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The main objective of this paper is to design energy consumption modeling systems to predict the energy consumption value due to today's energy use in cities increasing. A new Modified Fish Migration Optimization Algorithm-based Numerical Moment Matching (MFMOA-NMM) technique is applied as an initial indeterminacy evaluation method to forecast the electrical power use in large-scale datasets of single-family residential homes with the application of main characteristics. To develop energy modeling, the DesignBuilder is used. The energy performance of the homes is assessed by combining these techniques. With the application of the information from the energy audit and data of the assessor (8368 single-family homes), four effective parameters including attic insulation R-value, the efficiency of air conditioners (SEER), type of the window, and the area of homes are inputted into the model improvement. Waterloo in Iowa is selected as the case study. The results showed that the yearly electrical power use expected is equal to 10,195 kWh which is within 5% of the experimental electrical power use. Also, the monthly expected electrical power use Average Bias Error is equal to 2.4% and the Coefficient of Variation with the Root Average Square Error is equal to 6.7%. This technique can be applied to create a small group of typical buildings to show the energy performance of a bigger group of buildings. • Energy consumption modeling to predict energy consumption for single-family homes in Waterloo. • Energy performance optimization by a Modified Fish Migration Optimization Algorithm. • Combining the introduced new algorithm with Numerical Moment Matching technique. [ABSTRACT FROM AUTHOR]