The hybrid solar/gas heating systems are considered as promising technologies to reduce energy consumption and ecological impact, for a more sustainable environment. However, the complexity related to the process of hybridization often calls for multi-objective optimization problems to deal with the constraining objectives. In this paper, a multi-objective optimization methodology combining genetic algorithm, design of experiments and dynamic simulations is proposed. The present work is carried out to maximize the primary energy saving ratio (PESR), solar fraction (SF) and to minimize the levelized cost of heat of a hybrid solar/gas heating system intended for an office building located in Algiers, Algeria. The performance analysis of three control strategy modes showed how important the control strategies can improve the SF and the PESR. The suggested control mode demonstrated a seasonal SF and PESR of 40.31% and 31.32%, respectively. The proposed multi-objective optimization approach gave a better comprehensive energy and economic performance by identifying the pareto fronts. The Linear Programming Technique for Multidimensional Analysis of Preference decision-making technique was employed to determine the best optimal solution. The optimized system exhibited SF of 72.65%, PESR of 42.07% and the Levelized Cost of Heat of 0.054 $/kWh as per the design parameters, collector area of 10 m2, tank volume of 1.7 m3 and a flow rate of 0.2 kg s−1. Overall, the results showed that the proposed methodology is time-efficient and can be applied to optimize hybrid solar/gas systems.