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In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow problem, called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution operator in a single algorithmic framework. Additionally, an adaptive method is proposed to update the number of solutions evolved by each DE operator based on both the diversity of the population and the quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%. • Development of an adaptive method (AM) for optimizing diversity and solution quality. • Innovative constraint handling approach, progressively adding constraints for improved performance. • Incorporation of intermittent renewable energy models for realistic problem solving. • Extensive validation on IEEE 30-bus and IEEE 118-bus networks, outperforming state-of-the-art algorithms in cost, loss, and environmental impact reduction. [ABSTRACT FROM AUTHOR]

The existing algorithms for solving multi-objective optimization problems fall into three main categories: Decomposition-based, dominance-based, and indicator-based. Traditional multi-objective optimization problems mainly focus on objectives, treating decision variables as a total variable to solve the problem without considering the critical role of decision variables in objective optimization. As seen, a variety of decision variable grouping algorithms have been proposed. However, these algorithms are relatively broad for the changes of most decision variables in the evolution process and are time-consuming in the process of finding the Pareto frontier. To solve these problems, a multi-objective optimization algorithm for grouping decision variables based on extreme point Pareto frontier (MOEA-DV/EPF) is proposed. This algorithm adopts a preprocessing rule to solve the Pareto optimal solution set of extreme points generated by simultaneous evolution in various target directions, obtains the basic Pareto front surface to determine the convergence effect, and analyzes the convergence and distribution effects of decision variables. In the later stages of algorithm optimization, different mutation strategies are adopted according to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals, thus enhancing the performance of the algorithm. Evaluation validation of the test functions shows that this algorithm can solve the multi-objective optimization problem more efficiently. [ABSTRACT FROM AUTHOR]