Multi-objective optimization of the stack of a thermoacoustic engine using GAMS

We illustrate the optimization of the stack of a thermoacoustic engine taking into account thermal losses.We present a new mathematical programming approach to model and optimize the device.We demonstrate the interdependence between geometrical parameters to support this multi-objective approach.We have implemented a nonlinear programming approach in GAMS.We have determined Pareto optimal solutions for single and multiple objectives functions. This work illustrates the use of a multi-objective optimization approach to model and optimize the performance of a simple thermoacoustic engine. System parameters and constraints that capture the underlying thermoacoustic dynamics have been used to define the model. Work output, viscous loss, conductive heat loss, convective heat loss and radiative heat loss have been used to measure the performance of the engine. The optimization task is formulated as a five-criterion mixed-integer non-linear programming problem. Since we optimize multiple objectives simultaneously, each objective component has been given a weighting factor to provide appropriate user-defined emphasis. A practical example is given to illustrate the approach. We have determined a design statement of a stack describing how the design would change if emphasis is given to one objective in particular. We also considered optimization of multiple objectives components simultaneously and identify global optimal solutions describing the stack geometry using the augmented ?-constraint method. This approach has been implemented in GAMS (General Algebraic Modelling System).