Abstract
The linear ordering problem (LOP) is one of the classical combinatorial optimization problems which was already classified as NP-hard in 1979 by Garey and Johnson [50]. It has received considerable attention in various application areas ranging from archeology and scheduling to economics and even mathematical psy- chology. Solution methods for the LOP have been proposed since 1958, when Chen- ery and Watanabe outlined some ideas on how to obtain solutions for this problem. The interest in this problem has continued over the years, resulting in the book [111] and many recent papers in scientific journals. This chapter surveys the main LOP applications and instances. We have compiled a comprehensive set of benchmark problems including all problem instances which have so far been used for conduct- ing computational experiments. Furthermore we have included new instances. All of them form the new benchmark library LOLIB.We will use them in the next chap- ters to report our experiments with heuristics, meta-heuristics and exact approaches for the LOP.
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