1,062 research outputs found
A local branching heuristic for MINLPs
Local branching is an improvement heuristic, developed within the context of
branch-and-bound algorithms for MILPs, which has proved to be very effective in
practice. For the binary case, it is based on defining a neighbourhood of the
current incumbent solution by allowing only a few binary variables to flip
their value, through the addition of a local branching constraint. The
neighbourhood is then explored with a branch-and-bound solver. We propose a
local branching scheme for (nonconvex) MINLPs which is based on iteratively
solving MILPs and NLPs. Preliminary computational experiments show that this
approach is able to improve the incumbent solution on the majority of the test
instances, requiring only a short CPU time. Moreover, we provide algorithmic
ideas for a primal heuristic whose purpose is to find a first feasible
solution, based on the same scheme
A Two-Level Approach to Large Mixed-Integer Programs with Application to Cogeneration in Energy-Efficient Buildings
We study a two-stage mixed-integer linear program (MILP) with more than 1
million binary variables in the second stage. We develop a two-level approach
by constructing a semi-coarse model (coarsened with respect to variables) and a
coarse model (coarsened with respect to both variables and constraints). We
coarsen binary variables by selecting a small number of pre-specified daily
on/off profiles. We aggregate constraints by partitioning them into groups and
summing over each group. With an appropriate choice of coarsened profiles, the
semi-coarse model is guaranteed to find a feasible solution of the original
problem and hence provides an upper bound on the optimal solution. We show that
solving a sequence of coarse models converges to the same upper bound with
proven finite steps. This is achieved by adding violated constraints to coarse
models until all constraints in the semi-coarse model are satisfied. We
demonstrate the effectiveness of our approach in cogeneration for buildings.
The coarsened models allow us to obtain good approximate solutions at a
fraction of the time required by solving the original problem. Extensive
numerical experiments show that the two-level approach scales to large problems
that are beyond the capacity of state-of-the-art commercial MILP solvers
A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming
In this paper we deal with a network of agents seeking to solve in a
distributed way Mixed-Integer Linear Programs (MILPs) with a coupling
constraint (modeling a limited shared resource) and local constraints. MILPs
are NP-hard problems and several challenges arise in a distributed framework,
so that looking for suboptimal solutions is of interest. To achieve this goal,
the presence of a linear coupling calls for tailored decomposition approaches.
We propose a fully distributed algorithm based on a primal decomposition
approach and a suitable tightening of the coupling constraints. Agents
repeatedly update local allocation vectors, which converge to an optimal
resource allocation of an approximate version of the original problem. Based on
such allocation vectors, agents are able to (locally) compute a mixed-integer
solution, which is guaranteed to be feasible after a sufficiently large time.
Asymptotic and finite-time suboptimality bounds are established for the
computed solution. Numerical simulations highlight the efficacy of the proposed
methodology.Comment: 57th IEEE Conference on Decision and Contro
Graphical Models for Optimal Power Flow
Optimal power flow (OPF) is the central optimization problem in electric
power grids. Although solved routinely in the course of power grid operations,
it is known to be strongly NP-hard in general, and weakly NP-hard over tree
networks. In this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
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