Workshop on Recent Advances in Multi-Objective Optimization – RAMOO 2021

University of Wuppertal (Germany) – online
23.9.2021

Organizers: Michael Stiglmayr, Kathrin Klamroth, Britta Schulze

General Information

The workshop “Recent Advances in Multi-Objective Optimization” focuses on latest advances in exact methods in multi-objective (mixed) integer optimization. Topics of interest include (but are not limited to):

• Multi-objective discrete/combinatorial problems
• Multi-objective mixed integer (non)-linear problems
• Multi-objective continuous non-linear problems
• Multi-objective branch-and-bound algorithms
• Multi-objective branch-and-cut algorithms
• Column generation and branch-and-price algorithms
• Objective space algorithms
• Stochastic multi-objective optimization
• Robust multi-objective optimization
• Complexity analysis of multi-objective optimization algorithms
• Parallelization of exact algorithms in multi-objective optimization

Workshop Program (Including Abstracts)

Poster

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(in high resolution)

Keynote Talks:

• Sophie Parragh (Johannes Kepler University Linz)
  Towards multi-objective mixed integer linear programming
  
  In the single objective domain, general purpose mixed integer linear programming solvers have become indispensable tools for either solving the underlying optimization problems directly or as major building blocks for heuristics. While it has been acknowledged that many (if not all) practical optimization problems feature more than one objective, general purpose exact methods for solving any multi-objective mixed integer linear programming problem are still under development. In this talk, recent advances in important ingredients to such methods which rely on the branch-and-bound idea are presented. These ingredients range from bound (set) computation schemes to branching rules, node selection strategies, cutting plane generation and primal heuristics. The focus is put on those ideas which exploit the multi-objective nature of the underlying optimization problem and their potential advantages and disadvantages are highlighted. Furthermore, open challenges which include, e.g., stability issues, test instance design, and meaningful gap measures are discussed.
  
  
• Luís Paquete (University of Coimbra)
  Hypervolume-based Optimization: Results and Challenges
  
  The hypervolume indicator measures the multidimensional volume of the union of axis-parallel boxes, each of which spanned by a nondominated point and a pre-defined reference point. This indicator has shown to have
  interesting properties, and has gained popularity as a performance assessment method, as a selection criterion, and as an archiving strategy for multiobjective evolutionary algorithms. Moreover, under appropriate assumptions about the location of the reference point in the objective space, the hypervolume indicator takes its maximum value at the nondominated set. This result suggests that optimizing the hypervolume indicator might also be useful in the context of exact approaches for multiobjective optimization problems.
  
  In this talk, we consider two possibilities of applying the hypervolume indicator in the context of multiobjective combinatorial optimization: i) to consider the hypervolume indicator from the perspective of representation quality, where the goal is, given a nondominated set, to find a subset of a given cardinality that maximizes the hypervolume indicator, and ii) to use the hypervolume indicator as a scalarization method, leading to search procedures that find the nondominated set, or a subset of it. We discuss applications of these methods to particular biobjective
  combinatorial optimization problems as well as challenges that arise when considering more than two objectives.