Introduction

Optimization problems exist everywhere in our life. The goal of optimization is to find the best set of the admissible conditions to achieve some objectives in our decision-making process. One of fundamental requirements for an optimization algorithm is to find all optimal solutions within a reasonable amount of computing time. Many optimization problems are known to be NP-complete, which means that there exist no efficient algorithms to solve them. People have designed a variety of algorithms to solve these hard problem. Due to the intractability of these problems, heuristic search algorithms have become a popular means to find reasonably good solutions to these problems. The heuristic search algorithms trade in guaranteed correctness of the optimal solutions for quicker computing time. Solving the TSP is a way of thinking. The full challenge of the TSP is selecting the best tour among a set of tours and knowing it is the best. An exhausted search algorithm can meet the challenge, but it lacks practical efficiency. Can we reduce the search space to make exhausted search feasible? This book explores this possibility.