Logic-based Benders decomposition

Abstract

Benders decomposition uses a strategy of "learning from one's mistakes." The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an "inference dual." Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods. *

Allocation, Scheduling and Voltage Scaling on Energy Aware MPSoCs

“…The method we use for handling the DVSP uses the logic-based Benders decomposition technique [8]. Similarly to [2], the problem is decomposed into two parts: the first, called Master Problem, is the allocation of processors and frequencies to tasks and the second, called Subproblem, is the scheduling of tasks given the static allocation and frequency assignments provided by the master.…”

“…It has never been solved to optimality by the system design community and it cannot be solved by any complete commercial solver that models the problem as a whole. The method we use is the Logic Based Benders Decomposition [8], an extension of the well known OR Benders Decomposition [1] approach for dealing with solvers of any kind. In this setting, we allocate tasks to processors and decide their execution frequency in the master problem, while the subproblem schedules tasks with a fixed duration and static resource assignment.…”

Stochastic Allocation and Scheduling for Conditional Task Graphs in MPSoCs

“…Constraints (4) and (5) enforce that the communication queue of arc r can be locally allocated only if both the source and the destination tasks run on processor j. Finally, constraints (6) ensure that the sum of locally allocated state (s i ), computation (m i ) and communication (c r ) memory cannot exceed the scratchpad device capacity (C j ). All tasks have to be considered here, regardless they will execute or not at runtime, since a scratchpad memory is, by definition, statically allocated.…”

“…Therefore, after an accurate application profiling step, we have a probability distribution on each conditional branch that intuitively gives the probability of choosing that branch during execution. This paper proposes a non trivial extension to [5] that used Logic Based Benders decomposition [6] for resource assignment and scheduling in MPSoCs. In that paper, however, task graphs did not contain conditional activities.…”

Integrating Benders Decomposition Within Constraint Programming

“…Hybridization schemes have appeared recently and provided interesting computational results [4,5,7,8]. They have been extended [2,3,6] to take into account other kinds of sub-problems and not only the classical linear programming ones. However, decomposition has never been proposed to our knowledge in a generic constraint programming approach.…”