The corridor allocation problem (CAP) seeks the optimum arrangement of given facilities along two sides of a central corridor. The CAP is so far handled as an unconstrained optimization problem without imposing any restriction on the placement of the facilities. In practice, however, some facilities may need to satisfy certain constraints on their placement. Accordingly, a constrained bi-objective CAP (cbCAP) model is proposed here, where some facilities are restricted to fixed, same and/or opposite rows. Realizing the difficulties to any algorithm for handling such a combinatorial problem, a cbCAP specific permutation-based genetic algorithm (cbCAP-pGA) with specialized operators is also proposed for solving the cbCAP model by generating only feasible solutions. In the numerical experimentation, the cbCAP-pGA is found capable in searching promising solutions even for a set of large-size benchmark instances.