Biobjective Optimization Problems in Simple Neural Networks as Binary Associative Memories

This paper studies biobjective optimization problems in synthesis of binary associative memories characterized by ternary cross-connection parameters and the signum activation function. The system simplicity enables us to give a condition of parameters that guarantees storage of desired memories. In order to synthesize efficient associative memories, we define biobjective optimization problems based on two objectives which evaluate stability of stored desired memories and sparsity of connection parameters. In order to solve the problems, we have applied a simple evolutionary algorithm to typical examples and have obtained interesting results: a suitable connection sparsity exists where the memory stability is the strongest, and a trade-off exists between the memory stability and the connection sparsity.