Effective Algorithm for Obtaining the Pareto Solutions of a Multi-Objective Network Utilizing Network Properties

Abstract

There are many network systems in the world; for example, Internet, electricity networks and traffic networks. In this study, we consider two-objective network design problem with all-terminal reliability and construction/operation/maintenance costs. There is a trade-off relation between reliability and costs. In general, it is a rare case that a network system solution simultaneously provides both optimum all-terminal reliability and optimum cost. Therefore, we must consider an algorithm for obtaining Pareto solutions. The reliability and cost problems for network systems have been studied for a long time and numerous papers have been published. Existing algorithms are efficient for calculating only the all-terminal reliability for a network. However, these are inefficient for obtaining Pareto solutions, as we must calculate the all-terminal reliability and cost for all sub-networks. Therefore, algorithms require much time to obtain Pareto solutions when the number of nodes or edges is large. To ensure efficient calculation to obtain the Pareto front, we propose an algorithm that does not need to consider all sub-networks. The algorithm we propose selects parts of the networks for calculation. We researched relations between edges that tended to construct Pareto solutions and other edges, and obtained some properties that Pareto solutions are likely to satisfy to use in this process. These properties generate the search space in which networks take close values to Pareto solutions. Combining properties found in our study, we construct algorithms for obtaining Pareto solutions, which restricts the number of networks that must be calculated. The Pareto solutions obtained using this reduction are probably a proper subset of Pareto solutions. Therefore, we evaluate the computing time and accuracy of the algorithms proposed using numerical experiments.