Efficient traffic management in a modern urban road network seems impossible today without the support of artificial intelligence systems that use accurate travel demand data for predicting traffic congestions. However, despite researchers being equipped with different approaches and techniques to cope with travel demand estimation, there is still a gap between up-to-date accuracy requirements and available methods. The present paper is devoted to this urgent problem and investigates evolutionary strategies for the travel demand search task, formulated as an inverse traffic assignment problem. We develop polynomial regression models to estimate overall demand by observed congestions. The overall demand value allows one to restrict the set of feasible travel demand matrices. Eventually, we offer the travel demand estimation problem minimizing the deviation of both congestion and time on the simplex.