95 research outputs found
Graph-based Reinforcement Learning meets Mixed Integer Programs: An application to 3D robot assembly discovery
Robot assembly discovery is a challenging problem that lives at the
intersection of resource allocation and motion planning. The goal is to combine
a predefined set of objects to form something new while considering task
execution with the robot-in-the-loop. In this work, we tackle the problem of
building arbitrary, predefined target structures entirely from scratch using a
set of Tetris-like building blocks and a robotic manipulator. Our novel
hierarchical approach aims at efficiently decomposing the overall task into
three feasible levels that benefit mutually from each other. On the high level,
we run a classical mixed-integer program for global optimization of block-type
selection and the blocks' final poses to recreate the desired shape. Its output
is then exploited to efficiently guide the exploration of an underlying
reinforcement learning (RL) policy. This RL policy draws its generalization
properties from a flexible graph-based representation that is learned through
Q-learning and can be refined with search. Moreover, it accounts for the
necessary conditions of structural stability and robotic feasibility that
cannot be effectively reflected in the previous layer. Lastly, a grasp and
motion planner transforms the desired assembly commands into robot joint
movements. We demonstrate our proposed method's performance on a set of
competitive simulated RAD environments, showcase real-world transfer, and
report performance and robustness gains compared to an unstructured end-to-end
approach. Videos are available at https://sites.google.com/view/rl-meets-milp
Optimal clustering of a pair of irregular objects
Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects
Essays on Integer Programming in Military and Power Management Applications
This dissertation presents three essays on important problems motivated by military and power management applications. The array antenna design problem deals with optimal arrangements of substructures called subarrays. The considered class of the stochastic assignment problem addresses uncertainty of assignment weights over time. The well-studied deterministic counterpart of the problem has many applications including some classes of the weapon-target assignment. The speed scaling problem is of minimizing energy consumption of parallel processors in a data warehouse environment. We study each problem to discover its underlying structure and formulate tailored mathematical models. Exact, approximate, and heuristic solution approaches employing advanced optimization techniques are proposed. They are validated through simulations and their superiority is demonstrated through extensive computational experiments. Novelty of the developed methods and their methodological contribution to the field of Operations Research is discussed through out the dissertation
The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
We present a description of the adaptive mesh refinement (AMR) implementation
of the PLUTO code for solving the equations of classical and special
relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits,
in addition to the static grid version of the code, the distributed
infrastructure of the CHOMBO library for multidimensional parallel computations
over block-structured, adaptively refined grids. We employ a conservative
finite-volume approach where primary flow quantities are discretized at the
cell-center in a dimensionally unsplit fashion using the Corner Transport
Upwind (CTU) method. Time stepping relies on a characteristic tracing step
where piecewise parabolic method (PPM), weighted essentially non-oscillatory
(WENO) or slope-limited linear interpolation schemes can be handily adopted. A
characteristic decomposition-free version of the scheme is also illustrated.
The solenoidal condition of the magnetic field is enforced by augmenting the
equations with a generalized Lagrange multiplier (GLM) providing propagation
and damping of divergence errors through a mixed hyperbolic/parabolic explicit
cleaning step. Among the novel features, we describe an extension of the scheme
to include non-ideal dissipative processes such as viscosity, resistivity and
anisotropic thermal conduction without operator splitting. Finally, we
illustrate an efficient treatment of point-local, potentially stiff source
terms over hierarchical nested grids by taking advantage of the adaptivity in
time. Several multidimensional benchmarks and applications to problems of
astrophysical relevance assess the potentiality of the AMR version of PLUTO in
resolving flow features separated by large spatial and temporal disparities.Comment: 34 pages, 34 figures, accepted for publication in ApJ
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