This article explores the use of genetic algorithm to search for the assigned weightage pattern of objectives to obtain the best compromised thermal power generation schedule in the multi-objective framework. The multi-objective problem is formulated considering non-commensurable objectives viz. operating cost, NOx emission, and variance of real, as well as reactive, power generation mismatch with explicit recognition of statistical uncertainties in the thermal power generation cost curves, emission curves, and power demands, which are considered random variables. The solution set of such formulated problems is non-inferior due to contradictions among the objectives taken. The generation of non-inferior solutions requires an enormous amount of computation time when the objectives are more than two. In this article, the weighting method is used to convert the multi-objective optimization problem into a scalar optimization problem. Scalar optimization problem is solved many times for a different set of weight pattern to generate non-inferior solutions. The weighting patterns are either presumed on the basis of the decision maker's intuition or simulated with suitable step size. Such a simulation procedure may fail to provide the decision maker with the non-inferior solution that actually corresponds to the best compromised solution by virtue of the step size chosen. Thus, scalar weights are searched by genetic algorithms in the non-inferior domain. Among the generated population of scalar weights that generate non-inferior solutions, the system operator chooses the population of weighting pattern that provides maximum satisfaction level from the membership function of participating objectives and is termed as fitness function. The goals/objectives of fuzzy nature can be quantified by defining their membership functions. The validity of the proposed method has been demonstrated on an 11 node IEEE system comprising of five generators. The result of the proposed method is compared with the interactive method in which weighting patterns are simulated by giving suitable variation to weights in a specific manner.