We provide new theoretical insight on the generation of linear and non-convex cuts for value functions of multistage stochastic mixed-integer programs based on Lagrangian duality. First, we analyze in detail the impact that the introduction of copy constraints, and especially, the choice of the accompanying constraint set for the copy variable have on the properties … Read more
This paper proposes and evaluates a Multi-Reference Relaxation Enforced Neighborhood Search (MRENS) heuristic within the SCIP solver. This study marks the first integration and evaluation of MRENS in a full-fledged MILP solver, specifically coupled with the recently-introduced Lagromory separator for generating multiple reference solutions. Computational experiments on the MIPLIB 2017 benchmark set show that MRENS, … Read more
In this report, we present the BOBILib, a collection of more than 2600 instances of mixed integer bilevel linear optimization problems (MIBLPs). The goal of this library is to provide a large and well-curated set of test instances freely available for the research community so that new and existing algorithms in bilevel optimization can be … Read more
In the context of mixed-integer nonlinear problems (MINLPs), it is well-known that strong duality does not hold in general if the standard Lagrangian dual is used. Hence, we consider the augmented Lagrangian dual (ALD), which adds a nonlinear penalty function to the classic Lagrangian function. For this setup, we study conditions under which the ALD … Read more
We analyze the inverse of the Gomory corner relaxation (GCR) of a pure integer program (IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We present a linear programming (LP) formulation for solving the inverse GCR under the \(L_{1}\) … Read more
We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In … Read more
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We propose a flexible and general algorithmic framework for solving bi-objective mixed integer linear programming problems. The Pareto frontier of these problems can have a complex structure, as it can include isolated points, open, half-open and closed line segments. Therefore, its exact detection is an achievable though hard computational task. Operating in the criterion space, … Read more
We consider approaches for optimally organizing competitive sports leagues in light of competitive and logistical considerations. A common objective is to assign teams to divisions so that intradivisional travel is minimized. We present a bilinear programming formulation based on k-way equipartitioning, and show how this formulation can be extended to account for additional constraints and … Read more
Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify a new given point. In some scenarios, however, labels are only accessible for a proper subset of the given … Read more