The most important tasks for making optimal decisions using heuristic algorithms include improving accuracy and preventing premature convergence. Much of the research in this area focuses on developing new operators, tuning population metaheuristic parameters, and hybridizing several solution search strategies. Less attention is paid to initialization, which is an important operation in population-based algorithms that involves generating an initial population of solutions. We propose a new algorithm for initializing population solutions in metaheuristics. The Metropolis-Hastings method is used to generate an initial solution population. To demonstrate the potential of this algorithm, we integrated it into the basic Differential Evolution algorithm. The experimental verification was carried out by comparing it with well-known methods such as random initialization, learning based on opposition, chaos methods, and the diagonal uniform distribution method. The comparison was performed on a representative set of multimodal, unimodal, and hybrid functions. The convergence rates of the algorithms and accuracy of the solutions obtained were analyzed. Average values for the best solutions, median best solution, standard deviation from best solution, number of function calls, success rate, acceleration coefficient were used as indicators for comparison. The proposed algorithm worked faster, showed better convergence, and had higher accuracy. Statistical verification using the Friedman test confirmed that the algorithm provided the best balance between convergence rate and accuracy.