This paper proposes a hybrid optimization algorithm based on the combination of the merits of the backtracking search (BSA) and sine–cosine algorithm (SCA) to achieve the optimal design of a shell and tube evaporator. To the author’s best knowledge, this is the first application of the metaheuristic algorithms over shell and tube evaporator design problems. In order to test the accuracy of the proposed hybrid algorithm, 10 well-known optimization test functions have been solved. Numerical results obtained from the hybrid BSA–SCA have been compared with the literature optimizers including differential search, big bang–big crunch optimization, quantum-behaved particle swarm optimization, bat algorithm, intelligent tuned harmony search algorithm, and backtracking search algorithm. Comparison... results reveal that solutions obtained from the BSA–SCA are better than those of the results acquired by the aforementioned optimizers with respect to statistical analysis. Proposed optimization procedure is then utilized to obtain optimum values of the two heat exchanger design objectives including total cost and overall heat transfer coefficient. Six decision variables such as tube outer diameter, shell diameter, baffle spacing, tube length, number of tube passes, and tube bundle configuration are selected to be iteratively optimized. It is found that BSA–SCA provides better results than the compared literature optimizers for both objective functions. In addition, a sensitivity analysis is performed for the design parameters at the optimal point. Results show that variation of the design parameters at the optimum point has considerable effect on the objective function rates.