Modern practical optimization problems are too often complex, nonlinear, large-dimensional, and sometimes dynamic making gradient-based and convex optimization methods too inefficient. Moreover, most such problems which must be solved for a reasonably approximate solution routinely in every few hours or every day must use a computationally fast algorithm. In this paper, we present a formulation of a dynamic vessel-to-vessel service ship scheduling problem. In a span of several hours, the service ship must visit as many moving vessels as possible and complete the trip in as small a travel time as possible. Thus, the problem is bi-objective in nature and involves a time-dependent traveling salesman problem. We develop a level-wise customized evolutionary algorithm to find multiple trade-off solutions in a generative manner. Compared to a mixed-integer programming (MIP) algorithm, we demonstrate that our customized evolutionary algorithm achieves similar quality schedules in a fraction of the time required by the MIP solver. We are currently developing an interactive decision support tool based on our proposed method for finding multiple trade-off schedules simultaneously and selecting a single preferred one.