Thermal efficiency and total cost are essential parameters in the design of shell and tube heat exchanger. In this study, both of these parameters are considered as two separate objective functions. Total cost includes the cost of construction and the cost of operation. In this research, Copper oxide/ Iranol refinery oil nanofluids are used as cold side fluid to increase thermal efficiency. Optimization result will be a Pareto frontier curve instead of a single point. The NTU-epsilon method was used to calculate the thermal efficiency, and the Bel-Delawer method was used to calculate the pressure drop. In order to resolve this problem, natural base inspired algorithms have been used to minimize the chances of tapping into the optimal local minima. The results show that the difference in the predicted values is satisfactory, and the maximum error is less than 10% and related to the oil outlet temperature. Modeling results predict the heat transfer rate approximate 511 kW, while the actual results for heat duty were 490 kW (error: 4%). The results of sensitivity analysis show that the heat exchanger length and number of tubes have the greatest effect in increasing cost and increasing the efficiency. (C) 2019 Elsevier B.V. All rights reserved.