Lagrangian Decomposition for Classical Planning (Extended Abstract)

Optimal cost partitioning of classical planning heuristics has been shown to lead to excellent heuristic values but is often prohibitively expensive to compute. We analyze the application of Lagrangian decomposition, a classical tool in mathematical programming, to cost partitioning of operator-counting heuristics. This allows us to view the computation as an iterative process that can be seeded with any cost partitioning and that improves over time. In the case of non-negative cost partitioning of abstraction heuristics the computation reduces to independent shortest path problems and does not require an LP solver

Hamiltonian approach and quantization of D=3,N=1D=3, {\cal N}=1 supersymmetric non-Abelian multiwave system

We develop Hamiltonian formalism and quantize supersymmetric non-Abelian multiwave system (nAmW) in D=3 spacetime constructed as a simple counterpart of 11D multiple M-wave system. Its action can be obtained from massless superparticle one by putting on its worldline 1d dimensional reduction of the 3d SYM model in such a way that the new system still possesses local fermionic kappa-symmetry. The quantization results in a set of equation of supersymmetric field theory in an unusual space with su(N)-valued matrix coordinates. Their superpartners, the fermionic su(N)-valued matrices, cannot be split on coordinates and momenta in a covariant manner and hence are included as abstract operators acting on the state vector in the generic form of our D=3 Matrix model field equations. We discuss the Clifford superfield representation for the quantum state vector and in the simplest case of N=2 elaborate it in a bit more detail. As a check of consistency, we show that the bosonic Matrix model field equations obtained by quantization of the purely bosonic limit of our D=3 nAmW system have a nontrivial solution.Comment: 1+27 page

An index for dynamic product promotion and the knapsack problem for perishable items

This paper introduces the knapsack problem for perishable items (KPPI), which concerns the optimal dynamic allocation of a limited promotion space to a collection of perishable items. Such a problem is motivated by applications in a variety of industries, where products have an associated lifetime after which they cannot be sold. The paper builds on recent developments on restless bandit indexation and gives an optimal marginal productivity index policy for the dynamic (single) product promotion problem with closed-form indices that yield estructural insights. The performance of the proposed policy for KPPI is investigated in a computational study.Dynamic promotion, Perishable items, Index policies, Knapsack problem, Festless bandits, Finite horizon, Marginal productivity index