solving a stochastic multi-depot multi-objective vehicle routing problem by a simulated annealing

in this paper, a stochastic multi-depot multi-objective vehicle routing problem (vrp) is studied. based on observations in real-world problems, we develop an aspect of the problem, such as stochastic availability of routes. to solve the problem in this situation, a two-objective mathematical model is developed, in which the related objective functions are: (1) minimizing transportation costs and (2) maximizing probability of delivery to customers. the second objective function, which is nonlinear, has performed to a linear function. since this problem is np-hard, to solve it we propose simulated annealing (sa) that is a well-known meta-heuristic algorithm. to show the performance of this algorithm, we compare the related results in terms of run-time and objective function values with the lower bound and lingo 8 software for different sizes of the given problem.