An interactive augmented max-min MCS–RSM method for the multi-objective network reliability problem

Abstract

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. It is always desirable simultaneously to maximize network reliability and minimize resource consumption, e.g., the total cost [i.e., the multi-objective network reliability problem (MONR)]. In this study, we first construct the network reliability function using the formulations for simple networks and the MCS–RSM (the Monte–Carlo simulation & the response surface methodology) for complex networks of which the exact reliability functions are very difficult to find. Then, an intuitive interactive algorithm is developed using the augmented max-min method to solve the MONR based on a nonfuzzy nonlinear programming model. The feasibility of the proposed method by means of two numerical examples has been demonstrated.

Keywords:

• Multi-objective problem (MOP)
• The multi-objective network reliability problem (MONR)
• Reliability
• Reliability cost
• Augmented max-min method
• Monte–Carlo simulation (MCS)
• Response surface methodology (RSM)

Acknowledgment

I wish to thank both the anonymous editor and referees for their constructive comments and recommendations, which have significantly improved the presentation of this article. This research was supported in part by the National Science Council of Taiwan, R.O.C. under grant NSC 90-2218-E-035-006.