Fog computing has risen as a promising technology for augmenting the computational and storage capability of the end devices and edge networks. The urging issues in this networking paradigm are fog nodes planning, resources allocation, and offloading strategies. This paper aims to formulate a mathematical model which jointly tackles these issues. The goal of the model is to optimize the tradeoff (Pareto front) between the capital expenditure and the network delay. To solve this multiobjective optimization problem and obtain benchmark values, we first use the weighted sum method and two existing evolutionary algorithms (EAs), nondominated sorting genetic algorithm II and speed-constrained multiobjective particle swarm optimization. Then, inspired by those EAs, this paper proposes a new EAs, named particle swarm optimized nondominated sorting genetic algorithm, which combines the convergence and searching efficiency of the existing EAs. The effectiveness of the proposed algorithm is evaluated by the hypervolume and inverted generational distance indicators. The performance evaluation results show that the proposed model and algorithms can help the network planners in the deployment of fog networks to complement their existing computation and storage infrastructure.