The role of advanced start and dominance rules in simulated annealing for parallel processor scheduling problems

Simulated annealing (SA) has been widely used to solve hard combinatorial optimization problems during the last decade. The application of SA requires the initialization of certain parameters and an initial solution to start the search with. An emphasis in the application of SA has been on the determination of the best initial values of the parameters, however, the starting solution has traditionally been randomly generated. In this paper, we study the effects of the quality of the starting solution and the use of dominance rules on the performance of SA. We show that the better the initial solution used by the SA, the better the final solution produced by it, i.e. the level of improvement achieved by the SA is dependent on the quality of the initial solution. This is demonstrated using various parallel processor scheduling problems. We have also found that dominance rules (applied in conjunction with SA) may in some cases lead to further improved solutions, but their inclusion in an SA scheme must be determined during the preliminary experimentation, in parallel to the determination of the best SA-parameter values. These findings have a long-term impact, as they suggest that the performance of SA schemes that are currently available in the literature can be further improved by starting from a good solution, if available, or by implementing SA in a sequential manner, i.e. several times, by starting from the best solution found in the previous run.