A multi-objective genetic algorithm to solve the U-shaped line balancing problem using random weights

U-shaped lines are widely used in lean manufacturing environments. The U-line arranges machines around a U-shaped line in the order in which production operations are performed. Operators work inside the U-shaped layout. In this paper a multi-objective genetic algorithm is proposed for solving a U-shaped line balancing problem (U-ALBP Type I). The developed algorithm works towards optimizing three objectives: number of workstations, smoothness index and the line balancing efficiency. A weighted sum of these three objectives is used to select the best fitness values for parent selection. The selection is based on a weighted sum of these objectives with variable weights; the more important the objective, the smaller the weight. The most important objective is the number of workstations, followed by the smoothness index and lastly the line balancing efficiency. The randomness of these weights helps the algorithm to find the best solution. The line balancing tasks are represented as genes, which are part of a solution called a chromosome. The algorithm was applied to eleven problems selected from the literature and the new solutions were compared to the old solutions obtained from the previous researches. Finally, the results showed that the proposed algorithm produced good or near optimal solutions.