Softassign Versus SoftMax: Benchmarks in Combinatorial Optimization

Abstract

A new technique, termed soft assign, is applied for the first time to two classic combinatorial optimization problems, the travel(cid:173) ing 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 par(cid:173) titioning. 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 optimiza(cid:173) tion problems. The benchmarks present evidence that soft assign has clear advantages in accuracy, speed, parallelizabilityand algo(cid:173) rithmic simplicity over softmax and a penalty term in optimization problems with two-way constraints.