Abstract. Most optimization software performs numerical computation, in the sense that the main interest is to find numerical values to assign to the decision variables, e.g. a solution to an optimization problem. In mathematical programming, however, a considerable amount of symbolic transformation is essential to solving difficult optimization problems, e.g. relaxation or decomposition techniques. This step is usually carried out by hand, involves human ingenuity, and often constitutes the "theoretical contribution" of some research papers. We describe a Reformulation-Optimization Software Engine (ROSE) for performing (automatic) symbolic computation on mathematical programming formulations.
We study the parallel machine scheduling problem with release dates and we consider several "min-sum" objective functions including total weighted tardiness, total tardiness, total weighted completion time and total completion time. We describe several lower bounds for these problems, most of them being original ones. We provide experimental results to compare these lower bounds according to their quality and of their computational time requirement.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.