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This paper describes the implementation of a reconfigurable hardware-based genetic algorithm (HGA) accelerator using the hardware-software (HW/SW) co-design methodology. This HGA is coupled with a unique TRNG that extracts random jitters from a phase lock loop (PLL) to ensure proper GA operation. It is then applied and benchmarked with several case studies, which include the optimization of a simple fitness function, a constrained Michalewicz function, and the tuning of parameters in finger-vein biometrics. A HGA solution is necessary in systems that demand high performance during the optimization process. However, implementations that are completely designed in hardware will result in a very rigid architecture, making it difficult to reconfigure the system for use in different applications. This paper aims to solve this issue by proposing a HGA design that provides reconfigurability and flexibility by moving problem-dependent processes into software. The prototyping platform used is an Altera Stratix II EP2S60 FPGA prototyping board with a clock frequency of 50 MHz. The HW/SW co-design technique is applied, and system partitioning is done based on aspects such as system constraints, operational intensity, process sequencing, hardware logic utilization, and reconfigurability. Experimental results show that the proposed HGA outperforms equivalent software implementations compiled with an open-sourced C++ GA component library (GAlib) running on the same prototyping platform by 102 times at most. In the final case study, the application of the proposed HGA in tunable parameter optimization in finger-vein biometrics improved the matching rate, reducing the equal error rate (EER) value from 1.004% down to 0.101%.