An investigation of Multiple Objective Network Flows
Piercy, Craig Allan
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Single Objective Network Flow (SONF) optimization is one of the most widespread techniques for modeling real systems. Network flow models have been used for many diverse applications. Easier understanding of the models by decision makers and the impressive computational performance of network-based algorithms have been major factors contributing to the popularity of network models. Although models such as these with a single objective are well justified and have been successful in many situations, they do not accurately represent situations where there are multiple and often conflicting criteria for measuring the quality of feasible alternatives. In such situations, a Multiple Objective Network Flow (MONF) model would be more appropriate. The intent of this research is to investigate the nature and characteristics of MONF problems and to propose algorithms for finding “good” solutions. With this research, an approach to multiple objective network flow problems is proposed. A characterization of solutions is investigated and a network-based algorithm is developed. Software is developed to solve for all efficient extreme point solutions. A second set of software is developed for aiding a decision maker in searching through the nondominated set for the most preferred solution. By nature MONF problems are accompanied by a large set of potential solutions. Investigation of how the size of the solution set varies with problem parameters is described. Also, a method of solving the MONF on parallel processors is explored. In this way, research and knowledge of an important class of problems will be extended.