若干捆绑式装箱问题的复杂性理论、算法设计与分析及其应用研究

Some basic problems in scientific researches and practical applications can be transformed into several combinatorial structures and optimization problems in network constructions. It is an important content of combinatorial optimization theories to construct networks with stock poieces of different lengths, and it has important theoretical research values and wide application prospects. This project will aim to focus on some bundled bin-packing problems as well as a few problems of network constructions by using certain bundled stock pieces of different lengths, and we consider some combinatorial structures and optimization problems in these network construction models. With some helps of design of algorithms and analyses, graph theory, programming theory and game theory and so on, we will establish some mathematical models, and then design some approximation algorithms to solve the bundled bin-packing problems and their related optimization problems in network constructions, and finally analyze complexity of algorithm designed. This project is a cross field of combinatorial optimization, graph theory, computer science and other disciplines, it is a forward research direction in the world. As concerning the final outcomes in expectation, we should develop the theories and methods of combinatorial optimization, consider the bundled bin-packing problems and some basic problems in network constructions, and design some algorithms to solve these problems mentioned-above. We should focus on some basic topics in the frontier, finish a batch of high quality original new results, and expect to publish 14-18 research papers, some of which will be publishable in top journals in China and oversea. Meanwhile, we shall train some talented persons in combinatorial optimization, graph theory and theoretical computer science in order to strengthen and consummate our research team, and finally improve our scientific research level in these areas and related areas.

科学研究与实际应用中一些基本问题能够转化为网络构建中若干组合结构及优化问题。利用多种长度不等的若干材料进行网络构建是组合最优化研究的重要内容之一，具有重要研究意义和广泛应用价值。本项目重点研究捆绑式装箱问题，以及利用多种长度不等的若干捆绑式材料来构建网络模型，研究这种网络模型中若干组合结构及其优化问题。借助算法设计与分析、图论、规划理论与博弈理论等，建立数学模型，设计近似算法来解决所研究的这些优化问题及分析算法复杂性。本项目属组合最优化、图论、计算机科学和其它学科的交叉领域，是国际前沿研究方向。预期成果，发展组合最优化理论方法，研究捆绑式装箱问题与网络构建中若干基础性问题，寻找解决问题的算法，并瞄准国际上与其相关的前沿基本问题进行研究，产出一批高质量原创新性成果，预计发表核心论文14-18篇，培养组合最优化、图论、计算机科学与技术方面人才16名，完善研究梯队，提升研究水平。

科学研究与实际应用中一些基本构建问题能够转化为网络构建中若干组合结构及相关优化问题。如何利用长度不等的若干材料来进行网络构建是组合优化研究的重要内容之一，具有重要研究意义和广泛应用价值。该项目重点研究了捆绑式装箱问题，利用长度不等若干捆绑式材料来构建网络模型，以及所诱导出若干相关组合结构及其优化问题。我们研究了国际上相关的前沿基本问题，借助算法设计与分析、图论、规划理论等建立数学模型，利用了清晰组合结构，设计了若干近似算法来解决对应的优化问题，分析算法复杂性，达到发展组合优化理论与方法，产出一批高质量原创新性成果，已发表核心期刊论文19篇（含中国数学会推荐的T1期刊2篇，T2期刊10篇，T3期刊2篇），国际会议论文6篇，准备投期刊论文6篇，培养了博士4人，硕士15人，正在培养博士生5人，硕士生12名。经过实施了该科研项目，极大地完善我们的组合优化研究团队，提升团队成员的科学研究水平。

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