Redundancy queuing-location-allocation problems (RQLAPs) involve the economical allocation of facilities, each with a number of servers, to suitable locations with appropriate levels of redundancy or reliability. The goal in RQLAPs is to find the facilities which are both inexpensive and reliable. We take into consideration the congestion of the system by modeling each facility as an M/M/m queuing system and formulate the problem as a multiobjective nonlinear mixed integer programming problem. However, these problems are nondeterministic polynomial-time hard (NP-hard) problems where an exact solution cannot be produced in polynomial time. We propose a novel soft-computing approach based on the vibration theory called vibration damping optimization (VDO) to solve the RQLAP. We develop a multiobjective version of the VDO called multiobjective VDO (MOVDO) based on the fast nondominated sorting and crowding distance concepts in the literature. The performance of the proposed MOVDO is statistically compared with two other commonly used metaheuristic algorithms called the nondominated sorting genetic algorithm and multiobjective simulated annealing. A comparison of the results based on different problem sizes favors the MOVDO method proposed in this study.
