In practice, users are often stuck with an existing solution, despite agreeing on the fact that the solution needs a substantial change. The hesitation might stem from the hefty cost or amount of effort required to adopt a new solution or could just be human apathy to large changes. In this regard, a recent preliminary study proposed a step-constrained based bi-objective optimization approach which attempts to discover a set of acceptable intermediate solutions starting from the current solution to the desired target solution leading to an innovation path (IP). Intermediate solutions, obtained using a multiobjectivization approach, reduce the amount of change required between two successive steps, thereby facilitating multiple gradual changes more acceptable by the users. In this paper, we propose a directed domination concept to make the IP-seeking algorithm more computationally efficient. Results on a number of test and engineering problems reveal that the proposed new approach reaches closer to the target solution and finds closer to optimally trade-off solutions than the previous IP approach.