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Minimizing the cost of generating electricity is desirable and requires the optimization of the sources that make up the electricity matrix of an Electric Power System (SEP), with the Economic Dispatch (DE) of thermoelectric plants being one of the central problems in this context. The DE seeks to determine the optimal distribution of the power generated among the thermoelectric units of a system, minimizing the total operating cost and meeting the load demand and the physical limits of each generating unit. In this work, the problem is modeled by means of a quadratic cost function, to which the valve point effect (EPV) and the ramp limits (LR) are incorporated, representing in a more realistic way the operation of the steam turbines and the dynamics of the plants over time. Such increments give the formulation nonlinear, non-convex and time-coupled characteristics, increasing the difficulty of achieving the global optimum by classical optimization methods. To solve this problem, a hybrid methodology is used that integrates the Grey Wolf Optimizer (GWO) and Random-Key Optimizer (RKO) metaheuristics. In this architecture, RKO encodes the candidate solutions in random key vectors in the range [0,1), standardizing the search space regardless of the dimensionality of the problem, while a specialized decoder maps these keys to technically feasible power values, respecting the operating limits and the load balance
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