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Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problems is to combine sampling methods with optimal search methods. Sampling techniques have a serious problem when the sample size is small, so estimating the objective function values with noise is not accurate in this case. In this research, a new sampling technique is proposed based on fuzzy logic to deal with small sample sizes. Then, simulation-based optimization methods are designed by combining the estimation of distribution algorithms with the proposed sampling technique and other sampling techniques to solve the stochastic programming problems. Moreover, additive versions of the proposed methods are developed to optimize functions without noise in order to evaluate different efficiency levels of the proposed methods. In order to test the performance of the proposed methods, different numerical experiments were carried out using several benchmark test functions. Finally, three real-world applications are considered to assess the performance of the proposed methods.

This paper focuses on presenting an accurate, efficient, and fast pseudospectral method to solve tempered fractional differential equations (TFDEs) in both spatial and temporal dimensions. We use a tempered integration matrix that can be employed to evaluate 𝑛-fold tempered integrals of a real function 𝑔 for 𝑛 ∈ ℝ + . Also, it may be used to compute any non-integer order 𝜆 < 0 tempered derivatives of 𝑔. We employ the Chebyshev interpolating polynomial for 𝑔 at Gauss-Lobatto (GL) points in the range [−1, 1] and any identically shifted range. The proposed method carries with it a recast of the TFDE into integration formulas to actually take advantage of the adaptation of the integral operators, hence avoiding the ill-conditioning and reduction in the convergence rate of integer differential operators. Via various tempered fractional differential examples, the present technique shows many advantages, for instance, high accuracy, a much higher rate of running, fewer computational hurdles and programming, calculating the tempered-derivative/integral of fractional order and its exceptional accuracy in comparison with other competitive numerical schemes. The study includes the elapsed times taken to construct the collocation matrices and obtain the numerical solutions. Also, numerical examination of the produced condition number 𝜅(𝐴) of the resulted linear systems. The accuracy and efficiency of the proposed method are studied from the standpoint of the 𝐿 2 and 𝐿 ∞ -norms error and fast rate of spectral convergence.

Brain Storm Optimization (BSO) is one of the major effective swarm intelligence algorithms that simulate the human brainstorming process to find optimality for optimization problems. BSO method has successfully been applied to many real-world problems. This study employs BSO method, called BSO-IP, to solve the integer programming problem. Our method collects best solutions to generate new solutions that then search for optimal solutions in all areas of search space.The BSO-IP method solves some benchmark integer programming problems to test its efficiency. The BSO-IP is used to simulate the 3D protein structure prediction problem, which is mathematically presented as an integer programming problem to approve the viability and helpfulness of our proposed Algorithm. The experimental results of different benchmarks protein structure show that our proposed method is superior in high performance, convergence, and stability in predicting protein structure. We examined our strategy results to be promising compared to other results.