## 1 Introduction
In addition, in several articles, experts have tried to improve the obtained results by defining a one objective function (OF) using optimization evolutionary approaches, according to the defined functions in their researches. For example, an improved PSO algorithm has been used in reference [30] to perform economic dispatch of power plant units considering their constraints. Likewise, in the papers [31; 32], evolutionary programming approaches were applied for solving these kinds of problems. In recent years, a combination of economic and environmental dispatch (CEED) has been suggested as an efficient way to address the optimal dispatch and energy management issues since multi-objective optimizers could decrease the air pollution with lower operational costs. From this point of view, optimized power systems are capable of economic performance by considering various criteria of inevitable limitations while causing low negative environmental effects. Today, different optimization strategies have been performed to deal with the optimal dispatch and energy management issues in more effective manners [33]. For instance, optimal scheme methods under the carbon-emissionbased utilizing metaheuristic algorithms have been suggested by [PERSON] [34]. Similarly, authors of the paper [35] have surveyed different methods like genetic algorithm (GA), in that parameters have been regulated with fuzzy logic (FL) concepts. Additionally, in order to solve an economic and environmental dispatch (EED) issue, an improved decision shuffle frog leaping algorithm has been used in reference [36]. In paper [37], also, to address the EED issue, a stochastic method taking into account uncertainties was proposed; and in [38], authors performed a detailed research regarding evolutionary programming algorithm i.e., ant colony optimization (ACO) and GA to solve EED problems have been implemented. For optimal dispatch and operating electric energy, various multi-objective evolutionary algorithms were also suggested in the reference [39]. In reference [40], authors focused on the benefits of using neural-fuzzy methods to find an acceptable way to address multi-objective generation and energy management issue. The impacts of electric vehicles, smart homes, and smart buildings, including smart hospitals and smart schools, have been examined, optimized, and managed in references [41; 42]. Among the above-mentioned optimization techniques, differential evolutionary (DE) algorithm has been noticeably utilized in optimal operation and energy management issue, basically because of its population-based search ability and higher efficiency, more speed of convergence, and robustness; therefore, an improved multi-objective differential evolution (IMODE) technique is suggested in this research. To dominate the issues of falling into the local optimum and premature convergence, in our proposed IMODE algorithm, an immune operation technique is introduced to power the local search capability and improve optimization precision. The suggested method is successfully carried out on various case studies, and the efficiency measures consisting of convergence and divergence metrics are computed. Besides, the multi-objective optimization of a multi-operation energy management in SGs in presence of RESs procedure is performed using the presented IMODE algorithm. In order to show the impact of renewable energy on the cost, in the simulations, the operation is solved with maximum participation of RESs. In the final section, the sensitivity analysis on the number of populations in this problem is performed.