In this paper, the shell-and-tube heat exchangers design is formulated as an optimization problem and solved with particle swarm optimization (PSO). The objective is to minimize the global cost including area cost and pumping cost or just area minimization, depending on data availability, rigorously following the standards of the Tubular Exchanger Manufacturers Association and respecting pressure drops and fouling limits. Given fluids temperatures, flow rates, physical properties (density, heat capacity, viscosity, and thermal conductivity), pressure drop and fouling limits, and area cost data, the proposed methodology calculates the optimal mechanical and thermal-hydraulic variables. The Bell-Delaware method is used for the shell-side calculations. Some literature cases are studied and results show that in this type of problem, with a very large number of nonlinear equations, the PSO algorithm presents better results, avoiding local minima.