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Modern railway traction systems are often equipped with anti-slip control strategies to comply with performance and safety requirements. A certain amount of slip is needed to increase the torque transferred by the traction motors onto the rail. Commonly, constant slip control is used to limit the slip velocity between the wheel and rail avoiding excessive slippage and vehicle derailment. This is at the price of not fully utilizing the train's traction and braking capabilities. Finding the slip at which maximum traction force occurs is challenging due to the non-linear relationship between slip and wheel-rail adhesion coefficient, as well as to its dependence on rail and wheel conditions. Perturb and observe (P\&O) and steepest gradient (SG) methods have been reported for the Maximum Adhesion Tracking (MAT) search. However, both methods exhibit weaknesses. Two new MAT strategies are proposed in this paper which overcome the limitations of existing methods, using Fuzzy Logic Controller (FLC) and Particle Swarm Optimization (PSO) respectively. Existing and proposed methods are first simulated and further validated experimentally using a scaled roller rig under identical conditions. The results show that the proposed methods improve the traction capability with lower searching time and oscillations compared to existing solutions. Tuning complexity and computational requirements will also be shown to be favorable to the proposed methods., Comment: 16 pages, 21 figures