Efficient composite heuristics for integer bound constrained noisy optimization

This paper discusses a composite algorithm for bound constrained noisy derivative-free optimization problems with integer variables. This algorithm is an integer variant of the matrix adaptation evolution strategy. An integer derivative-free line search strategy along affine scaling matrix directions is used to generate candidate points. Each affine scaling matrix direction is a product of the … Read more

Learning to Use Local Cuts

An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more

PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming

In deterministic optimization, it is typically assumed that all parameters of the problem are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this … Read more

BilevelJuMP.jl: Modeling and Solving Bilevel Optimization in Julia

In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Due to the generality and flexibility our library inherits from JuMP’s syntax, our package … Read more

Automatic Reformulations for Convex Mixed-Integer Nonlinear Optimization: Perspective and Separability

Tight reformulations of combinatorial optimization problems like Convex Mixed-Integer Nonlinear Programs (MINLPs) enable one to solve these problems faster by obtaining tight bounds on the optimal value. We consider two techniques for reformulation: perspective reformulation and separability detection. We develop routines for the automatic detection of problem structures suitable for these reformulations and implement new … Read more

Distributed Projections onto a Simplex

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, all but one of these algorithms are serial. We address this gap by developing a method that preprocesses the input vector by decomposing and distributing it … Read more

Parallel Dual Dynamic Integer Programming for Large-Scale Hydrothermal Unit-Commitment

Unit commitment has been at the center of power system operation for well over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle this challenging problem, and often resort to simplifications to make the problem more tractable and solvable in … Read more

Metaheuristic, Models and Software for the Heterogeneous Fleet Pickup and Delivery Problem with Split Loads

This paper addresses a rich variant of the vehicle routing problem (VRP) that involves pickup and delivery activities, customer time windows, heterogeneous fleet, multiple products and the possibility of splitting a customer demand among several routes. This variant generalizes traditional VRP variants by incorporating features that are commonly found in practice. We present two mixed-integer … Read more

Using an Analytical Computational-Geometry Library to Model Nonoverlap and Boundary-Distance Constraints and their Application to Packing Poly-Bézier Shapes

In this paper we will show how to model nonoverlap as well as uniform and nonuniform boundary-distance constraints between poly-Bézier shapes using an analytical computational-geometry library. We then use this capability to develop, implement and analyze analytical-optimization solutions to minimum-area rectangular-boundary packing-problems as well as minimum-area one- and two-dimensional puzzle-piece packing-problems. In the process, we … Read more

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type … Read more