Motivated by the increasing transition from fossil fuel-based centralized systems to renewable energy-based decentralized systems, we consider a bi-objective investment planning problem of a grid-connected decentralized hybrid renewable energy system. In this system, solar and wind are the main electricity generation resources. A national grid is assumed to be a carbon-intense alternative to the renewables and is used as a backup source to ensure reliability. We consider both total cost and carbon emissions caused by electricity purchased from the grid. We first discuss a novel simulation-optimization algorithm and then adapt multi-objective metaheuristic algorithms. We integrate a simulation module to these algorithms to handle the stochastic nature of this bi-objective problem. We perform extensive comparative analysis for the solution approaches and report their performances in terms of solution time and quality based on well-known measures from the literature.