This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer nonlinear programs (MINLPs) with linear complicating constraints and integer linking variables. If the complicating constraints are removed, the problem becomes easy to solve, e.g. due to decomposable structure. Integrality of the linking variables allows us to apply a discretization approach to derive a Dantzig-Wolfe reformulation and solve the problem to global optimality using branch-andprice. It is a remarkably simple idea; but to our surprise, it has barely found any application in the literature. In this work, we show that many relevant problems directly fall or can be reformulated into this class of MINLPs. We present the branch-and-price algorithm and demonstrate its effectiveness (and sometimes ineffectiveness) in an extensive computational study considering multiple large-scale problems of practical relevance, showing that, in many cases, orders-of-magnitude reductions in solution time can be achieved.

这项工作试图结合近三十年来已经成熟的两种主要技术的优势：全局混合整数非线性优化和分支价格。我们考虑一类通常具有线性复杂约束和整数链接变量的非凸混合整数非线性程序（MINLP）。如果消除了复杂的约束，则该问题变得易于解决，例如由于可分解的结构。链接变量的完整性允许我们应用离散化方法来导出Dantzig-Wolfe重新公式化，并使用分支和价格将问题解决为全局最优性。这是一个非常简单的想法。但令我们惊讶的是，它在文献中几乎没有发现任何应用。在这项工作中，我们表明，许多相关问题直接落入或可以重新归类为此类MINLP。我们提出了分支价格算法，并在考虑了多个与实际相关的大规模问题的广泛计算研究中证明了其有效性（有时甚至无效），表明在许多情况下，求解时间的数量级减少可以取得成就。