Solution-Guided Multi-Point Constructive Search (SGMPCS) is a novel constructive search technique that performs a series of resource-limited tree searches where each search begins either from an empty solution (as in randomized restart) or from a solution that has been encountered during the search. A small number of these "elite solutions is maintained during the search. We introduce the technique and perform three sets of experiments on the job shop scheduling problem. First, a systematic, fully crossed study of SGMPCS is carried out to evaluate the performance impact of various parameter settings. Second, we inquire into the diversity of the elite solution set, showing, contrary to expectations, that a less diverse set leads to stronger performance. Finally, we compare the best parameter setting of SGMPCS from the first two experiments to chronological backtracking, limited discrepancy search, randomized restart, and a sophisticated tabu search algorithm on a set of well-known benchmark problems. Results demonstrate that SGMPCS is significantly better than the other constructive techniques tested, though lags behind the tabu search.

Most classical scheduling formulations assume a fixed and known duration for each activity. In this paper, we weaken this assumption, requiring instead that each duration can be represented by an independent random variable with a known mean and variance. The best solutions are ones which have a high probability of achieving a good makespan. We first create a theoretical framework, formally showing how Monte Carlo simulation can be combined with deterministic scheduling algorithms to solve this problem. We propose an associated deterministic scheduling problem whose solution is proved, under certain conditions, to be a lower bound for the probabilistic problem. We then propose and investigate a number of techniques for solving such problems based on combinations of Monte Carlo simulation, solutions to the associated deterministic problem, and either constraint programming or tabu search. Our empirical results demonstrate that a combination of the use of the associated deterministic problem and Monte Carlo simulation results in algorithms that scale best both in terms of problem size and uncertainty. Further experiments point to the correlation between the quality of the deterministic solution and the quality of the probabilistic solution as a major factor responsible for this success.