Bioinformatics has always been a prolific domain for generating complex satisfiability and optimization problems. For instance, the synthesis of multi-scale models of biological networks has recently been associated with the resolution of optimization problems mixing Boolean logic and universally quantified linear constraints (OPT+qLP), which can be benchmarked on real-world models. In this paper, we introduce a CounterExample Guided Abstraction Refinement (CEGAR) to solve such problems efficiently. Our CEGAR exploits monotone properties inherent to linear optimization in order to generalize counterexamples of Boolean relaxations. We implemented our approach by extending Answer Set Programming (ASP) solver Clingo with a quantified linear constraints propagator. Our prototype enables exploiting independence of sub-formulas to further exploit the generalization of counterexamples. We evaluate the impact of refinement and partitioning on two sets of OPT+qLP problems inspired by system biology. Additionally, we conducted a comparison with the state-of-the-art ASP solver Clingo[lpx] that handles non-quantified linear constraints, showing the advantage of our CEGAR approach for solving large problems.