A fuzzy evolutionary approach with Taguchi parameter setting for the set covering problem

Abstract

The set covering problem has a very wide area of applications, and scheduling is one of its most important applications. At CEC2001, a fuzzy simulated evolution algorithm was reported for a set covering problem in bus and rail driver scheduling. This paper reports on the generalisation of the approach to the class of set covering, which is basically to cover the rows of a zero-one matrix with a subset of columns at minimal cost. The simulated evolution method iteratively transforms a single solution treating its selected columns as a population. At each iteration a portion of the population is probabilistic ally, biased towards selecting the 'weaker' columns, discarded; and the broken solution is then reconstructed by means of a greedy heuristic. The columns are evaluated under several criteria formulated based on fuzzy set theory. The set of weights associated with the evaluation criteria were previously either fixed in advance or calibrated by means of a simplified genetic algorithm. In this paper, we consider some discrete levels of values instead of a continuous range from 0 to 1 for each weight. We have also included two other parameters driving the evolutionary process as additional factors having some discrete levels of values. Taguchi's orthogonal experimental design is applied. This has the effect of comprehensively evaluating the combinations of factors, although only a small fraction of the possible combinations is explicitly experimented. Better results have been obtained, and comparisons with those previously reported are discussed.