Traveling salesman problem heuristics: Leading methods, implementations and latest advances

Heuristics for the traveling salesman problem (TSP) have made remarkable advances in recent years. We survey the leading methods and the special components responsible for their successful implementations, together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric TSP benchmark problems. The foremost algorithms are represented by two families, deriving from the Lin–Kernighan (LK) method and the stem-and-cycle (S&C) method. We show how these families can be conveniently viewed within a common ejection chain framework which sheds light on their similarities and differences, and gives clues about the nature of potential enhancements to today’s best methods that may provide additional gains in solving large and difficult TSPs.