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.
翻译:网络优化模型为数学地代表许多真实生活问题提供了一种有效的方法。在过去几十年中,网络优化领域研究人员和从业者对网络优化的兴趣急剧上升。本论文中考虑的网络模型大致分为四类,包括运输问题、最短路径问题、最小横跨树木问题和最大流程问题。我们经常遇到的情况是,网络优化问题的决定参数不准确,其特点是各种不确定因素,如数据不足或不完整、缺乏证据、不适当的判断和随机性。考虑到确定性环境,对网络优化问题进行了一些研究。然而,在文献中,对单一和多目标网络优化问题的调查不多,在不同的不确定框架下观察。本论文提出了7个不同的网络模型,不同的不确定模式是(一) 预期价值模型,(二) 机会限制模型和(三) 依赖性机会限制模型。随后,不确定的网络模型的相应精确等值正在用不同的解决方案方法得到解决。我们使用的解决方案方法可以大致分为两种,即:分析方法、分析性方法和演算方法。这里使用的是分析方法、分析性方法、分析方法、分析方法、分析方法、分析方法中采用。