Unsupervised Up-to-Bottom Hierarchical Clustering Elastic Net Algorithm for TSP

Elastic net is an efficient neural network algorithm to solve combinational optimization problems, especially to solve traveling salesman problem. However, aimed to solve large problems, elastic net illustrates insufficient solving capability. Based on our observations and analysis of router properties in the optimal/near-optimal solutions of TSP, we introduce a novel neural network algorithm named unsupervised up-to-bottom hierarchical clustering elastic net (UBHCE) to solve TSP in parallel. Combined with the remarkable geometrical property of elastic net, the UBHCE partitions TSP hierarchically through utilizing an embedded suitable clustering method (UBHC), which is able to decrease problem complexity gradually. Through summarizing and analyzing the coefficient setting regularity of activity function in elastic net, we present a flexible coefficient tuning strategy to adapt to the UBHCE for the process of gradually decreasing TSP. The experimental results on a large amount of instances of random TSP and benchmark TSP suggest that the UBHCE has a higher average success rate for obtaining globally optimal/near-optimal solutions, moreover, it is more suitable to deal with complex problems in parallel.