This study aims to develop a multi-objective version of the search group algorithm (SGA) called the multi-objective search group algorithm (MOSGA) to help determine thermo-economic optimization of flat-plate solar collector (FPSC) systems. Search mechanisms of the SGA were modified to determine non-dominated solutions through mutation, generation, and selection stages. Authors also mined the Pareto archive with a selection mechanism to maintain and intensify convergence and distribution of solutions. The study tested the proposed MOSGA with well-known multi-objective benchmark problems. Results were compared with outcomes from conventional algorithms using the same performance metrics to validate the capability and performance of the MOSGA. Afterward, MOSGA was applied to find the best design parameters to simultaneously optimize thermal efficiency and the total annual cost of FPSC systems. Four case studies were conducted with four different working fluids (pure water, SiO2, Al2O3, and CuO nanofluids). Optimization results obtained by the MOSGA were analyzed and compared with solutions provided by other algorithms. The findings revealed relative improvement in thermal efficiency and reduced annual cost for all nanofluids compared to pure water. Thermal efficiency was improved by 2.2748, 2.4298, and 2.7948 for SiO2, Al2O3, and CuO case studies, respectively, compared to pure water. Meanwhile, TAC rates were increased by 2.4111, 2.3403, and 2.9133 for these case studies, respectively. Comparative results also demonstrated that MOGSA was robustly effective and superior in the selection of appropriate design parameters of FPSC systems. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.