Linear Assignment Problems in Combinatorial Optimization

Abstract

In this chapter we introduce the notion of a “pattern” in the Linear Assignment Problem and show that patterns may be useful to create new insights and approaches for many combinatorial optimization problems defined on a rectangular input matrix. We define a pattern as a specific collection of cells in the rectangular matrix reflecting the structure of an optimal solution to the original combinatorial optimization problem (COP). We illustrate the notion of pattern by means of some well-known problems in combinatorial optimization, including the variations of the Linear Ordering Problem, the Cell Formation Problem, and some others. Then, we give a detailed consideration to pattern-based solution approaches for the two mentioned problems.