Many objective optimization problems have turned out to be a considerable challenge for evolutionary algorithms due to the difficulty of finding and visualizing high-dimensional Pareto frontiers. Fortunately, however, the task can be simplified whenever an interaction with a human decision maker is possible. Instead of finding the entire Pareto frontier, the evolutionary search can be guided to the parts of the space that are most relevant for the decision maker. In this paper, we propose an interactive method for solving many objective optimization problems. Drawing on the recent developments in multiple criteria decision making, we introduce an effective strategy for leveraging polyhedral preference cones within an evolutionary algorithm. The approach is mathematically motivated and is applicable to situations, where the user’s preferences can be assumed to follow an unknown quasi-concave and increasing utility function. In addition to considering the preference cones as a tool for eliminating non-preferred solution candidates, we also present how the the cones can be leveraged in approximating the directions of steepest ascent to guide the subsequent search done by the evolutionary algorithm through a proposed merit function. To evaluate the performance of the algorithm, we consider well known test problems as well as a practical facility location problem.