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Component-based Software Engineering (CBSE) uses components to construct systems, being a means to increase productivity by promoting software reuse and increasing software quality. The process of assembling component is called component composition. Components are themselves compositions of components. This give rise to the idea of composition levels, where a component on level i may be decomposed (using more components) at level i + 1 or compositions at level i + 1 serves as component at level i. We are approaching the multilevel component composition problem. We formulate the problem as multiobjective, involving 4 objectives. The approach used is an evolutionary computation technique.