Multi-objective multi-layer congested facility location-allocation problem optimization with Pareto-based meta-heuristics

Facility location-allocation problems arise in many practical settings from emergency services to telecommunication networks. We propose a multi-objective multi-layer facility location-allocation (MLFLA) model with congested facilities using classical queuing systems. The goal is to determine the optimal number of facilities and the service allocation at each layer. We consider three objective functions aiming at: (1) minimizing the sum of aggregate travel and waiting times (2) minimizing the cost of establishing the facilities; and (3) minimizing the maximum idle probability of the facilities. The problem is formulated as a multi-objective non-linear integer mathematical programming model. To find and analyze the Pareto optimal solutions, we propose a Pareto-based multi-objective meta-heuristic approach based on the multi-objective vibration damping optimization (MOVDO) and the multi-objective harmony search algorithm (MOHSA). We demonstrate the effectiveness of the proposed model and exhibit the efficacy of the procedures and algorithms by comparing MOVDO and MOHSA with two well-known evolutionary algorithms, namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective simulated annealing (MOSA).