The High-level synthesis (HLS) is a key step in the digital VLSI circuit design. HLS can be seen in the present study as an important matter of intelligently map a Data Flow Graph (DFG) specification of digital filters to FPGA. In this article, the powerful features of the Harris hawks optimization (HHO) and Cuckoo search (CS) algorithm have improved the performance of the proposed method. This proposed strategy is also known as the GChO algorithm. In GChO, the phase of CS helps to force the HHO to escape from stagnation, to ignore local optima and premature convergence. In addition for HLS, the three retiming-based models were also proposed in the work. The standard pipelining was employed in Model 1. The modified Min-Period Retiming on the multiplier less digital filters was incorporated by Model 2 and led to a significant improvement in clock frequency. Model 3 adopted modified Min-Area Retiming on digital filters and reduced the complexity of the circuit; however these designs therefore offer single parameter-based heuristic solution. This can be resolved by using meta-heuristic approach focused on retiming. The use of meta-heuristic methods and swarm intelligence has been considered as a highly desirable choice when searching the digital block solution space with higher frequency and reduced complexity in HLS problems. The robustness of the GChO method has been verified on IEEE CEC’ 2020 standard benchmark test suites. The paper analyzes that the performance of the proposed GChO algorithm outperforms the Harris hawks optimization (HHO), Moth Flame optimization algorithm, Particle Swarm optimization algorithm, Chimp optimization algorithm for the HLS digital filters. The experimental results show that the proposed Model 2 and 3 for retimed PDR-FIR filter is improved in term of MUF by 7.38% and utilized slices by 37.77%, PRO-DFII IIR retimed filter by 10.54%, and complexity reduced by 29.69%, PRO-LAT-ARF by 41.61% and slice by 11.17% and PRO-LATLAD-IIR improved in term of MUF, slices by 35.69% and 38.095% in relative to the standard retimed filters of various architecture. For the evolutionary GChO-retimed filter, an improvement in MUF by 58.52%, and utilized slices by 49.61%, for PDR-FIR, 48.09%, 80.76% for PRO-DFII-IIR , 52.68%, 54.33% for PRO-LAT-ARF, 27.85% and 18.46% for PRO-LATLAD-IIR are achieved in respect of Model 2 and 3 whereas an improvement in term of MUF by 34.60%, and utilized slices by 37.61%, for PDR-FIR, 40.55%, 39.66% for PRO-DFII-IIR, 40.08%, 31.33% for PRO-LAT-ARF, 26.95%, 24.41% for PRO-LATLAD-IIR are achieved with respect of other meta-heuristic methods.