The primary goal in designing a heat exchanger is to determine the necessary heat transfer area for a given heat duty, as it directly impacts the overall cost of the heat exchanger. There are multiple design options available, involving various parameters such as outer diameter, pitch, tube length, tube passes, baffles, baffle spacing, and baffle cut. In our experiment, we focused on designing and evaluating a heat exchanger using experimental data. Specifically, we conducted the experiment using the HT30X Heat Exchanger Service unit and utilized the HT33 Shell and Tube software in conjunction with it. Previous research has extensively explored the optimization of shell and tube heat exchangers from an economic standpoint using different techniques and algorithms. However, optimization involving multiple objectives is relatively uncommon. In our work, we aimed to optimize the heat exchanger design based on two objectives: a) minimizing the length of the heat exchanger, and b) minimizing the overall cost. We have outlined a clear methodology for our study and conducted case studies to demonstrate how one objective affects the other. To facilitate the optimization process, we employed the Multi-Objective Optimization solver, which utilizes a genetic algorithm (gamultiobj). This solver is available in the optimization toolbox of the MATLAB software. Our experimental setup included a HT33 shell and tube heat exchanger with one shell, seven tubes, one pass, and two baffles. We performed iterations on the variables, including the shell diameter, outer tube diameter, and baffle spacing, to identify the optimal solution using the optimization solver.