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This paper presents a new optimization method for solving multi-objective problems using a weighted-sum genetic algorithm (WSGA) method. This method is more popular because it is a straight forward fitness formulation and computationally efficient. However, this approach has some limitations because of the difficulty in selecting an appropriate weight for each objective and the need for some knowledge about the problems. The weight selection is usually based on trial and error and which impractical for complex engineering problems. In order to overcome these problems, the authors of this paper propose a new self organizing genetic algorithm (SOGA) for multi-objective optimization problems. The SOGA involves GA within the GA evaluation process which optimally tunes the weight of each objective function and applies a weighted-sum approach for fitness evaluation process. This algorithm has been tested for optimization of components placement on printed circuit board. The results show that SOGA is able to obtain a better minimum value as compared to random weight GA method.