A normalized deep neural network with self-attention mechanisms based multi-objective multi-verse optimization algorithm for economic dispatch

Traditional economic dispatch (ED) methods suffer from high costs, high carbon dioxide (CO2) emissions, and slow calculation speeds. Therefore, finding a new ED method that can effectively reduce costs and environmental pollution, and improve computational speed, is crucial. This study proposes a normalized deep neural network with a self-attention mechanism based multi-objective multi-verse optimization algorithm (NDNN-SAM-MOMVO). NDNN-SAM-MOMVO combines deep neural network and multi-objective multiverse optimization (MOMVO) with the introduction of self-attention mechanism and layer normalization networks. In this study, NDNN-SAM-MOMVO is simulated in IEEE 118-, IEEE 2869-, and 11,476-bus systems; the performance of NDNN-SAM-MOMVO is contrasted with other algorithms. Simulation results show that: (1) reducing costs and CO2 emissions; the proposed NDNN-SAM-MOMVO reduces the cost by 2.81 % and 1.14 % and CO2 emissions by 2.81 % and 0.63 % over MOMVO in these two systems, respectfully; (2) accelerating computational efficiency, the proposed NDNN-SAM-MOMVO saves 24.95 % and 20.33 % time over MOMVO in these two systems, respectively; (3) Euclidean distance performance metrics reflect the superb performance of the proposed NDNN-SAM-MOMVO.