Heuristic Methods

Abstract

Since the linear ordering problem is NP-hard, we cannot expect to be able to solve practical problem instances of arbitrary size to optimality. Depending on the size of an instance or depending on the available CPU time we will often have to be satisfied with computing approximate solutions. In addition, under such circumstances, it might be impossible to assess the real quality of approximate so- lutions. In this and in the following chapter we will deal with the question of how to find very good solutions for the LOP in short or reasonable time. The methods described in this chapter are called heuristic algorithms or simply heuristics. This term stems from the Greek word heuriskein which means to find or discover. It is used in the field of optimization to characterize a certain kind of problem-solving methods. There are a great number and variety of difficult problems, which come up in practice and need to be solved efficiently, and this has promoted the development of efficient procedures in an attempt to find good solutions, even if they are not op- timal. These methods, in which the process speed is as important as the quality of the solution obtained, are called heuristics or approximative algorithms.