Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems

Abstract Scalarization is a common technique to transform multiobjective optimization problem into scalar-valued problem. This article deals with the weighted Tchebycheff scalarization applied discrete problems. consists of minimizing maximum distance image feasible solution some desirable reference point. By choosing suitable weight, any Pareto optimal can be obtained. In this article, we provide comprehensive theory set eligible weights. particular, analyze polyhedral and combinatorial structure all weights yielding same as well decomposition weight whole. The structural insights are linked properties solutions, thus providing profound understanding method and, consequence, also methods for problems using building block.