Mathematics and algorithms for intelligent decision-making

A meeting in a modern officespace. — gorodenkoff

There are many benefits of using mathematics and algorithms to aid decision-making in complex settings. Our main focus is on discrete optimisation for decision problems that aim to schedule or allocate resources. In our research projects, we both find new ways to address decision problems by optimisation and develop new methods for solving them.

Artificial intelligence

Thanks to digitalisation, the available amount of data to support decision-making has reached a high level of maturity, and so has the capability of processing this data. Alongside the data science disciplines, optimisation — used for decision support — plays a key role in the further development of tools to support advanced decision-making. The scale and complexity of the problems relevant to address continue to increase and this calls for research that address the mathematics and algorithms needed in optimisation methods.

Intelligent decision-making

We believe that truly intelligent decision-making is achieved through an integration of model-based and data-driven approaches that are designed or used in interaction with a human decision-maker. To successfully apply mathematics and algorithms as part of real-world decision-making requires careful mathematical modelling and data collection. An inherent property of many decision problems of practical relevance is that they are computationally challenging. Solving such a problem within a reasonable amount of time often requires the development of specialised methods that exploit the mathematical structure of the problem.

More information

On the journey towards sustainability, our contribution is to develop mathematical models and solution methods for practically relevant but computationally challenging problems in scheduling and resource allocation.

Discrete optimisation

There are many types of decision problems that aim to schedule or allocate resources, and these lend themselves to be addressed as discrete optimisation problems. Most practically relevant discrete optimisation problems are NP-hard, which means that their worst-case solution times grow exponentially with the problem size. The practical consequence of this is that, for challenging instances, even the state-of-the-art optimisation solvers will frequently fail to deliver a solution within weeks or even thousands of years of computational time.

Over the last decades, there has been an impressive development of methods for solving discrete optimisation problems. Thanks to this, many important planning and scheduling problems can be solved with a reasonable computational effort—however, many practically relevant problems still pose great challenges.

Organisation

This research direction, formerly called Operations Research Methods for Scheduling and Resource Allocation Problems has been established through funding from the Center for Industrial Information Technology (CENIIT) and is carried out at the Division of Applied Mathematics (TIMA) in the Department of Mathematics (MAI). Leader of the group is Elina Rönnberg.

Some of our applied projects and PhD thesis projects are highlighted in the list of research projects below.

Ongoing projects

Resource allocation and scheduling for future avionic systems

To fully utilize the potential in modern modular avionic systems, very difficult allocation and scheduling problems may have to be solved. In cooperation with Saab Aeronautics, we develop specialized solution methods for future sysems.

Route planning of heavy-duty electric vehicles

Electrification of heavy-duty vehicles calls for intelligent methods to optimize the planning of their use and charging. With Scania and Ragn-Sells we develop mathematical models and algorithms for the next generation of transportation systems.

OPT@ATM

Some of the planning tasks involved in air traffic management can be considered as optimisation problems. These are typically large scale and difficult to solve.

ELLIIT PhD student project

Discrete optimisation for automatic decision-making in large-scale complex systems, in collaboration with Lund University.

Previous projects

A SJ-train driving through a beautiful landscape.

Decision support for railway crew planning

For our society to fully reap the benefits of sustainable train travel, careful resource planning is essential. Passengers need to be able to rely on that trains are on time and train operators need to make efficient use of their vehicles and crew.

Pilot controls the plane in the cockpit.

Scheduling of Avionic Systems

In an avionic system, communications and activities need to be scheduled to ensure the functionality of the aeroplane. Efficient methods for such scheduling are of importance for the development of future avionic systems.

Instrument panels inside the cockpit of an airplane.

Operations Research Methods for Scheduling and Dimensioning of Real-Time Systems

Decision problems for dynamic systems with timeliness or performance requirements can be formulated as discrete optimization problems.

Telecommunication tower on blue sky background.

Decision Support for Scheduling: Models, Methods and Validation

In this project we have developed column generation methods for a kind of scheduling in telecommunication and for solving transportation problems with both fixed and linear costs.

Silver metal briefcase against white background.

Mean-Variance Portfolio Optimization

We have developed solution methods for computationally challenging large scale instances of Markowitz's mean-variance portfolio optimization problem. We are also studying the cardinality-constrained version of the problem.

Contact

Researchers

Elina Rönnberg

Deputy Head of Department, Senior Associate Professor

Aban Ansari-Önnestam

PhD student

Roghayeh Hajizadeh

Lecturer

Lukas Eveborn

PhD student

Collaborations and co-supervision network

Daniel Jung

Associate Professor, Docent

Svante Johansson

Christiane Schmidt

Senior Associate Professor

Aigerim Saken

PhD Student

Stephen J. Maher

Senior Lecturer

Günther Raidl

Associate Professor

Anders Forsgren

Professor

Susanna F. de Rezende

Assistant Professor

Working methodology for optimisation: Problem-Model-Calculations-Evaluation-Decision

Optimization Aims at Finding the Best Solutions to Difficult Problems

Activities in society and industry must be based on good decisions to be efficient and economical. Optimization is about identifying, formulating and solving large, complex problems.