Experiments on networks of employee timetabling problems

Abstract

The natural representation of employee timetabling problems (ETPs), as constraint networks (CNs), has variables representing tasks and values representing employees that are assigned to tasks. In this representation, ETPs have binary constraints of non-equality (mutual exclusion), the networks are non uniform, and variables have different domains of values. There is also a typical family of non-binary constraints that represent finite capacity limits. These features differentiate the networks of ETPs from random uniform binary CNs. Much experimental work has been done in recent years on random binary constraint networks (cf. [10,11, 9]) and the so called phase transitions have been connected with certain value combinations of the parameters of random binary CNs.

This paper designs and experiments with a random testbed of ETPs that includes all of the above features and is solved by standard constraint processing techniques, such as forward checking (FC) and conflict directed backjumping (CBJ). Random ETPs are characterized by the usual parameters of constraint networks, like the density of constraints p1. One result of the experiments is that random ETPs exhibit a strong change in difficulty, as measured by consistency checks, (a phase transition). The critical parameter for the observed phase transition is the average size of domains of variables. Non binary constraints of finite capacity are part of the experimental testbed. An enhanced FC-CBJ search algorithm is used to test these random networks and the experimental results are presented.