Landscapes, embedded paths and evolutionary scheduling

Abstract

Heuristic search methods such as evolutionary algorithms have often to scheduling problems. Whenever we apply such an algorithm, we implicitly construct a landscape over which the search traverses. The nature of this landscape is not an invariant of the problem instance, but depends on a number of algorithmic choices-most obviously, the type of neighbourhood operator used as a means of exploring the search space. In this chapter, after discussing the basic ideas of a landscape, we show how this variation in the landscape of a particular instance manifests itself in terms of an important property-the number of local optima-and discuss ways in which local optima can be avoided. We then review evidence for a particular conformation of local optima in a variety of scheduling and other combinatorial problems the 'big valley' property. We then turn to the question of how we can exploit such effects in terms of a fruitful search strategy-embedded path tracing- for flowshop scheduling problems. While many approaches could be taken, the one described here embeds the path tracing strategy within a genetic algorithm, and experimental evidence is presented that shows this approach to be capable of generating very high-quality solutions to different versions of the permutation flowshop scheduling problem. Finally, some recent research is reported into the use of data from the search trace that provides some clues as to the quality of the results found. In particular, it is possible to use data on the re-occurrence of previous local optima to estimate the total number of optima and, indirectly, to quantify the probability that a global optimum has been reached. © Springer-Verlag Berlin Heidelberg 2007.