Conference Agenda

One of the most important aspects of mathematical optimization and Operations Research is getting your data into a form that optimization solvers can understand and work with. The "art of modeling", as it is often referred to, can all too easily get in the way of actually solving the problem at hand.

Gurobi's open-source OptiMods are data-driven Python APIs for common optimization use cases. They enable practitioners and learners to compute solutions without requiring extensive modeling experience. This session presents the project's goals and design and explains how to use and extend it.

Network optimization problems are recognised by their underlying graph(s) and constraints. Examples are within planning & scheduling, vehicle routing, and multi-commodity flow problems. Flowty’s solver exploits the graph structure and solves resource constrained shortest path problems to generate variables using a column generation scheme.

Graphs are described as edge sets and a source and target vertices for a path. Paths can additionally be constrained with a set of resources. Constraint modeling is done directly on the vertices and edges of the graphs, the subproblem itself, as well as on traditional mixed integer variables. This allows for very compact models, e.g., set partitioning constraints on vertices and edge design variables in network design problems, and the graph and resource constraints avoids the need for linearisation of constraints (big-M).

The literature has shown that column generation based algorithms are superior for many network optimization problems. The solver combines the familiarity of mixed integer programming models and graph structures with algorithmic speed.

In this talk we will dive into modeling examples in Python, take a quick look under the hood, and present recent performance benchmarks.

Hexaly is a new kind of global optimization solver that combines exact and heuristic methods designed to tackle large-scale industrial problems. Several approaches have been developed by the operations research community to solve these large problems (e.g., heuristics, column generation, model decomposition, etc.). One of the main challenges for a model & run solver is to offer a modeling formalism, both generic and sparse. The genericity ensures that most of the problems can be modeled in the formalism while the sparsity ensures that the model stays linear in the size of the input. While SAT and MIP formalisms offer genericity, certain models require a quadratic or an exponential number of decisions and constraints (e.g. traveling salesman problem, bin packing or scheduling). Conversely, CP models offer global constraints that ensure sparsity but may lack genericity (e.g. non overlap with complex setup times for instance). To overcome these issues, Hexaly added set-based models to its formalism. Intervals, sets and lists can be used as decision variables and functions can be used to derive numerical expressions that can later be constrained or optimized. Vehicle routing problems, scheduling problems and most variants of bin packing can be easily modeled with a combination of sets, lists and intervals. The resolution of these problems is done using heuristics and exact techniques. This presentation will describe Hexaly models for packing, routing, and scheduling and give benchmark results on large instances with hundreds of thousands of items, clients, or tasks.

OptimIzation pipelines contain many tasks such as mathematical modeling, data processing, and developing algorithms. Python and its vast array of packages provide a convenient way of data gathering, pre/post-processing of the data, the visualization of the data and developing necessary algorithms by utilizing existing ones. On the other hand, GAMS has been providing tools with great performance for the mathematical modeling part for decades. In this talk, we will talk about a new tool GAMSPy that aims to combine the best of both worlds.