Thermoacoustic engines convert heat energy into acoustic energy. Then, the acoustic energy can be used to pump heat or to generate electricity. It is well-known that the acoustic energy and therefore the exergetic efficiency depend on parameters such as the stack's hydraulic radius, the stack's position in the resonator and the traveling-standing-wave ratio. In this paper, these three parameters are investigated in order to study and analyze the best value of the produced acoustic energy, the exergetic efficiency and the product of the acoustic energy by the exergetic efficiency of a thermoacoustic engine with a parallel-plate stack. The dimensionless expressions of the thermoacoustic equations are derived and calculated. Then, the Particle Swarm Optimization method (PSO) is introduced and used for the first time in the thermoacoustic research. The use of the PSO method and the optimization of the acoustic energy multiplied by the exergetic efficiency are novel contributions to this domain of research. This paper discusses some significant conclusions which are useful for the design of new thermoacoustic engines. (C) 2011 Elsevier Ltd. All rights reserved.