Some Network Optimization Models under Diverse Uncertain Environments

Abstract

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.