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This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.
Cheng et al. (Mon,) studied this question.