ABSTRACT. This tutorial covers algorithmic aspects of conflict-driven clause learning and important extensions developed in recent years, including decision heuristics, restart schemes, various pre- and inprocessing techniques as well as proof generation and checking. Programmatic incremental usage of SAT solvers is discussed next. The talk closes with an overview on the state-of-the-art in parallel SAT solving and open challenges in general.

ABSTRACT. The most well-known optimisation version of the SAT problem is the Maximum Satisfiability (MaxSAT) problem. This talk will provide a practical approach to MaxSAT. We will start by illustrating how to encode a problem in MaxSAT. In addition, modern MaxSAT algorithms, that are based on iterative calls to a SAT solver, will be described.

ABSTRACT. In the first part of the talk, we will focus on metaheuristics based on Local Search (aka Neighborhood Search), and in particular we focus on Simulated Annealing, which is recognised as the oldest (1983)  metaheuristic technique in the scientific literature. Despite its age, it is still very popular in academic publications and practical applications. We review the basic components of Simulated Annealing and we discuss and classify its uncountable variants, some of which gained their own names and metaphors (Great Deluge, Threshold Accepting, ...). 

In the second half we will consider metaheuristic approaches for discrete optimization problems that rely on or link to machine learning techniques in order to ``learn how to better optimize''. After observing that this general idea is not that new in the field of metaheuristics and briefly surveying established approaches, we will in particular look at a few more recent combinations of heuristic search and reinforcement learning.

ABSTRACT. Numerically challenging mixed-integer programs (MIPs) appear in many practical applications. In this master class presentation, we will discuss recent advances how to handle or even avoid numerical issues while solving such problems.

To this end, we will address the following questions:

- Which part of the MIP solution process is most vulnerable for numeric issues?

- What different types of numeric issues are there?

- How can I recognize whether my MIP model is prone to numeric issues?

- And, most importantly, what methods are there that help solving numerically challenging MIPs?

To (partially!) answer the last question, we will introduce three techniques: Iterative LP Refinement, MIP Solution Refinement and Learning to Scale.

We will discuss their effectiveness in reducing numerical errors and their impact on performance in terms of solver running time.

ABSTRACT. Numerical Constraint Programming

ABSTRACT. CP-SAT won all gold medals in the Minizinc challenge in the tracks it participated in the last 3 years. It also proved 5 open problems in the MIPLIB 2017 suite, and improved bounds on a few more.

In a sense, it realizes the old dream of having a good MIP solver and a good CP solver in the same engine. In this presentation, we will present how the SAT technology has enabled this merging of the two techniques in a competitive way.