Multiple Traveling Salesman Problem (MTSP) is able to model and solve various real-life applications such as multiple scheduling, multiple vehicle routing and multiple path planning problems, etc. While Traveling Salesman Problem (TSP) focuses on searching a path of minimum traveling distance to visit all cities exactly once by one salesman, the objective of the MTSP is to find m paths for m salesmen with a minimized total cost -the sum of traveling distances of all salesmen through all of the respective cities covered. They have to start from a designated depot which is the departing and returning location of all salesmen. Since the MTSP is a NP-hard problem, a new effective Genetic Algorithm with Local operators (GAL) is proposed in this paper to solve the MTSP and generate high quality solution within a reasonable amount of time for real-life applications. Two new local operators, Branch and Bound (BaB) and Cross Elimination (CE), are designed to speed up the convergence of the search process and improve the solution quality. Results demonstrate that GAL finds a better set of paths with a 9.62% saving on average in cost comparing to two existing MTSP algorithms.
The Binary Relation Inference Network (BlUN) emerges as a powerful topological network to solve various constrained optimization problems. In this paper, the BRIN solution is reviewed for the sake of reference. The analog and digital realization of BlUN is presented. For the analog implementation, we studied the BRIN solution for transitive closure problem. We used the common available integrated circuits and general minimum and maximum building blocks. The network response was discussed. The worst solution time for a general path problem was estimated. For digital implementation, Field Programmable Gates Arrays (FPGA) with million gates for BRIN solution was studied with Xilinx's System Generator. The detailed implementation is presented. The network response and the solution time are analyzed. The comparisons between both platforms are discussed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.