19,022 research outputs found
One Benders cut to rule all schedules in the neighbourhood
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant,
namely Branch-and-Check, enjoy an extensive applicability on a broad variety of
problems, including scheduling. Although LBBD offers problem-specific cuts to
impose tighter dual bounds, its application to resource-constrained scheduling
remains less explored. Given a position-based Mixed-Integer Linear Programming
(MILP) formulation for scheduling on unrelated parallel machines, we notice
that certain OPT neighbourhoods could implicitly be explored by regular
local search operators, thus allowing us to integrate Local Branching into
Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining
their local optima - hence, proving that they are suboptimal - a local
branching cut (applied as a Benders cut) eliminates all their solutions at
once, thus avoiding an overload of the master problem with thousands of Benders
cuts. However, to guarantee convergence to optimality, the constructed
neighbourhood should be exhaustively explored, hence this time-consuming
procedure must be accelerated by domination rules or selectively implemented on
nodes which are more likely to reduce the optimality gap. In this study, the
realisation of this idea is limited on the common 'internal (job) swaps' to
construct formulation-specific -OPT neighbourhoods. Nonetheless, the
experimentation on two challenging scheduling problems (i.e., the minimisation
of total completion times and the minimisation of total tardiness on unrelated
machines with sequence-dependent and resource-constrained setups) shows that
the proposed methodology offers considerable reductions of optimality gaps or
faster convergence to optimality. The simplicity of our approach allows its
transferability to other neighbourhoods and different sequencing optimisation
problems, hence providing a promising prospect to improve Branch-and-Check
methods
Solving DCOPs with Distributed Large Neighborhood Search
The field of Distributed Constraint Optimization has gained momentum in
recent years, thanks to its ability to address various applications related to
multi-agent cooperation. Nevertheless, solving Distributed Constraint
Optimization Problems (DCOPs) optimally is NP-hard. Therefore, in large-scale,
complex applications, incomplete DCOP algorithms are necessary. Current
incomplete DCOP algorithms suffer of one or more of the following limitations:
they (a) find local minima without providing quality guarantees; (b) provide
loose quality assessment; or (c) are unable to benefit from the structure of
the problem, such as domain-dependent knowledge and hard constraints.
Therefore, capitalizing on strategies from the centralized constraint solving
community, we propose a Distributed Large Neighborhood Search (D-LNS) framework
to solve DCOPs. The proposed framework (with its novel repair phase) provides
guarantees on solution quality, refining upper and lower bounds during the
iterative process, and can exploit domain-dependent structures. Our
experimental results show that D-LNS outperforms other incomplete DCOP
algorithms on both structured and unstructured problem instances
Scheduling commercial advertisements for television
The problem of scheduling the commercial advertisements in the television industry is investigated. Each advertiser client demands that the multiple airings of the same brand advertisement should be as spaced as possible over a given time period. Moreover, audience rating requests have to be taken into account in the scheduling. This is the first time this hard decision problem is dealt with in the literature. We design two mixed integer linear programming (MILP) models. Two constructive heuristics, local search procedures and simulated annealing (SA) approaches are also proposed. Extensive computational experiments, using several instances of various sizes, are performed. The results show that the proposed MILP model which represents the problem as a network flow obtains a larger number of optimal solutions and the best non-exact procedure is the one that uses SA
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