A multi-objective harmony search algorithm to optimize multi-server location–allocation problem in congested systems

• A novel bi-objective multi-server location–allocation model is developed.
• Capacity and budget limitations are provided to make the problem more realistic.
• Multi-objective harmony search algorithm is developed to solve the presented model.
• A new presentation scheme that satisfies most of the model constraints is proposed.
• The parameters of all algorithms are calibrated by Taguchi method using a novel metric.

A novel bi-objective multi-server location–allocation (LA) model is developed in this paper, in which the facilities are modeled as an M/M/m queuing system. Further, capacity and budget limitations are provided to make the LA problem more realistic. The two objective functions include (1) minimizing aggregate waiting times and (2) minimizing the maximum idle time of all facilities. Since the proposed model is NP-hard, a meta-heuristic algorithm called multi-objective harmony search algorithm (MOHA) is developed to solve it. In this algorithm, a new presentation scheme that satisfies most of the model constraints is proposed. Since there is no benchmark available in the literature to validate the results obtained, the performance of MOHA is statistically compared with the ones of two other common meta-heuristics called multi-objective genetic algorithm (MOGA) and multi-objective simulated annealing (MOSA). The parameters of all algorithms are first calibrated by means of the Taguchi method using a novel metric. The comparison results based on different problem sizes are in favor of MOHA.