Mixed-Integer Bilevel Optimization with Nonconvex Quadratic Lower-Level Problems: Complexity and a Solution Method

We study bilevel problems with a convex quadratic mixed-integer upper-level and a nonconvex quadratic, purely continuous lower-level problem. We prove $\Sigma_p^2$-hardness of this class of problems, derive an iterative lower- and upper-bounding scheme, and show its finiteness and correctness in the sense that it computes globally optimal points or proves infeasibility of the instance. To … Read more

On parametric formulations for the Asymmetric Traveling Salesman Problem

The traveling salesman problem is a widely studied classical combinatorial problem for which there are several integer linear formulations. In this work, we consider the Miller-Tucker-Zemlin (MTZ), Desrochers-Laporte (DL) and Single Commodity Flow (SCF) formulations. We argue that the choice of some parameters of these formulations is arbitrary and, therefore, there are families of formulations … Read more

An Efficient Algorithm to the Integrated Shift and Task Scheduling Problem

Abstract   This paper deals with operational models for integrated shift and task scheduling problem. Staff scheduling problem is a special case of this with staff requirements as given input to the problem. Both problems become hard to solve when the problems are considered with flexible shifts. Current literature on these problems leaves good scope … Read more

Approximating the Gomory Mixed-Integer Cut Closure Using Historical Data

Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of this paper is to generate good cutting-planes for such instances using historical data. Gomory mixed integer cuts (GMIC) for a general MILP can be parameterized … Read more

Accelerating Benders decomposition for solving a sequence of sample average approximation replications

Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statistical estimates on the optimal value of the true problem can be obtained by solving … Read more

Cut-based Conflict Analysis in Mixed Integer Programming

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

Models for two-dimensional bin packing problems with customer order spread

In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to … Read more

A Row-wise Algorithm for Graph Realization

\(\) Given a \(\{0,1\}\)-matrix \(M\), the graph realization problem for \(M\) asks if there exists a spanning forest such that the columns of \(M\) are incidence vectors of paths in the forest. The problem is closely related to the recognition of network matrices, which are a large subclass of totally unimodular matrices and have many … Read more

Machine Learning for Optimization-Based Separation: the Case of Mixed-Integer Rounding Cuts

Mixed-Integer Rounding (MIR) cuts are effective at improving the dual bound in Mixed-Integer Linear Programming (MIP). However, in practice, MIR cuts are separated heuristically rather than using optimization as the latter is prohibitively expensive. We present a hybrid cut generation framework in which we train a Machine Learning (ML) model to inform cut generation for … Read more

Optimizing the lead time of operational flexibility trading from distributed industrial energy systems in future energy and flexibility markets

To meet the challenges of increasing volatile and distributed renewable energy generation in the electric grid, local flexibility and energy markets are currently investigated. These markets aim to encourage prosumers to trade their available flexible power locally, to be used if a grid congestion is being predicted. The markets are emerging, but the characterizing parameter … Read more