Spiral plate heat exchangers should be efficient devices because they are widely employed in the petrochemical and food industries; furthermore, their operation has a direct impact on electricity consumption in such sectors. For those reasons, this article aims to improve the efficiency of heat exchangers by means of optimization techniques. Using as an objective function the maximization of the overall heat transfer coefficient of a spiral plate heat exchanger. The mathematical formulation includes several variables in the problem: width, length, spacing between the plates, and plate thickness. And as a set of constraints the heat duty and the pressure drop, along with technical considerations associated with this type of system. The General Algebraic Modelling System (GAMS) was purposed as a solution method and compared with the Particle Swarm Optimization (PSO) algorithm, a Genetic Algorithm (GA), the original design proposed by Minton, and the Tuned Wind-Driven Optimizer (TWDO). Results show that the purposed method obtains the highest value of objective function being 1.5% better than the best of the used comparison methods with a computing time of 1e-4s, finding a solution with high quality at a low computational cost.