The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 10.0. The updates in SCIP 10.0 include a new solving mode for exactly solving rational mixed-integer linear programs, a new presolver … Read more
In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more
Implied-integer detection is a well-known presolving technique that is used by many Mixed-Integer Linear Programming solvers. Informally, a variable is said to be implied integer if its integrality is enforced implicitly by integrality of other variables and the constraints of a problem. In this work we formalize the definition of implied integrality by taking a … Read more
The decarbonization of energy systems at energy-intensive sites is an essential component of global climate mitigation, yet such transitions involve substantial capital requirements, ongoing technological progress, and the operational complexities of renewable integration. This study presents a dynamic strategic planning framework that applies multi-stage stochastic programming to guide clean electricity transitions at the campus level. … Read more
The increasing penetration of renewable energy into power systems necessitates the development of effective methodologies to integrate initially disconnected generation sources into the grid. This paper introduces the Longest Shortest-Path-Connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of Transmission Expansion Planning (TEP) using valid inequalities (VIs). Traditional approaches for … Read more
For almost two decades, mixed integer programming (MIP) solvers have used graph- based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this paper, we improve MIP conflict analysis by instead using reasoning based on cuts, inspired by the development of conflict-driven solvers for pseudo- Boolean optimization. Phrased in MIP terminology, this type … Read more
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
This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more
LTL freight carriers operate consolidation networks that utilize cross-docking terminals to facilitate thetransfer of freight between trailers and enhance trailer utilization. This research addresses the problem ofdetermining an optimal schedule for unloading inbound trailers at specific unloading doors using teams ofdock workers. The optimization objective is chosen to ensure that outbound trailers are loaded with … Read more
We propose an extension of matrix games where the row player may select rows and remove columns, subject to a budget constraint. We present an exact mixed-integer linear programming (MILP) formulation for the problem, provide analytical results concerning its solution, and discuss applications in the security domain. Our computational experiments show heuristic approaches on average … Read more