Advanced Biased Random Sampling in Serial and Parallel Scheduling

Most combinatorial scheduling problems are notoriously intractable, so the majority of algorithms for them are heuristic in nature. Of these, priority rule-based methods despite their age still constitute the most important class of which. in turn, parameterized biased random sampling methods have attracted particular interest, due to the fact that they outperform all other priority rulebased methods known. Different random sampling schemes have been proposed of which the regretbased scheme (RBRS) of Drexl (1991) is the best-performing one currently known. Careful analysis, however, reveals that each of these schemes possesses some immanent flaw whose effects may lead to significant distortions of the scheduling process. We therefore propose some new sampling schemes, each of which completely avoids some of the adverse effects while grossly reducing others. Focussing on the resource-constrained project scheduling problem (RCPSP) as a vehicle, we discuss the results from a comprehensive experimental evaluation of both classical and new schemes; in addition, we substantially extend the analysis on serial and parallel scheduling heuristics presented in Kolisch (1996b). Our results indicate that some of the new schemes offer significant improvements over existing sampling algorithms, the best-performing one improving upon the RBRS by more than ten percent. Also, we expose detailed insight indtto which parameter settings are the most beneficial for different algorithmic schemes.