We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions (boxes) in the objective space and returns the set of nondominated points. We implement the algorithm with different strategies, where the choices of the scalarization model parameters and splitting rule differ. We then derive bounds on the number of scalarization models solved; and demonstrate the performances of the variants through computational experiments both as exact algorithms and as solution approaches under time restriction. The experiments demonstrate that different strategies have advantages in different aspects: while some are quicker in finding the whole set of nondominated solutions, others return good-quality solutions in terms of representativeness when run under time restriction. We also compare the proposed approach with existing algorithms. The results of our experiments show the satisfactory behaviour of our algorithm, especially when run under time limit, as it achieves better coverage of the whole frontier with a smaller number of solutions compared to the existing algorithms.

我们提出了一种精确的算法，用于解决运筹学的各种应用中出现的双目标整数规划问题。该算法基于求解Pascoletti-Serafini标量来搜索目标空间中的指定区域（框），并返回非支配点的集合。我们用不同的策略来实现该算法，其中标量化模型参数和分割规则的选择是不同的。然后，我们得出求解的标量模型数量的界限；并通过计算实验证明了变体的性能，无论是精确算法还是时间限制下的求解方法。实验表明，不同的策略在不同方面都有优势：尽管有些策略可以更快地找到整套非支配解决方案，在有时间限制的情况下，其他人则可以根据代表性返回优质解决方案。我们还将提议的方法与现有算法进行比较。实验结果表明，该算法具有令人满意的性能，尤其是在有时间限制的情况下运行，因为与现有算法相比，它以较少的解决方案可以更好地覆盖整个边界。