Probability distribution arithmetic optimization algorithm based on variable order penalty functions to solve combined economic emission dispatch problem

The optimization objective of combined economic emission dispatch (CEED) problem is to minimize the total cost of power generation and the emission of harmful gases under the premise of satisfying the load demand and operation constraints. In today's world, energy and environmental problems are becoming more and more serious. Solving CEED problems can reduce costs, save energy, and reduce environmental pollution. By adopting the maximum/maximum price penalty factor, the multi-objective CEED optimization problem is transformed into a single objective optimization problem, and a probability distribution arithmetic optimization algorithm (AOA) based on variable order penalty function was proposed to solve the CEED problem. The energy attenuation strategy was proposed to replace the variation trend of Math optimizer accelerated (MOA) in the original AOA, which better balances the exploration and exploitation of AOA. Five probability distribution functions, including exponential distribution, uniform distribution, normal distribution, beta distribution and gamma distribution, are used to replace a control parameterμ, so as to enhance its searching ability, improve the convergence speed, and enhance the ability to jump out of the local optimal. Based on the CEC-BC-2017 benchmark functions, the original AOA is compared with the five improved AOA to select the best improved strategy, and the effectiveness of the improved strategy is verified by simulation comparison with other intelligent optimization algorithms. In dealing with the constraint of CEED problem, five kinds of penalty functions with varying order were proposed, which are sine function, hyperbolic tangent function, arctangent function, V-type function and hyperbolic secant function, respectively, to replace the traditional fixed penalty function. The CEED problem with 6 units are selected and solved under the total demand of 150 MW, 175 MW, 200 MW and 225 MW respectively. The experimental results show that the AOA based on probability distribution is better than other optimization algorithms in solving CEED problems, and the variable order penalty strategy improves the solution quality and convergence speed compared with the fixed penalty strategy.