The traveling salesman problem, edited by E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B Shmoys, John Wiley & Sons, Chichester, 1985, 463 pp

Abstract

is an expertly guided tour of combinatorial optimization. The theme of the tour is the traveling salesman problem (TSP). In the course of exploring different facets of TSP research and results, our guides expose concepts, methods, and ideas from computational complexity, graph theory, probabilistic analysis of algorithms, statistical methods for comparing heuristics, polyhedral theory, and more generally, the entire field of combinatorial optimization. This well-written book more than fulfills the editors' hopes of providing comprehensive coverage of the techniques of combinatorial optimization as well as being a state-of-the-art survey of the traveling salesman problem. We highly recommend this book to advanced students and researchers in operations research, computer science, discrete mathematics, and quantitative business studies.The TSP is a classic 'hard' problem: easy to describe and difficult to solve. Precisely how difficult became clearer as computational complexity theory developed. Chapter 1 (A.J. Hoffman and P. Wolfe) explores the history of the problem. In Chapter 2, R.S. Garfinkel discusses motivations for the problem and some of its many applications and generalizations. Chapter 3 (D.S. Johnson and C.H. Papadimitriou) introduces computational complexity theory and shows how the difficulty of the TSP optimization problem can be specified as NP-hard. This chapter delivers the bad news of the TSP's intractability. P.C. Gilmore, E.L. Lawler, and D.B. Shmoys survey well-solved special cases of the TSP in Chapter 4. Several results are new. The authors categorize these special cases (those with restrictions on arc lengths and those with network structures) and show how the theory of subtour patching is used to give optimal solutions to several special cases. Knowing the well-solved

Combinatorial optimization by iterative partial transcription

“…One of the most popular such tasks is the traveling salesman problem (TSP): how to find the shortest roundtrip through a given set of cities. For recent surveys on various approaches to the TSP see [3,4].…”

“…They are mainly based on branch-and-bound and branch-and-cut ideas [30,31]. Thus, a specific TSP instance including 7397 cities was solved [3,32]. However, for a fixed size, the effort necessary to find the exact solution can vary enormously from problem to problem.…”

Explaining clinical decisions by extracting regularity patterns

“…Our aim is to get a base that minimizes the number of items, bringing up the granular knowledge. Searching for solutions in the space of possible attribute permutations with a fixed domain order is a combinatorial optimization problem, which is known to be NP-hard [8]. During the search, it may be very time-consuming, or even intractable to compute the new storage space that each base requires and copy the information from one KBM2L to another in a different base.…”

Traveling Salesman Problem

“…Such schemes are very unlikely to exist for the traveling salesman problem. Johnson and Papadimitriou (1985) show that, unless P=NP, there does not exist a fully polynomial approximation scheme for the Euclidean traveling salesman problem. This also holds in general for TSP instances satisfying the triangle inequality.…”