6,187 research outputs found
Particle algorithms for optimization on binary spaces
We discuss a unified approach to stochastic optimization of pseudo-Boolean
objective functions based on particle methods, including the cross-entropy
method and simulated annealing as special cases. We point out the need for
auxiliary sampling distributions, that is parametric families on binary spaces,
which are able to reproduce complex dependency structures, and illustrate their
usefulness in our numerical experiments. We provide numerical evidence that
particle-driven optimization algorithms based on parametric families yield
superior results on strongly multi-modal optimization problems while local
search heuristics outperform them on easier problems
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
On Degeneracy Issues in Multi-parametric Programming and Critical Region Exploration based Distributed Optimization in Smart Grid Operations
Improving renewable energy resource utilization efficiency is crucial to
reducing carbon emissions, and multi-parametric programming has provided a
systematic perspective in conducting analysis and optimization toward this goal
in smart grid operations. This paper focuses on two aspects of interest related
to multi-parametric linear/quadratic programming (mpLP/QP). First, we study
degeneracy issues of mpLP/QP. A novel approach to deal with degeneracies is
proposed to find all critical regions containing the given parameter. Our
method leverages properties of the multi-parametric linear complementary
problem, vertex searching technique, and complementary basis enumeration.
Second, an improved critical region exploration (CRE) method to solve
distributed LP/QP is proposed under a general mpLP/QP-based formulation. The
improved CRE incorporates the proposed approach to handle degeneracies. A
cutting plane update and an adaptive stepsize scheme are also integrated to
accelerate convergence under different problem settings. The computational
efficiency is verified on multi-area tie-line scheduling problems with various
testing benchmarks and initial states
Combinatorial persistency criteria for multicut and max-cut
In combinatorial optimization, partial variable assignments are called
persistent if they agree with some optimal solution. We propose persistency
criteria for the multicut and max-cut problem as well as fast combinatorial
routines to verify them. The criteria that we derive are based on mappings that
improve feasible multicuts, respectively cuts. Our elementary criteria can be
checked enumeratively. The more advanced ones rely on fast algorithms for upper
and lower bounds for the respective cut problems and max-flow techniques for
auxiliary min-cut problems. Our methods can be used as a preprocessing
technique for reducing problem sizes or for computing partial optimality
guarantees for solutions output by heuristic solvers. We show the efficacy of
our methods on instances of both problems from computer vision, biomedical
image analysis and statistical physics
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