Softassign versus Softmax: Benchmarks in Combinatorial Optimization

A new technique, termed soft assign, is applied for the first time to two classic combinatorial optimization problems, the traveling salesman problem and graph partitioning. Soft assign, which has emerged from the recurrent neural network/statistical physics framework, enforces two-way (assignment) constraints without the use of penalty terms in the energy functions. The soft assign can also be generalized from two-way winner-take-all constraints to multiple membership constraints which are required for graph partitioning. The soft assign technique is compared to the softmax (Potts glass). Within the statistical physics framework, softmax and a penalty term has been a widely used method for enforcing the two-way constraints common within many combinatorial optimization problems.