The resource-constrained modulo scheduling problem: an experimental study

Abstract

In this paper, we focus on the resource-constrained modulo scheduling problem, a general periodic scheduling problem, abstracted from the problem solved by compilers when optimizing inner loops at instruction level for VLIW parallel processors. Heuristic solving scheme have been proposed since many years to solve this problem, among which the decomposed software pipeling method. In this method, a cyclic scheduling problem ignoring resource constraints is first considered and a so-called legal retiming of the operations is issued. Second, a standard acyclic problem, taking this retiming as input, is solved through list scheduling techniques. In this paper, we propose an hybrid approach, which uses the decomposed software pipeling method to obtain a good retiming. Then the obtained retiming is used to build an Integer Linear Programming formulation of reduced size, which allows to solve it exactly. Experimental results show that a lot more problems are solved with this new approach. The gap to the optimal solution is really small (0 or 1%) on all the tested problem instances.

Cyclic Data Flows in Computers and Embedded Systems

“…Although it can be easily proved that periodic schedules are not dominating schedules, their simple formulation make them very easy to implement and thus often used in loop parallelization context. Firstly the ILP formulations, for example in [3,20,19] combining classical ILP formulations of resource constraints (either time-indexed or not), and linear expression of uniform constraints. In [3], several models are described and experimentally compared.…”

“…Computations are done by physical components that, from a scheduling point of view are similar to usual processors or machines in production process though parallel processors or more complex resources from RCPSP problems are usually used [3]. However, energy saving may induce unusual constraints on the scheduling process, in particular grouping of tasks processed by the same component, in order to avoid too many on/off.…”

A robust basic cyclic scheduling problem

“…Let us reconsider the two-stage robust optimization problem (5)- (6). In order to decide if a given cycle timeᾱ is feasible or not we define the following separation problem.…”

“…in robotics industry ( [1]; [2]), in manufacturing systems ( [3]; [4]), in parallel computing and computer pipelining ( [5]; [6]; [7]). Depending on the target application, different mathematical models exist, based on graph theory, mixed linear programming, Petri nets or (max, +) algebra.…”

Energy Optimization of Robotic Cells

“…The cycle time is typically shorter than the duration of the start-up phase; thus, there are usually more unfinished workpieces in the robotic cell at a given time. Such parallelism is analogous with the cyclic scheduling of the processor pipeline (see, e.g., [17] and [18]). However, Wigström and Lennartson [10] presumed that the whole robotic cell is dedicated to one workpiece during the entire processing time, which the authors called the work cycle time; hence, the overall throughput may be limited because there is no parallelism.…”