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首页> 外文期刊>Mathematical Problems in Engineering >Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics
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Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics

机译：带有自适应启发式模糊选择器的算子疫苗减少组合优化问题的大小

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摘要

Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs) that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-Optimize-Expand (ROE) method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions.
机译：如今，解决最优组合问题是一个开放的问题。确定元素的最佳排列证明是一项非常复杂的任务，当问题规模增大时，这一任务就变得至关重要。研究人员提出了各种算法，这些算法考虑了可伸缩性来解决组合优化问题（COP）。但是，较大的COP仍然存在有关硬件限制（例如内存和CPU速度）的问题。研究表明，使用相同的资源，减少优化扩展（ROE）方法可以更快地解决COP。在这种方法中，减少步骤是最重要的过程，因为不适用于该问题的减少会在后续阶段产生次佳的结果。在这项工作中，提出了一种改进减少步骤的算法。它基于模糊推理系统对问题的各个部分进行分类并删除它们，从而使COP解决算法可以通过处理较小的问题大小以及元数据和自适应启发式算法来更好地利用硬件资源。研究中使用了旅行商问题。从343个城市到3056个城市的实例被用来证明模糊逻辑方法成功减少的比例更高。

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