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A diving heuristic for mixed-integer problems with unbounded semi-continuous variables
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DOI：10.1016/j.ejco.2025.100107.png)
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Abstract
En 中文
Semi-continuous decision variables arise naturally in many real-world applications. They defined to take either value zero or any value within a specified range, and occur mainly prevent small nonzero values in the solution. One particular challenge that can come with continuous variables in practical models is that their upper bound may be large or even infinite. In this article, we briefly discuss these challenges, and present a new diving heuristic tailored for mixed-integer optimization problems with general semi-continuous variables. The heuristic is designed to work independently of whether the semi-continuous variables are bounded above, and thus circumvents the specific difficulties that come with unbounded semi-continuous variables. We conduct extensive computational experiments on three different test sets, integrating the heuristic in an open-source MIP solver. The results indicate that this heuristic is a successful tool for finding high-quality solutions in negligible time. At the root node the primal gap is reduced by an average of 5% up to 21%, and considering the overall performance improvement, the primal integral is reduced by 2% to 17% on average.
Keywords:
Integer programming
Semi-continuous variables
Indicator constraints
Diving heuristic
Supply chain management
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