Balancedness in the Weighted Rectangles Partitioning Problem

A rectangle is subdivided into pixels which are either active or inactive. The weighted rectangles partitioning problem (WRP) is finding a partition of the active pixels into weighted, smaller rectangles and maximizing the total weight. Using an IP formulation, instances with an integral relaxation polyhedron are characterized by the balancedness of the problem matrix. Is … Read more

Projective Cutting Planes for General QP with Indicator Constraints

General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous … Read more

Computing Optimized Path Integrals for Knapsack Feasibility

A generating function technique for solving integer programs via the evaluation of complex path integrals is discussed from a theoretical and computational perspective. Applying the method to solve knapsack feasibility problems, it is demonstrated how the presented numerical integration algorithm benefits from pre-optimizing the path of integration. After discussing the algorithmic set-up in detail, a … Read more

Solving IP via Complex Integration on Shortest Paths

Using the weighted geometric series expansion, it is shown how integer programming can be solved by evaluating complex path integrals based on a multi-path version of Cauchy’s integral formula. In contrast to existing generating function approaches, the algorithm relies only on complex quadrature and no algebraic techniques are needed. In view of fast implementations of … Read more

Exact solution of the donor-limited nearest neighbor hot deck imputation problem

Data quality in population surveys suffers from missing responses. We use combinatorial optimization to create a complete and coherent data set. The methods are based on the widespread nearest neighbor hot deck imputation method that replaces the missing values with observed values from a close unit, the so-called donor. As a repeated use of donors … Read more