Abstract Scheduling problems are quite difficult to solve since in many cases no exact algorithms exist which can obtain the optimal solution in a reasonable amount of time. Therefore, these problems are often solved by using various metaheuristic methods, like genetic algorithms. To use these methods, the first step which needs to be performed is to define an encoding scheme that will be used to represent the solutions. Until now, several encoding schemes were proposed for the unrelated machines environment, each of which comes with its own benefits and drawbacks. However, the performance of metaheuristic methods depends on the applied encoding scheme. Unfortunately, no extensive research was performed in the literature to compare different solution representations for the unrelated machines scheduling problem. Therefore, the choice of the solution representation used is mostly provisional and is usually not based on any existing knowledge of how it would perform on the considered problem. This can cause the algorithms to obtain suboptimal results, which can lead to wrong conclusions about the performance. Thus, the goal of this paper is to test seven solution representations that were used in previous studies to represent solutions for the unrelated machines scheduling problem. The selected solution representations were tested for optimising four scheduling criteria, while additionally measuring the execution time of the genetic algorithm when using each of the encodings. The obtained results demonstrate that the encoding which is based on the permutation of jobs obtains the best results, making it the superior encoding scheme for this type of scheduling problem.

中文翻译：

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非相关机器环境的解决方案表示的比较研究

摘要 调度问题是很难解决的，因为在许多情况下，不存在可以在合理的时间内获得最优解的精确算法。因此，这些问题通常通过使用各种元启发式方法来解决，例如遗传算法。要使用这些方法，需要执行的第一步是定义将用于表示解决方案的编码方案。到目前为止，已经为不相关的机器环境提出了几种编码方案，每种方案都有其自身的优点和缺点。然而，元启发式方法的性能取决于应用的编码方案。不幸的是，在文献中没有进行广泛的研究来比较无关机器调度问题的不同解决方案表示。所以，所使用的解决方案表示的选择大多是临时性的，通常不基于它在所考虑的问题上将如何执行的任何现有知识。这可能导致算法获得次优结果，从而导致对性能的错误结论。因此，本文的目标是测试先前研究中用于表示无关机器调度问题的解决方案的七种解决方案表示。对选定的解决方案表示进行了测试，以优化四个调度标准，同时在使用每种编码时额外测量遗传算法的执行时间。获得的结果表明，基于作业排列的编码获得了最好的结果，使其成为此类调度问题的优越编码方案。