What designs for genetic algorithms are there, if they are classified differently and/or have different names, that leverage models for epigenetics in evolution? What are the pros/cons of the designs? Are there vast insufficiencies or wide-open questions about their usefulness?
Genetic algorithms are an analogy to biology, not a copy of it. The core piece of the analogy is that the "phenotype", or the observable portion of a solution, is constructed from the "genotype", or the internal portion of a solution.
For example, a number (the phenotype) can be stored as a binary series of "0"s and "1"s (the genotype), and by changing individual bits we make potentially dramatic changes in the resulting number, and by combining two genotypes we can get a broad range of 'related' numbers.
Epigenetics are wrinkles in the genotype -> phenotype mapping, making it a non-deterministic function, and so incorporating them would degrade the performance of a genetic algorithm by adding unnecessary noise.