Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Reliability demonstration for safety-critical systems

This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model; the test equipment required and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, Single Risk Sequential Testing (SRST), with the standard Probability Ratio Sequential Testing method (PRST), and concludes that: • SRST provides higher chances of success than PRST • SRST takes less time to complete than PRST • SRST satisfies the consumer risk criterion, whereas PRST provides a much smaller consumer risk than the requirement

Optimal Number, Location, and Size of Distributed Generators in Distribution Systems by Symbiotic Organism Search Based Method

This paper proposes an approach based on the Symbiotic Organism Search (SOS) for optimal determining sizing, siting, and number of Distributed Generations (DG) in distribution systems. The objective of the problem is to minimize the power loss of the system subject to the equality and inequality constraints such as power balance, bus voltage limits, DG capacity limits, and DG penetration limit. The SOS approach is defined as the symbiotic relationship observed between two organisms in an ecosystem, which does not need the control parameters like other meta-heuristic algorithms in the literature. For the implementation of the proposed method to the problem, an integrated approach of Loss Sensitivity Factor (LSF) is used to determine the optimal location for installation of DG units, and SOS is used to find the optimal size of DG units. The proposed method has been tested on IEEE 33-bus, 69-bus, and 118-bus radial distribution systems. The obtained results from the SOS algorithm have been compared to those of other methods in the literature. The simulated results have demonstrated that the proposed SOS method has a very good performance and effectiveness for the problem of optimal placement of DG units in distribution systems