Constraint based methods for allocation and scheduling of periodic applications

This work presents exact algorithms for the Resource Allocation and Cyclic Scheduling Problems (RA&CSPs). Cyclic Scheduling Problems arise in a number of application areas, such as in hoist scheduling, mass production, compiler design (implementing scheduling loops on parallel architectures), software pipelining, and in embedded system design. The RA&CS problem concerns time and resource assignment to a set of activities, to be indefinitely repeated, subject to precedence and resource capacity constraints. In this work we present two constraint programming frameworks facing two different types of cyclic problems. In first instance, we consider the disjunctive RA&CSP, where the allocation problem considers unary resources. The proposed method has broad applicability, but it is mainly motivated by applications in the field of Embedded System Design. Instances are described through the Synchronous Data-flow (SDF) Model of Computation. Data-Flow models are attracting renewed attention because they lend themselves to efficient mapping on multi-core architectures. The key problem of finding a maximum-throughput allocation and scheduling of Synchronous Data-Flow graphs onto a multicore architecture is NP-hard and has been traditionally solved by means of heuristic (incomplete) algorithms with no guarantee of global optimality. We propose an exact (complete) algorithm for the computation of a maximumthroughput mapping of applications specified as SDFG onto multi-core architectures. Results show that the approach can handle realistic instances in terms of size and complexity. The basic idea of the approach we present is to model the effects of allocation and scheduling choices by means of graph modifications. During the search process, whenever allocation and scheduling decision are taken, the graph is modified accordingly. The efficiency of this approach hinges on an original global throughput constraint. Next, we tackle the Cyclic Resource-Constrained Scheduling Problem (i.e. CRCSP). We propose a Constraint Programming approach based on modular arithmetic: in particular, we introduce a modular precedence constraint and a global cumulative constraint along with their filtering algorithms. We discuss two possible formulations. The first one (referred to as CROSS ) models a pure cyclic scheduling problem and makes use of both our novel constraints. The second formulation (referred to as CROSS ∗) introduces a restrictive assumption to enable the use of classical resources constraints, but may incur a loss of solution quality. Many traditional approaches to cyclic scheduling operate by fixing the period value and then solving a linear problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model and tackles the problem as a whole: the period value is inferred from the scheduling decisions. The proposed framework has been used in the MPOpt-Cell framework: a High-Performance Data-Flow Programming Environment for the Cell BE Processor by IBM, Sony and Toshiba. The proposed approaches have been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances achieving good results on practical size problem. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.