A genetic algorithm for bin packing and line balancing
نویسندگان
چکیده
The bin packing problem can be best described in 'transportation' terms: given a set of boxes of different sizes, how should one pack them all into containers of a given size, in order to use as few containers as possible? The task of balancing of (robotized) assembly lines is of considerable industrial importance. It consists of assigning operations from a given set to workstations in a production line in such a way that (1) no assembly precedence constraint is violated, (2) no workstation in the line takes longer than a predefined cycle time to perform all the tasks assigned to it, and (3) as few workstations as possible are needed to perform all the tasks in the set. This paper presents a genetic grouping algorithm for the two problems. We first define the two problems precisely and specify a cost function suitable for the bin packing problem. Next, we show why the classic genetic algorithm performs poorly on grouping problems and then present an encoding of solutions fitting them. We present efficient crossover and mutation operators for the bin packing. Then we give the modification necessary to fit these operators for the line balancing. We follow with results of performance tests on randomly generated data. Especially the line balancing tests largely cover the real-world problem size. We conclude with a discussion of the results and areas of further research.
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