Abstract
The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid method to solve the simple version of the problem in which the number of stations is fixed, a problem known as SALBP-2. The hybrid differs from previous approaches by encoding individuals of a genetic algorithm as instances of a modified problem that contains only a subset of the solutions to the original formulation. These individuals are decoded to feasible solutions of the original problem during fitness evaluation in which the resolution of the modified problem is conducted using a dynamic programming based approach that uses new bounds to reduce its state space. Computational experiments show the efficiency of the method as it is able to obtain several new best-known solutions for some of the benchmark instances used in the literature for comparison purposes.
Highlights
The Assembly Line Balancing Problem (ALBP) is a classic problem that has been a subject of research for nearly seventy years [1]; see [2,3,4] for reviews on the problem
The hybrid outperforms the basic Bounded Dynamic Programming (BDP) and is able to improve the previously best-known solution for six of the instances. This improvement shows the importance of diversifying the states constructed during the enumerate step of the BDP, as opposed to the intensification provided by increasing the value of its parameters
We can conclude the following: (1) the considerable run times are only required for the hardest instances of the set, and (2) the proposed genetic algorithm (GA) offers a slow convergence rate and a degree of diversification, which are desirable characteristics to hybridise with the intensification provided by the BDP
Summary
The Assembly Line Balancing Problem (ALBP) is a classic problem that has been a subject of research for nearly seventy years [1]; see [2,3,4] for reviews on the problem. While the SALBP-1 reference set contains no open instances, the reference set for SALBP-2 contains 14 open instances out of 302 This perceived difficulty could be explained by the fact that a reformulation method is required to solve several SALBP-1 instances, including the instance with the smallest possible total idle time and the desired number of stations. An exact reformulation method needs to verify that there is no feasible assignment for the instance with a cycle time that is one unit lower Both the practical relevance and the greater perceived difficulty of the SALBP-2 drive us to the study of this problem and the development of a new algorithm to solve hard instances. The proposed method is based on a SALBP-1 solution procedure but modifies the search space to add additional exploration in order to tackle these more challenging instances
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