This paper presents exergo-economic and enviro-economic assessment of a novel building integrated photovoltaic thermal-compound sensible rotary heat exchanger (BIPVT-SRHX) system. The innovative BIPVT-SRHX system preheats/precools the outdoor air in winter/summer and generates electric power. The performance of the system are analyzed from the energy/exergy viewpoints for Kermanshah, Iran climatic conditions. Then, the multi-objective genetic algorithm (MOGA) optimization is used to optimize to determine the optimum values of geometric and operating parameters in order to maximize the annual average exergo-economic and enviro-economic aspects of the system. The considered geometric and operating parameters include the length, width and depth of the air channel located underneath the PV modules, the air mass flow rate, and the diameter, rotational velocity and length of the SRHX. Moreover, the annual performance of the optimized and non-optimized BIPVT-SRHX systems are compared. The results showed that the annual average exergo-economic and enviro-economic aspects of the optimized BIPVT-SRHX system are 0.0076 $/annum and 246.9 kWh/$, respectively. Furthermore, it was found that the annual average enviro-economic aspect, annual average exergo-economic aspect, and yearly sum of CO2 mitigation of the optimized BIPVT-SRHX system are respectively 36.8%, 23.1% and 37.7% higher than the non-optimized system. •An innovative exhaust air energy recovery system consisting of a BIPVT and a SRHX.•Pre-heating/pre-cooling ambient air in winter/summer and producing electricity.•Genetic algorithm-based multi-objective optimization approach for BIPVT-SRHX system.•Optimization leads to a 36.8% increase in annual average enviroeconomic parameter.•Optimization leads to a 23.1% increase in annual average exergoeconomic parameter.