Approximate Algorithms for some NP-hard problems: Some Novel Heuristics and Meta-heuristics for the TSP and the HCP problems

In this era of information technology, many decisions are made rapidly by computers in various industries to achieve some best possible goal or objective, from routing vehicles, to deciding inventory, model networks and for efficient data retrieval.For many such problems, we cannot conduct an exhaustive search of all the solutions to find the optimal solution in polynomial time, as they have an exponential population of possibilities. Such problems are referred to as NP-hard and we have focused on such type of problems in this monograph.We have proposed some interesting approximate algorithms and heuristics to solve the Traveling Salesman Problem and the Hamiltonian Cycle Problem and get good quality solutions.The computer simulations performed show the effectiveness of our algorithms.