Application of efficient metaheuristics to solve a new bi-objective optimization model for hub facility location problem considering value at risk criterion

In this paper, a new bi-objective hub facility location problem is studied where the demands of customers are stochastic and follow a normal distribution function. The first objective is to minimize total amount of value at risk which has a new probabilistic criterion and optimizes amount of lost demand. In addition, the second objective minimizes total costs of the network. Furthermore, some constraints are nonlinear in this model and it is aimed to linearize them by efficient approximate procedures. This paper tries to apply three efficient solution procedures to solve the bi-objective model. Thus, three algorithms are ε -constraint, non-dominated sorting genetic algorithm-II (NSGA-II), and multi-objective particle swarm optimizers (MOPSO) which are creativity ways used in this paper to approximate the Pareto-optimal solutions. Taguchi experimental design is used to find the right parameter settings for metaheuristic algorithms. A comparative study of three proposed algorithms demonstrates the most effectiveness algorithm with respect to five existing performance measures for numerous test problems. Finally, the comparison within each two algorithms is completed by applying multiple statistical tests and diagrams. The obtained solutions by MOPSO are better than NSGA-II at 95 % confidence level.