The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within a fixed given cycle time), where the aim is to minimize the number of workstations. After establishing the method, the results from previous research studies were compared with the results from this study. For the UALBP, two groups of benchmark problems were used for the experiments: (1) For the medium-sized UALBP (21–45 tasks), it was found that the DE algorithm DE/best/2 to Exponential Crossover 1 produced better solutions when compared to the other metaheuristic methods: it could generate 25 optimal solutions from a total of 25 instances, and the average time used for the calculation was 0.10 seconds/instance; (2) for the large-scale UALBP (75–297 tasks), it was found that the basic DE algorithm and improved differential evolution algorithm generated better solutions, and DE/best/2 to Exponential Crossover 1 generated the optimal solutions and achieved the minimum solution search time when compared to the other metaheuristic methods: it could generate 36 optimal solutions from a total of 62 instances, and the average time used for the calculation was 4.88 seconds/instance. From the comparison of the DE algorithms, it was found that the improved differential evolution algorithm generated optimal solutions with a better solution search time than the search time of the basic differential evolution algorithm. The basic and improved DE algorithm are the effective methods for balancing UALBP-1 when compared to the other metaheuristic methods.
We describe a Differential Evolution (DE) algorithm for solving U-shaped Assembly Line Balancing Problems -Type 2 (UALBP-2). The minimum cycle time in a just-in-time production line for producing a single product with a certain number of workstations was investigated by developing solution methods and testing on 15 problem sets (101 instances). The problems were divided into 10 medium-scale problem sets (50 instances) and 5 large-scale problem sets (51 instances). When comparing the results with those obtained from the rule-based heuristic; three rules and two rules, the DE algorithm could generate 14 better solutions (28%) in the medium-scale problems, and 3 better solutions (about 6%) in the large-scale problems. In terms of computational time, DE algorithm was faster than rule-based heuristic methods in medium-scale problems. In large problems, our DE algorithm used computational times that were shorter by 73% (for two rules) and 98% (for three rules).
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