| Summary: | 碩士 === 國立清華大學 === 工業工程研究所 === 82 === In this paper, we investigate a special structure of Symmetric
Chinese Postman Problems (SCPPs). The Chinese Postman Problem
(CPP) has been studied extensively in the literatures. When a
CPP is formulated in a form of an Interger Programming (IP)
model, it can be solved by a method of linear programming (LP)
if and only if it satisfies the symmetric and even-degree
properties. Recent years, the cutting-plane algorithm for a
CPP is developed by way of finding out the odd cuts of a graph.
But, in general, the complexity of finding out all odd cuts is
bad, and even though all odd cuts in a graph are found out, it
still cannot guarantee to obtain the optimal integral
solutions. So, we investigate the Symmetric Postman Problems
of special CPPs, of which the symmetric weights and symmetric
graph are defined. Numerically, we can obtain the optimal
integral solutions of a SCPP by way of finding out some
partial odd cuts, namely, the single cuts. Therefore, a prop
-osed cutting plane algorithm is developed for the SCPPs. This
proposed algorithm can also be applied to some symmetric
directed and mixted postman problems. Meanwhile, we extend the
algorithm to the problems that relax the condition of
symmetric weights. Finally, we evaluate the performance of the
proposed algorithm with some illustrative examples.
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