Combinatorial Optimization Using Electro-Optical Vector by Matrix Multiplication Architecture

A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.