algorithms are studied. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the performance of the presented algorithms through simulations in system identification and acoustic echo cancellation scenarios. The good agreement between theoretically predicted and actually observed performances is also demonstrated.

Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradient-like method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of a nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of the finite number of H ̈, older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands.

In this paper, we present some gradient projection algorithms for solving optimization problems with a convex-constrained set. We derive the optimality condition when the convex set is a cone and under some mild assumptions, we prove the convergence of these algorithms. Finally, we apply them to quadratic problems arising in training support vector machines for the Wisconsin Diagnostic Breast Cancer (WDBC) classification problem.

Engineering materials and structures have crack-like defects leading to premature failures. The usage of fracture mechanics to assess the structural integrity requires knowledge on the type, location, shape, size, and orientation of the flaws. Tomographic reconstruction is one of the commonly used nondestructive testing methods for flaw characterization. The cross sectional image of the object being tested is obtained through the application of various reconstruction methods that are categorized as either analytical methods or iterative methods. In this work, an iterative algorithm that works on the principles of genetic algorithms is developed and used for the reconstruction. The results of simulation studies on the tomographic reconstructions using genetic algorithms for the identification of defects in isotropic materials are discussed in the paper. The solution methodology based on the use of genetic algorithms is applied to reconstruct the cross sections of test specimens with different flaw characteristics. Simulated time-of-flight data of ultrasound rays transmitted through the specimen under investigation is used as input to the algorithm. The time-of-flight data is simulated neglecting the bending of ultrasound rays and assuming straight ray paths. Numerical studies performed on several specimens with flaws of known materials but unknown location, size and shape are presented. The number of ultrasonic transmitters and receivers needed for complete scanning of the specimen’ s cross section is analyzed and presented. The findings of the parametric analysis and sensitivity analysis in order to choose appropriate range of algorithm parameters for performance quality and robustness of the algorithm are presented. The performance of the present algorithm with noisy projection data is also discussed.

Since system identification of a tumor model is a primary need for controlling tumor model system, accessing suitable and applicable identification methods is a necessary object. In this paper, firstly, for estimating controlled auto-regressive moving average (CARMA) systems, two  identification methods, namely Generalized projection algorithm (GPA) and two-stage GPA (2S-GPA), are introduced and presented in order to estimate unknown parameters of a specific and vital tumor model. Furthermore, effectiveness of such methods, like convergence rate and estimation error, are discussed and considered. The introduced algorithms are simulated to prove these methods effectiveness, and data derived from the simulations are depicted through tables and figures.

This paper presents a genetic algorithm (GA) for solving a Generalized model of single-item resource constrained aggregate production planning (APP) with linear cost functions. APP belongs to a class of production planning problems in which there is a single production variable representing the total production of all products. We linearize a linear mixed-integer model of APP subject to hiring/firing of workforce, available regular/over time, and inventory/shortage/subcontracting allowable level where the total demand must fully be satisfied at end of the horizon planning. Due to NP-hard class of APP, the real-world sized problems cannot optimality be solved within a reasonable time. In this paper, we develop the proposed genetic algorithm with effective operators for solving the proposed model with an integer representation. This model is optimally solved and validated in small-sized problems by an optimization software package, in which the obtained results are compared with GA results. The results imply the efficiency of the proposed GA achieving to near optimal solutions within a reasonably computational time.