  In this paper, we introduce a novel rate-profile design based on
search-constrained optimization techniques to assess the performance of
polarization-adjusted convolutional (PAC) codes under Fano (sequential)
decoding. The results demonstrate that the resulting PAC code offers much
reduced computational complexity compared to a construction based on a
conventional genetic algorithm without a performance loss in error-correction
performance. As the fitness function of our algorithm, we propose an adaptive
successive cancellation list decoding algorithm to determine the weight
distribution of the rate profiles. The simulation results indicate that, for a
PAC(256, 128) code, only 8% of the population requires that their fitness
function be evaluated with a large list size. This represents an improvement of
almost 92% over a conventional evolutionary algorithm. For a PAC(64, 32) code,
this improvement is about 99%. We also plotted the performance of the high-rate
PAC(128, 105) and PAC(64, 51) codes, and the results show that they exhibit
superior performance compared to other algorithms.
