Extending the power and capacity of constraint satisfaction networks

This work focuses on improving the Hop eld network for solv ing optimization problems Although much work has been done in this area the performance of the Hop eld network is still not satisfactory in terms of valid convergence and quality of solutions We address this issue in this work by combing a new activation function EBA and a new relax ation procedure CR in order to improve the performance of the Hop eld network Each of EBA and CR has been in dividually demonstrated capable of substantially improving the performance The combined approach has been eval uated through simulations based on randomly generated city distributions of the city traveling salesman problem The result shows that combining the two methods is able to further improve the performance Compared to CR without combining with EBA the combined approach increases the percentage of valid tou rs by and de creases the error rate by As compared to the original Hop eld method using neither EBA nor CR the combined approach increases the percentage of valid tours by and decreases the error rate by Combinatorial optimization problems Most of them are NP problems Many maximum or minimum points Examples Traveling Salesman Problem TSP Routing in communication networks Graph partitioning in circuit design Why study TSP by Hop eld network TSP is one early application by Hop eld network HN TSP is representative of combinational problems TSP is a benchmark for comparing algorithms A good algorithm for TSP could be mapped to solve other combinatorial problems Hop eld networks vs other heuristics Examples of other heuristics Divide and Conquer Form outline contour The procedure of HN is more generalwhile other methods are more problem speci c HN can use parallel processing while other methods usu ally use sequential processing HN can have convenient hardware implementation HN can achieve an optimal or sub optimal solution in short time Example Architecture for a city TSP