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Based on the research of population migration algorithms (PMAs), a population migration genetic algorithm (PMGA) is proposed, combining a PMA with a genetic algorithm. A scheme of area and power optimization for a ternary FPRM circuit is proposed by using the PMGA. Firstly, according to the ternary FPRM logic function expression, area and power estimation models are established. Secondly, the PMGA is used to search for the best area and power polarity. Finally, 10 MCNC Benchmark circuits are used to verify the effectiveness of the proposed method. The results show that the ternary FPRM circuits optimized by the PMGA saved 13.33% area and 20.00% power on average than the corresponding FPRM circuits optimized by a whole annealing genetic algorithm.

Polarity optimization for mixed polarity Reed-Muller (MPRM) circuits is a combinatorial issue. Based on the study on discrete particle swarm optimization (DPSO) and mixed polarity, the corresponding relation between particle and mixed polarity is established, and the delay-area trade-off of large-scale MPRM circuits is proposed. Firstly, mutation operation and elitist strategy in genetic algorithm are incorporated into DPSO to further develop a hybrid DPSO (HDPSO). Then the best polarity for delay and area trade-off is searched for large-scale MPRM circuits by combining the HDPSO and a delay estimation model. Finally, the proposed algorithm is testified by MCNC Benchmarks. Experimental results show that HDPSO achieves a better convergence than DPSO in terms of search capability for large-scale MPRM circuits.

Having the advantage of simplicity, robustness and low computational costs, the particle swarm optimization (PSO) algorithm is a powerful evolutionary computation tool for synthesis and optimization of Reed-Muller logic based circuits. Exploring discrete PSO and probabilistic transition rules, the discrete ternary particle swarm optimization (DTPSO) is proposed for mixed polarity Reed-Muller (MPRM) circuits. According to the characteristics of mixed polarity OR/XNOR expression, a tabular technique is improved, and it is applied in the polarity conversion of MPRM functions. DTPSO is introduced to search the best polarity for an area of MPRM circuits by building parameter mapping relationships between particles and polarities. The computational results show that the proposed DTPSO outperforms the reported method using maxterm conversion starting from POS Boolean functions. The average saving in the number of terms is about 11.5%; the algorithm is quite efficient in terms of CPU time and achieves 12.2% improvement on average.