In the energy transition of energy networks, multi-energy systems (MES) are promising technologies as they enable synergies between multiple energy carriers (electricity, gas, heat). Multi-objective optimization is then needed to determine both the optimal design of the energy conversion technologies and their operation parameters, over multiple objectives (e.g.: costs and environmental criteria). However, the objective functions of a MES model might not be linear, meaning some linearization techniques such as piecewise linear approximation must be used to write a mathematical model of a MES, introducing integer variables in the model. This work presents first a mixed-integer linear programming (MILP) model to solve the problem of the optimal design and operation of a MES over two objectives. The limitations of this approach are then presented, and a new matheuristic model is proposed, in which a metaheuristic is used to solve the nonlinear parts of the model, i.e. the design of the MES, and a mathematical program is used to solve optimally the operation of the MES with respect to the constraints of the metaheuristic. This work is applied to the optimization of a MES in Nantes, France, using one year of historical data with an hourly resolution.