In this report, we present the BOBILib, a collection of more than 2500~instances of mixed integer linear bilevel optimization problems. The goal of this library is to make 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 tested and … 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 an aerial survey operation in which a fleet of unmanned aerial vehicles (UAVs) is required to visit several locations and then land in one of the available landing sites while optimising some performance criteria, subject to operational constraints and flight dynamics. We aim to minimise the maximum flight time of the UAVs. To … Read more
We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop’s user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented … Read more
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial optimization. In this formulation, we assume that the variables are partitioned into a fixed number of sets, and … Read more
The multi-depot vehicle scheduling problem (MDVSP) is a critical planning challenge for transit agencies. We introduce a novel approach to MDVSP by incorporating service reliability through chance-constrained programming (CCP), targeting the pivotal issue of travel time uncertainty and its impact on transit service quality. Our model guarantees service reliability measured by on-time performance (OTP), a … 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
The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the simplest polytope/compact feasible set). As a problem class, StQPs may be nonconvex with an exponential number of inefficient local solutions. StQPs arise in a … Read more
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