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An Embedded Connectionist Approach for the Inverse Shortest Paths Problem
, 1996
"... The Inverse Shortest Path (ISP) problem has recently been considered for applications involving the precise determination of unknown path costs, given only limited experts' knowledge of some shortest paths. Unlike previous approaches which are usually restrictive (such as the minimum change requirem ..."
Abstract

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The Inverse Shortest Path (ISP) problem has recently been considered for applications involving the precise determination of unknown path costs, given only limited experts' knowledge of some shortest paths. Unlike previous approaches which are usually restrictive (such as the minimum change requirement) and algorithmically complicated, a more general but simple optimization scheme based on embedded shortest paths computation is proposed. Confliciting experts' knowledge can also be readily accomodated as multiple objectives instead of hard constraints. In particular, the possibility of embedding a class of connectionist network, called the binary relation inference network, to solve the ISP problem is explored. The inference network has been recently applied in solving constrained optimization problems, such as the shortest path problem, transitive closure, minimax problem, etc. Its inherently parallel operating nature can be well exploited for potential speedup by embedding it as a re...
A Connectionist Network for Dynamic Programming Problems
"... Dynamic programming is wellknown as a powerful modeling technique for dealing with the issue of making optimal decisions sequentially. Many practical problems, such as finding shortest paths in route planning, multistage optimal control, can be formulated as special cases of the general sequential ..."
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Dynamic programming is wellknown as a powerful modeling technique for dealing with the issue of making optimal decisions sequentially. Many practical problems, such as finding shortest paths in route planning, multistage optimal control, can be formulated as special cases of the general sequential decision process. This paper proposes a connectionist network architecture, called the binary relation inference network, which solves a special class of dynamic programming problems in the continuous time. They include the allpair solutions for a family of closed semiring path problems, such as shortest paths, transitive closure, minimum spanning tree, and minimax path problems. The allpair inference network specifies a basic and uniform computation of its individual units which then collectively emerge towards a global optimal solution. The computational order in its discretetime variants, either as synchronous or asynchronous networks, bear a close resemblance to the FloydWarshall al...
A Continuoustime Inference Network and its Hybrid Implementations
"... A class of binary relation inference network has been recently proposed for applications in graph (or network) optimization and in timing analysis of microprocessor systems. In handling the timing consistency problem between different events, there are some intrinsic weaknesses underlying this type ..."
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A class of binary relation inference network has been recently proposed for applications in graph (or network) optimization and in timing analysis of microprocessor systems. In handling the timing consistency problem between different events, there are some intrinsic weaknesses underlying this type of discretetime inference network , namely, network instability and oscillation under specific circumstances, and the slow convergence rate commonly observed in large networks. To circumvent the potential shortcomings of existing inference networks, statespace techniques are used to derive a more robust continuoustime inference network. Simulation studies on two hybrid schemes indicate significant improvements over discretetime inference network, and demonstrate their practical viability for applications in timevarying cases. 1 Introduction In a complex system consisting of many entities (objects or events), the inference process to deduce a binary relation becomes more complicated as ...