Kezang Yuden

• Linear parametric optimization has been used for decades to combine multiple objective functions into a single problem. The solution to this problem is a set of optimal solutions, containing a solution that is optimal for each parameter. Multi-objective optimization is commonly used when multiple objectives are optimized simultaneously, and these objectives are often conflicting. Because these objective functions are conflicting, there is usually no unique optimal solution. Instead, the goal is to find all nondominated images that represent the trade-offs among the objectives. The weighted sum scalarization method is a well-known approach for finding nondominated images by transforming a multi-objective optimization problem into a single-objective optimization problem. In this thesis, we consider linear parametric programming problems with multiple objective functions depending linearly on some parameters. Both parametric (single-objective) linear programming and (non-parametric) multi-objective linear programming are well-researched topics. However, literature on the combination of both, parametric linear programming with multiple objectives, is scarce. This research gap encourages our work in this field. More precisely, we examine linear parametric programs with multiple objective functions that depend linearly on some parameters. We investigate various cases of parametric biobjective linear programs and multi-parametric biobjective linear programs. We establish a connection of these problems to non-parametric multi-objective problems. Using the so-called weight set decomposition, we are able to explain the behavior of parametric biobjective linear programs when the parameter value is variated. We prove that there is a one-to-one correspondence between the solution of some parametric biobjective programs and the solution of the corresponding multi-objective linear program using the weighted sum scalarization. We provide structural insights to the solution of parametric biobjective linear programs with respect to extreme weights of the weight set of the multi-objective linear program and develop solution strategies for the parametric program. Similarly, we extend our analysis to biparametric biobjective linear programs and a generalization of our findings to parametric multi-objective linear programs. We characterize the structure of the parameter set of both single and biparametric problems using the weight set of the multi-objective linear programs. Finally, we develop algorithms to solve parametric biobjective linear programs based on the weight-set decomposition.