This is a past event
Title: Multiobjective combinatorial optimization: methods and applications
In this talk, we will present methods to solve multiobjective combinatorial optimization problems. In multiobjective optimization, a feasible solution is evaluated with a set of objective functions. This formulation better suits to real problems that often involve multiple conflicting objectives. When the objectives are conflicting, a solution simultaneously minimizing each objective does not exist, but a set of solutions called Pareto optimal solutions. A Pareto optimal solution is a solution for which it is impossible to find another solution that dominates it, that is at least as good on all objectives and better for at least one objective.
The main difficulties related to the generation of all Pareto optimal solutions of a multiobjective combinatorial optimization problem will be presented: NP-Hardness even when the single-objective counterpart is in P, an exponential number of Pareto optimal solutions, and the presence of non-supported Pareto optimal solutions, that cannot be obtained by solving weighted single-objective problems. Therefore, this is mainly metaheuristics based methods that have been developed in order to solve multiobjective problems. We will develop some of them and show how they have been adapted to solve the multiobjective version of classic combinatorial problems (traveling salesman, knapsack, set covering). We will also present an application that occurs in the radiotherapy treatment of cancer patients. In this problem, a non-negative integer matrix has to be decomposed into a linear combination of particular binary matrices, where different objectives have to be taken into account to evaluate the quality of a decomposition.
Finally, we will say few words about a new promising stream of research, that is fair multi-agent optimization.
- Speaker
- Thibaut Lust, Louvain School of Management
- Hosted by
- Wei Pang, Computing Science dept. and Inst. for Complex Systems and Mathematical Biology, University of Aberdeen
- Venue
- Meston 203
- Contact
-
Thibaut Lust holds a PhD in Engineering Science (2009) from the University of Mons (Belgium) and a Master in Engineering Science (Computer and Management Sciences) (2005) from the Faculté Polytechnique de Mons (Belgium). He currently conducts post-doctoral research at the Université Catholique de Louvain (Belgium) in the Louvain School of Management. His research interests include multiobjective optimization, multiobjective combinatorial problems (traveling salesman, knapsack, set covering), metaheuristics, algorithmic decision theory, fair optimization and radiotherapy optimization.
Best regards and see you soon,
Thibaut Lust
Post-doctoral researcher
Louvain School of Management
Université Catholique de Louvain - UCL Mons
Chaussée de Binche, 151
7000 Mons - Belgium
http://sites.google.com/site/thibautlust/