The European electricity markets' integration aims at the market coupling among interconnected power systems and the enhancement of market competitive forces. This process is facilitated by the adoption of a common clearing algorithm among European power exchanges, entitled EUPHEMIA (Pan-European Hybrid Electricity Market Integration Algorithm), which however lacks to capture critical technical aspects of power systems, as done by the unit commitment problem including start-up and shut-down decisions, time constraints (minimum on- and off-times), as well as the consideration of ancillary services. This paper presents an optimization-based framework for the optimal joint energy and reserves market clearing algorithm, further utilizing the hourly offers module of the EUPHEMIA algorithm. In particular, through the formulation of a mixed integer linear programming (MILP) model and employing an iterative approach, it determines the optimal energy and reserves mix, the resulting market clearing prices, and it calculates the welfares of the market participants. The model incorporates infra-hourly power reserve constraints, as well as introduces new market products such as the option of forming linked groups of power units, aiming at supplying additional flexibility in the decision-making of the market participants. The model applicability has been assessed in the Greek power system and its interconnections with neighboring power systems in Southeast Europe. The proposed optimization framework can provide useful insights on the determination of the optimal generation and interconnection portfolios that address the new market-based operational challenges of contemporary power systems subject to technical and economic constraints.