Europe has set carbon reduction targets, aiming for a 55% decrease in emissions by 2030 and carbon neutrality by 2050. The construction sector faces regulations under the Energy Performance of Building Directive recast 2020, which requires all new buildings to be Zero Emission Buildings (ZEBs) by 2030. Anticipating stricter regulations, such as Nearly-Zero Carbon Buildings (NZCB), the focus will shift to the entire lifecycle emissions. Bio-based materials, like timber, will likely replace traditional high carbon footprint materials. A simulation-based multi-objective optimization framework is developed to address the challenge of optimizing building design for minimal carbon impact (LCCO2) at lowest costs. This framework is applied on a case study, with different timber systems, envelope insulations and PV panels parameters as design variables.