On the Multiple-Objectives and Single Nonlinear Objective Optimization Problems with Addition-Min Type Constraints

This two-year research project continues our study on an optimization problem subject to fuzzy relational inequalities with the addition-min composition. This optimization problem is relatively new due to its constraint part and possible application in file-sharing area. Motivated by various managerial considerations, Research efforts could be spent on theoretical developments (single linear or nonlinear objective function, multi-objectives), algorithmic study for finding an optimal solution or an efficient solution, etc. We have been working on this issue since year 2015. Our previous result could be found in Sy-Ming Guu and Yan- Kuen Wu (2016), ``A linear programming approach for minimizing a linear function under fuzzy relational inequalities with addition-min composition," IEEE Transactions on Fuzzy Systems)(SCI) 07/20/2016. DOI: 10.1109/TFUZZ.2016.2593496. The ideas of two-year research project come from our recent work `On the optimal data transmission in BitTorrent-like peer-to-peer file sharing systems," by Sy-Ming Guu, JiaJun Yu and Yan-Kuen Wu, Working paper, College of Management, Chang Gung University. This manuscript has been submitted to IEEE Transactions on Fuzzy Systems in 12/2016. During the study, we noticed the optimal solution by Yang et al. [39] is not a minimal solution which otherwise could have better managerial implication like to yield the least cost. In this working paper, we pointed out this drawback in Yang et al. [39] and proposed a linear programming approach for generating an optimal solution but again no guarantee to have it a minimal one. Therefore, in the first year of study, we would like to resolve this weakness. On the other hand, the working paper is the first one to study two managerial goals at the same time. In the literature, so far, only single managerial goal (like to find an optimal cost) has been considered. We believe for practical consideration, managers may have to consider more than one goal. In our working paper, we used a two-phase approach to handle two managerial goals simultaneously. However, in the second year, we use multi-objective optimization framework to handle two, three or more goals.

Project ID:PB10608-2397
External Project ID:MOST106-2221-E182-038-MY2