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Knowledge-based Genetic Algorithm for the 0-1 Multidimensional Knapsack Problem

机译:基于知识的0-1多维背包问题遗传算法

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摘要

This paper presents an improved version of Genetic Algorithm (GA) to solve the 0-1 Multidimensional Knapsack Problem (MKP01), which is a well-known NP-hard combinatorial optimisation problem. In combinatorial optimisation problems, the best solutions have usually a common partial structure. For MKP01, this structure contains the items with a high values and low weights. The proposed algorithm called Genetic Algorithm Guided by Pretreatment information (GAGP) calculates these items and uses this information to guide the search process. Therefore, GAGP is divided into two steps, in the first, a greedy algorithm based on the efficiency of each item determines the subset of items that are likely to appear in the best solutions. In the second, this knowledge is utilised to guide the GA process. Strategies to generate the initial population and calculate the fitness function of the GA are proposed based on the pretreatment information. Also, an operator to update the efficiency of each item is suggested. The pretreatment information has been investigated using the CPLEX deterministic optimiser. In addition, GAGP has been examined on the most used MKP01 data-sets, and compared to several other approaches. The obtained results showed that the pretreatment succeeded to extract the most part of the important information. It has been shown, that GAGP is a simple but very competitive solution.
机译:本文提出了一种改进的遗传算法(GA),用于解决0-1多维背包问题(MKP01),这是一个众所周知的NP硬组合优化问题。在组合优化问题中,最佳解决方案通常具有共同的部分结构。对于MKP01,此结构包含具有高值和低权重的项目。所提出的称为“遗传算法的预处理信息指导”(GAGP)的算法将计算这些项目,并使用此信息指导搜索过程。因此,GAGP分为两个步骤,第一步,基于每个项目效率的贪心算法确定了可能出现在最佳解决方案中的项目子集。第二,利用这些知识来指导GA流程。基于预处理信息,提出了生成初始种群和计算遗传算法的适应度函数的策略。另外,建议操作员更新每个项目的效率。已经使用CPLEX确定性优化器研究了预处理信息。此外,GAGP已针对最常用的MKP01数据集进行了检查,并与其他几种方法进行了比较。所得结果表明,预处理成功地提取了大部分重要信息。已经证明,GAGP是一个简单但非常有竞争力的解决方案。

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