This study aimed at the development of an algorithm for the computational optimization of free-piston Stirling engines. The design algorithm includes an optimization method and two compatible strategies. The optimization method is an improved version of traditional conjugate gradient method and is named the variable-step simplified conjugate gradient method (VSCGM). The free-piston Stirling engine is operable only in narrow-bounded parameter regions. Using the present approach, the operable variable combinations can be found efficiently. Two compatible strategies, the wake-up and backward-comparison strategies, are integrated with the VSCGM. The present design algorithm can handle multiple-parameter optimization with more flexible objective function definitions. Meanwhile, it features faster convergence as compared with the traditional conjugate gradient methods. Moreover, the feasibility of the VSCGM and the two compatible strategies is demonstrated in two test cases. It was found that the present approach can optimize the ten designed variables simultaneously, and the optimal designs can be yielded in a finite number of iterations. The results show that the inoperable initial designs were successfully optimized to reach a high power output.
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