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A learning automaton systematically updates a strategy to enhance the performance of a system output. The authors apply, a variable-structure learning automaton to achieve a best compromise solution between the economic operation and stable operation in a power system when the loads vary randomly. Both the generation cost for economic operation and the modal performance measure for stable operation of the power system are considered as performance indices for multi-objective optimal operation. In particular, it is shown that the S-model learning automata can be applied satisfactorily to the multi-objective optimisation problem to obtain the best trade-off between the conflicting objectives of economy and stability in the power system.