# General Solution Methods

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## Abstract

The disjunctive scheduling problem which will be treated more closely in the next chapter is a combinatorial search and optimization problem. This chapter provides an overview of some popular methods for solving these kinds of problems. Since many of them can be modelled as special subclasses of the constraint satisfaction or constraint optimization problem, we will give a short introduction to the field of constraint satisfaction in section 2.1. In section 2.2, constraint propagation techniques are described which some years ago have been mainly studied in the field of Artificial Intelligence and only recently have been integrated in Management Science solution methods some of which are presented in section 2.3 and 2.4. The main idea that these methods are based upon is to replace the original “difficult” problem by one or several “related” but “easier” problems whose solution hopefully contributes to the solution of the original problem. A recursive application of this process leads to a tree of modified problems which is examplarily depicted in figure 2.1. Section 2.3 describes the well-known backtracking and branch-and-bound solution approaches which create and explore a particular problem tree in a systematic, exhaustive fashion and compute an exact solution. Since finding exact solutions in a reasonable amount of time is not always possible due to the intractable nature of the problems examined, heuristic search algorithms are often the last recourse. In general, these algorithms only find approximate solutions, however, they do so with much less computation time. The most simple heuristics work in a greedy fashion and explore one path of the problem tree that seems favourable with respect to some “shortsighted” measure or rule. More sophisticated heuristics which have shown excellent approximation results in recent years are based on the paradigm of local search and iterative improvement. These methods which repeatedly explore branches of the problem tree are discussed in section 2.4.

## Keywords

Search Space Local Search Tabu Search Constraint Satisfaction Problem Constraint Propagation## Preview

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