TwoPILP: An Integer Programming Method for HCSP in Parallel Computing Centers

Scheduling is a problem in computer science with a wide range of applicability in industry. The Heterogeneous Computing Scheduling Problem (HCSP) belongs to the parallel computing area and is applicable to scheduling in clusters and high performance data centers. HCSP has been solved traditionally as a mono-objective problem that aims at minimizing the makespan (termination time of the last task) and has been solved by Branch and Bound (B&B) algorithms. HCSP with energy is a multi-objective optimization problem with two objectives: minimize the makespan and the energy consumption by the machines. In this paper, an integer linear programming model for HCSP is presented. In addition, a multi-objective method called TwoPILP (Two-Phase Integer Linear Programming) is proposed for this model. TwoPILP consists of two phases. The first minimizes the makespan using a classic branch and bound method. The second phase minimizes the energy consumption by selecting adequate voltage levels. The proposed model provides advantages over mono-objective models which are discussed in the paper sections. The experimentation presented compares TwoPILP versus B&B and NSGA-II, showing that TwoPILP achieves better results than B&B and NSGA-II. This method offers the advantage of providing only one solution to the user, which is particularly useful for applications where there is no decision maker for choosing from a set of solutions delivered by multi-objective optimization methods.