Faster Optimal State-Space Search with Graph Decomposition and Reduced Expansion

Traditional AI search methods, such as BFS, DFS, and A*, look for a path from a starting state to the goal in a state space most typically modelled as a directed graph. Prohibitively large sizes of the state space graphs make optimal search difficult. A key observation, as manifested by the SAS+ formalism for planning, is that most commonly a state-space graph is well structured as the Cartesian product of several small subgraphs. This paper proposes novel search algorithms that exploit such structure. The results reveal that standard search algorithms may explore many redundant paths. Our algorithms provide an automatic and mechanical way to remove such redundancy. Theoretically we prove the optimality and complexity reduction of the proposed algorithms. We further show that the proposed framework can accommodate classical planning. Finally, we evaluate our algorithms on various planning domains and report significant complexity reduction

A Duality Theory with Zero Duality Gap for Nonlinear Programming

Duality is an important notion for constrained optimization which provides a theoretical foundation for a number of constraint decomposition schemes such as separable programming and for deriving lower bounds in space decomposition algorithms such as branch and bound. However, the conventional duality theory has the fundamental limit that it leads to duality gaps for nonconvex optimization problems, especially discrete and mixed-integer problems where the feasible sets are nonconvex. In this paper, we propose a novel extended duality theory for nonlinear optimization that overcomes some limitations of previous dual methods. Based on a new dual function, the extended duality theory leads to zero duality gap for general nonconvex problems defined in discrete, continuous, and mixed-integer spaces under mild conditions

Functional Optimization Models for Active Queue Management

Active Queue Management (AQM) is an important problem in networking. In this paper, we propose a general functional optimiza-tion model for designing AQM schemes. Unlike the previous static func-tion optimization models based on the artificial notion of utility function, the proposed dynamic functional optimization formulation allows us to directly characterize the desirable system behavior of AQM and design AQM schemes to optimally control the dynamic behavior of the system. Such a formulation also allows adaptive control which enables the AQM scheme to continuously adapt to dynamic changes of networking con-ditions. In this paper, we present the Pontryagin minimum principle, a necessary condition, for the functional optimization model of AQM with TCP AIMD congestion control. As an example, we investigate a queu-ing stability criteria and apply the necessary conditions to optimize the functional model