Topological Optimization Models For Reliable Network Under Fuzziness

Reliability of a network is its ability to perform a required function under statedconditions for a stated period of time. We can discuss the reliability of a network fromits topological structure or its functional items. This dissertation resents a brief intro-duction to network reliability and then mainly discusses the topological optimizationunder network reliability constraints.The network optimization under reliability constraints usually depends on prob-ability theory, but it is not sufficient to deal with uncertainties in fuzziness, e.g., theimprecision caused by the existence of human beings in systems. Thus, we bring theconception of fuzzy variables.Fuzzy variables are mathematical descriptions for fuzzy phenomena, and are de-fined as functions from a credibility space to the set of real numbers. Credibility theoryis an axiomatic fuzzy theory, and a branch of mathematics that studies the behaviorof fuzzy phenomena. We introduced several conceptions such as credibility measure,membership function, excepted value and fuzzy simulation. They are the theoreticalfoundations to optimize network topology under fuzziness..In practice, there are mainly two ways to design an optimal topology for balancingsystem reliability and cost. One is to minimize the total cost subject to a reliabilityconstraint, while the other is to maximize the reliability subject to a cost constraint.We present some new types of optimization models for network topology with multiplereliability goals.It has been proved that network reliability problems are NP-hard. Therefore, afuzzy simulation-based genetic algorithm is designed to solve the proposed models.Finally, a numerical example is presented to illustrate the effectiveness of the algorithm.In conclusion, this dissertation brings forth the following new ideas: (a). withthe help of credibility theory, the concepts of network reliability under fuzziness areinitiated; (b). three kind of fuzzy optimization models, say, the fuzzy excepted valuemodel, fuzzy chance-constrained programming and fuzzy dependence-constrained pro-gramming of network reliability are defined; (c). the genetic algorithm combined withfuzzy simulation for calculating the corresponding models is established and a numer-ical example is presented.