The paper develops an improved social spider optimization algorithm (ISSO) for finding optimal solutions of economic load dispatch (ELD) problems. Different ELD problem study cases can bring huge challenges for testing the robustness and effectiveness of the proposed ISSO method since discontinuous objective functions as well as complicated constraints are taken into account. The improved method is different from original social spider optimization algorithm (SSSO) by performing several modifications directly related to three processes of new solution generation. Namely, the proposed method keeps one formula for the first and the second generations and modify them effectively while SSSO has two different formulas for each generation. In the third generation, the proposed method applies a new formula for determining the mating radius of dominant males and females with the intent to expand search space and avoid falling into local zones. The modifications can support the proposed ISSO method find better solutions with faster manner than SSSO while the number of control parameters and the number of computational processes can be reduced. As a result, the proposed method can find much less generation cost and achieve faster search speeds than SSSO for all considered systems. On the other hand, the search ability evaluation of the proposed method is also given by comparing results with other existing methods available in previous studies. The proposed method can obtain approximate or better results and faster convergence than nearly all compared methods excluding for the last system. Consequently, the proposed ISSO method can be recommended to be a strong method for ELD problem and it can be tried for other mathematical problems in engineering.

In this paper, an improved coyote optimization algorithm (ICOA) is developed for determining control parameters of transmission power networks to deal with an optimal reactive power dispatch (ORPD) problem. The performance of ICOA method is superior to its conventional coyote optimization algorithm (COA) thanks to modifications of two new solution generations of COA. COA uses a center solution to generate an update step size in the first solution generation and produced one new solution by using random factors to diversify the search space in the second solution generation. By tackling the drawbacks of COA, ICOA can reduce control parameters and computation steps, shorten execution time, and provide better results. ICOA is compared to its conventional COA for three standard IEEE systems of 30-, 57-, and 118-buses with continuous and discrete control variables. Moreover, three other algorithms such as water cycle algorithm (WCA), salp swarm algorithm (SSA), and sunflower optimization algorithm (SFOA) have been also implemented for further investigation of the real performance of the proposed method. All the applied methods are metaheuristic algorithms based on population and randomization. The result comparison from the test systems has indicated that ICOA can provide higher solution quality than other methods with reasonable execution time. Therefore, ICOA is a reliable tool for finding optimal solutions of the ORPD problem.

This paper presents the application of an improved firefly algorithm (IFA) for minimizing total electricity generation fuel cost while all loads are supplied by thermal generating units. The proposed IFA was developed by combining two proposed improvements of the firefly algorithm (FA), i.e. improvement of the distance between two considered solutions and improvement of the new-solution production technique. The effect of each proposed improvement on the conventional firefly algorithm (FA) and the performance of IFA were investigated in two study cases, i.e. single-and multi-fuel option based thermal generating units. In the first case, three different systems with three, six and twenty units were employed, while a ten-unit system with four different loads was tested in the second case. The comparison results between IFA and existing methods, including three other FA variants, revealed that the two proposed improvements of FA are very efficient and make IFA a very promising meta-heuristic algorithm for minimizing fuel cost of thermal generating units.

<p>Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique.</p>

This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.