647 research outputs found
A General Large Neighborhood Search Framework for Solving Integer Programs
This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi
A simple iterative algorithm for maxcut
We propose a simple iterative (SI) algorithm for the maxcut problem through
fully using an equivalent continuous formulation. It does not need rounding at
all and has advantages that all subproblems have explicit analytic solutions,
the cut values are monotonically updated and the iteration points converge to a
local optima in finite steps via an appropriate subgradient selection.
Numerical experiments on G-set demonstrate the performance. In particular, the
ratios between the best cut values achieved by SI and the best known ones are
at least and can be further improved to at least by a
preliminary attempt to break out of local optima.Comment: 30 pages, 1 figure. Subgradient selection, cost analysis and local
breakout are adde
A Class of Semidefinite Programs with rank-one solutions
We show that a class of semidefinite programs (SDP) admits a solution that is
a positive semidefinite matrix of rank at most , where is the rank of
the matrix involved in the objective function of the SDP. The optimization
problems of this class are semidefinite packing problems, which are the SDP
analogs to vector packing problems. Of particular interest is the case in which
our result guarantees the existence of a solution of rank one: we show that the
computation of this solution actually reduces to a Second Order Cone Program
(SOCP). We point out an application in statistics, in the optimal design of
experiments.Comment: 16 page
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