In this paper, we first formulate the molten iron allocation problem as an integer programming model and then reformulate it as a set partitioning model by applying the Dantzig–Wolfe decomposition.
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Such a problem can be viewed as a parallel machine scheduling problem with time windows which is known to be NP-hard. This objective reflects the practical consideration of improving steel-making efficiency and reducing operation cost caused by the need for reheating.
![programming hanoi towers programming hanoi towers](https://3.bp.blogspot.com/-QRy1aXlFPI0/UUFvGuG36TI/AAAAAAAAAKc/hl3e5YnHMrw/s1600/Tower+of+Hanoi.jpg)
The objective is to find a schedule with minimum total weighted completion time. Time window constraints for processing the molten iron must be satisfied to avoid freezing.
![programming hanoi towers programming hanoi towers](https://www.javainterviewpoint.com/wp-content/uploads/2016/08/Towers-Of-Hanoi.png)
The allocation needs to observe the release times of the molten iron defined by the draining plan of the blast furnaces and the transport time between the iron-making and steel-making stages. The molten iron allocation problem (MIAP) is to allocate molten iron from blast furnaces to steel-making furnaces. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository. The consideration of irredundant rules only does not change the results of optimization. We can also change the order of optimization. We can describe all irredundant β-decision rules with minimum length, and after that among these rules describe all rules with maximum coverage. This algorithm finishes the partitioning of a subtable when its uncertainty is at most β.The graph Δβ(T) allows us to describe the whole set of so-called irredundant β-decision rules. Our algorithm constructs a directed acyclic graph Δβ(T) which nodes are subtables of the decision table T given by systems of equations of the kind “attribute = value”. localize rows in subtables of T with uncertainty at most β. For a nonnegative real number β, we consider β-decision rules that. We introduce an uncertainty measure R(T) which is the number of unordered pairs of rows with different decisions in the decision table T. This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. Extensive experimental results on 11 real world data sets and a case study on a Protein-Protein Interaction (PPI) data set demonstrate the effectiveness of our proposed method. Multiple consensuses are finally obtained by applying consensus clustering algorithms to each cluster of the partition. A dynamic programming algorithm is proposed to obtain a flat partition from the hierarchical tree using the modularity measure. Instead of generating a single consensus, MCC organizes the different input clusterings into a hierarchical tree structure and allows for interactive exploration of multiple clustering solutions. In this paper, we develop a new framework, called Multiple Consensus Clustering (MCC), to explore multiple clustering views of a given dataset from a set of input clusterings. There is a significant drawback in generating a single consensus clustering since different input clusterings could differ. Given a set of input clusterings of a given dataset, consensus clustering aims to find a single final clustering which is a better fit in some sense than the existing clusterings. Consensus clustering has emerged as an important extension of the classical clustering problem.