This paper presents a new adaptive traffic signal control algorithm within the model predictive control framework. It aims to increase throughput of the traffic network under high traffic congestion. In order to do that, a detailed traffic flow model and specially designed target metric are used. The predictive model of the transport network is based on the second-order macroscopic traffic model. It can predict the formation of waves and other nonlinear effects occurring in the traffic. Also, it is possible to fine-tune the model with historical data to improve the quality of predictions. The paper describes both the model and the numerical scheme for its computation. Proposed optimization metric is based on the fundamental diagram of traffic flows and considers the characteristics of traffic dynamics. This metric minimization leads to a more uniform distribution of vehicles in the transport network. To solve the discrete optimization problem that emerges during the search for the optimal control, a genetic algorithm based on the local search heuristic was used. We carried out computer approbation of the proposed traffic signal control algorithm in the traffic simulation package SUMO. The accuracy of the transport network model predictions and performance of the control system were tested in several synthetic scenarios.