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arXiv 2103.08327cs.AIcs.NEmath.OC
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多种不确定环境下的网络优化模型

Some Network Optimization Models under Diverse Uncertain Environments

National Institute of Technology Durgapur(杜尔加布尔国立理工学院)

Saibal Majumder

摘要:

网络模型提供了一种有效的方法来表示数学上的许多现实生活中的问题。在过去的几十年里,网络优化领域已经见证了研究人员和实践者的兴趣高涨。本文所研究的网络模型大致分为四类:运输问题、最短路问题、最小生成树问题和最大流问题。网络优化问题的决策参数往往是不精确的,存在着各种形式的不确定性,如数据不充分或不完整、证据不足、判断不当、随机性等。在确定性环境下,网络优化问题的研究有很多.然而,在文献中,没有太多的研究,单目标和多目标网络优化问题的观察下,不同的不确定性框架。本文提出了七种不同不确定范式下的网络模型。在这里,用于制定不确定网络模型的不确定规划技术是(i)期望值模型,(ii)机会约束模型和(iii)相关机会约束模型。随后,相应的不确定网络模型的清晰的等价物,使用不同的解决方案的方法。本文所采用的求解方法大致可以分为经典方法和进化算法。本文所使用的经典方法有Dijkstra和Kruskal算法、修正的粗糙Dijkstra算法、全局准则法、模糊约束法和模糊规划法。而在进化算法中,我们提出了具有不确定交叉的变种群遗传算法,并考虑了两种多目标进化算法。

英文摘要:

Network models provide an efficient way to represent many real life problems mathematically. In the last few decades, the field of network optimization has witnessed an upsurge of interest among researchers and practitioners. The network models considered in this thesis are broadly classified into four types including transportation problem, shortest path problem, minimum spanning tree problem and maximum flow problem. Quite often, we come across situations, when the decision parameters of network optimization problems are not precise and characterized by various forms of uncertainties arising from the factors, like insufficient or incomplete data, lack of evidence, inappropriate judgements and randomness. Considering the deterministic environment, there exist several studies on network optimization problems. However, in the literature, not many investigations on single and multi objective network optimization problems are observed under diverse uncertain frameworks. This thesis proposes seven different network models under different uncertain paradigms. Here, the uncertain programming techniques used to formulate the uncertain network models are (i) expected value model, (ii) chance constrained model and (iii) dependent chance constrained model. Subsequently, the corresponding crisp equivalents of the uncertain network models are solved using different solution methodologies. The solution methodologies used in this thesis can be broadly categorized as classical methods and evolutionary algorithms. The classical methods, used in this thesis, are Dijkstra and Kruskal algorithms, modified rough Dijkstra algorithm, global criterion method, epsilon constraint method and fuzzy programming method. Whereas, among the evolutionary algorithms, we have proposed the varying population genetic algorithm with indeterminate crossover and considered two multi objective evolutionary algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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