Economic Load Dispatch (ELD) is an important part of cost minimization procedure in power system operation. Di erent derivative and probabilistic methods are used to solve ELD problems. This paper proposes a powerful Sine CoSine Algorithm (SCA) to explain the ELD issue including equality and inequality restrictions. The main aim of ELD is to satisfy the entire electric load at minimum cost. The SCA is a population-based probabilistic method, which guides its search agents that are randomly placed in the search space towards an optimal point using their  tness functions and keeps a track of the best solution achieved by each search agent. SCA was used to solve the ELD problem due to its favorable exploration and local optima escaping technique. This Algorithm con rmed that promising areas of the search space were exploited to have a smooth transition from exploration to exploitation using Sine and coSine functions. Simulation results proved that the proposed Algorithm surpassed other existing optimization techniques in terms of quality of the solution obtained and computational e ciency. The  nal results also proved the robustness of the SCA.

Colliding Bodies Optimization (CBO) is a population-based metaheuristic Algorithm that complies physics laws of momentum and energy. Due to the stagnation susceptibility of CBO by premature convergence and falling into local optima, some meritorious methodologies based on Sine CoSine Algorithm and a mutation operator were considered to mitigate the shortcomings mentioned earlier. Sine CoSine Algorithm (SCA) is a stochastic optimization method that employs Sine and coSine based mathematical models to update a randomly generated initial population. In this paper, we developed a new hybrid approach called hybrid CBO with SCA (HCBOSCA) to obtain reliable structural design optimization of discrete and continuous variable structures, where a memory was defined to intensify the convergence speed of the Algorithm. Finally, three structural problems were studied and compared to some state of the art optimization methods. The experimental results confirmed the competence of the proposed Algorithm.

This paper proposes a modified Sine coSine Algorithm (MSCA) for discrete sizing optimization of truss structures. The original Sine coSine Algorithm (SCA) is a populationbased metaheuristic that fluctuates the search agents about the best solution based on Sine and coSine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical functions has been demonstrated in literature. However, its performance in tackling the discrete optimization problems of truss structures is not competitive compared with the existing metaheuristic Algorithms. In the framework of the proposed MSCA, a number of worst solutions of the current population is replaced by some variants of the global best solution found so far. Moreover, an efficient mutation operator is added to the Algorithm that reduces the probability of getting stuck in local optima. The efficiency of the proposed MSCA is illustrated through multiple benchmark optimization problems of truss structures.

The Sine-coSine Algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified Sine-coSine Algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of Sine and coSine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed Algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic Algorithms and its enhancement with respect to the standard Sine-coSine Algorithm.

In this article, the problem of pricing discrete double barrier options which only monitored at specific times is investigated. According to the Black-Scholes framework, the option price would be obtained from recursively solving the Black-Sholes partial differential equations on the monitoring intervals. In this way, the Sine-coSine wavelet approach is applied in approximating the yielded analytical expression. Finally, an operational matrix form is derived which is highly comparable with other methods. According to the method of the present paper, the computational time is nearly fixed against increases in the number of monitoring dates.

In this study, optimal energy management is addressed in the residential building. The residential building is equipped with renewable energies including wind turbines (WT) and photovoltaic (PV) systems. Stochastic programming is used to model the uncertainty of renewable energy resources. To manage these uncertainties and reduce the total daily cost of energy, the load control program is adopted. In this respect, five different types of loads are modeled in the building, including interruptible, uninterruptible, constant-energy, constant-power and movable loads. The above charges are properly adjusted and shipped to minimize energy costs and address the uncertainties of renewable energy by hybrid Sine coSine shuffled frog leaping Algorithm. The residential building is considered as later active in the network, which transfers energy from network to the building and vice versa. The simulation results show that the proposed model can efficiently harness all the energy possible from WT-PV systems, manage uncertainties, minimize total daily costs and operate as an island. All of these objectives are achieved by optimal load distribution and control within the proposed load control program.