The book, which are generalizations of the “Traveling Salesman problems” and “Assignment Problems”. For each of the problems an algorithm based on 'Lexisearch Search Approach? is developed to get an optimal feasible solution using 'Pattern Recognition Approach'.Each problem is studied and the necessary computational results are presented in it, and the actual computer program of the algorithm written in 'C' language is given. In the usual 'Lexi-search Algorithm for the problems developed so far, when a partial word is considered, it is first checked for feasibility. In this context the feasibility checking is easy and hence it is checked first and when it is feasible, the difficult part of calculating the bounds is taken up later, for developing an efficient algorithm. For some problems the difficulty may be the other way, that is, effective bounds can be calculated easily and feasibility checking technique called the 'Pattern Recognition Technique for is used in this book.