A liquefied petroleum gas plant facility (LPGPF) is a series of binary distillation columns used to separate natural gas into four alkanes: ethane, propane, butane, and pentane. The conventional distillation column design consists of three binary distillation columns and six heat exchangers to perform the process. Each heat exchanger consumes immense energy to heat up the reboiler and condense the distillate. There are several process technologies that can minimize distillation column energy consumption. In this research, a fully thermally coupled distillation column (FTCDC) was proposed to minimize energy consumption by reducing the number of heat exchangers and tray columns. An FTCDC has the capability to reduce capital expenditure, operational expenditure, and total annual cost (TAC). The complexity of the FTCDC arises from its process integration. In each column, the intersection composition depends on complex mass and energy balances at the column inlet and outlet and each tray. Process integration, including material recycling and heat recovery, increases the complexity significantly. Moreover, the decision variables are multi-intersection composition for each column to achieve optimum objective function, increasing the number and complexity of the computational load such that effective stochastic optimization algorithms are required. The proposed method was designed using a rigorous vapor liquid equilibrium (VLE) FTCDC model and incorporated with recent stochastic optimization algorithms, such as a genetic algorithm, particle swarm optimization (PSO), an imperialist competitive algorithm, and a duelist algorithm, to determine hydrocarbon composition in the FTCDC intersection. To increase the efficiency and effectiveness of the FTCDC optimization design, cloud computing was utilized. The result was compared with conventional methods such as Fenske-Underwood-Gilliland, a Fenske-Underwood-Gilliland modification, and VLE. The optimization objective function is to minimize TAC with hydrocarbon composition in the FTCDC intersection as decision variables. The optimization using the VLE-PSO method reduces TAC up to 26.28%. All designs were validated using a rigorous model with Aspen HYSYS commercial software. This study's primary goal is to improve the performance of FTCDCs using stochastic algorithms and cloud-based computing capacity. The large amount of computation is handled by cloud-based computing resources, enabling reliability and durability.