Parallel Genetic Algorithm for Minimizing Total Weighted Completion Time

We have considered the problem of job scheduling on a single machine with deadlines. The objective is to find a feasible job sequence (satisfying the deadlines) to minimize the sum of weighted completion times. Since the problem is NP-hard, heuristics have to be used. Methods of artificial intelligence: simulated annealing, neural networks and genetic algorithms, are some of the recent approaches. We propose a very effective parallel genetic algorithm PGA and methods of determining lower and upper bounds of the objective function. Since there are difficulties with determining the initial population of PGA for this scheduling problem, therefore the algorithm also adds random generated unfeasible solutions to the population. We announce a method of elimination of these kind of solutions. The examined algorithms are implemented in Ada95 and MPI. Results of computational experiments are reported for a set of randomly generated test problems.