Gray-Box Tunneling for Multi-Objective Combinatorial Optimization

Assignment
Multi-objective combinatorial optimization
aims at simultaneously optimizing several, potentially conflicting, objective functions over a discrete decision space. In many combinatorial optimization problems, objective functions exhibit a
gray-box structure
, e.g., they can be decomposed into sub-functions involving only a restricted number of decision variables. Such structure can be exploited to design specialized and computationally efficient optimization algorithms.
For example, for many binary optimization problems, objective functions can be represented using a bounded-degree
Walsh/Fourrier transform
, providing a natural framework for analyzing and exploiting variable interactions. Other combinatorial problem representations may also be considered, provided that they expose a suitable structure that can be leveraged by specialized gray-box evolutionary and search operators.
While gray-box optimization has received increasing attention in the single-objective setting, the study of gray-box multi-objective optimization remains largely unexplored. This internship aims to contribute to this emerging research direction by
developing new algorithmic approaches for efficiently navigating the landscape of multi-objective combinatorial optimization problems
.
A particular focus will be placed on
Pareto Local Optima (PLOs)
. PLOs generalize the notion of local optima to the multi-objective setting by considering the dominance relation.
The general objective of the internship is to develop new tunneling mechanisms
that allow optimization algorithms to efficiently navigate between PLO solutions, potentially enabling the discovery of high-quality regions of the Pareto set that are difficult to reach through conventional local search.
Depending on the candidate's background and interests, the work may involve theoretical analysis, algorithm design, experimental evaluation, or a combination of these aspects.
Main activities
The internship may focus on one or more of the following research directions:
Analyzing Pareto Local Optima under tunneling mechanisms such as partition crossover
. Study the structure and properties of Pareto Local Optima (PLOs) that can be exploited by partition crossover and related gray-box operators.
Designing new multi-objective tunneling mechanisms
. Develop and investigate partition-crossover-based mechanisms to efficiently move between PLOs, with a particular focus on (i) decomposition-based multi-objective optimization and cooperation between neighboring subproblems and/or (ii) Dominance based techniques.
Integrating tunneling into (HPC-)accelerated multi-objective search algorithms
. Incorporate partition crossover and related tunneling mechanisms into specialized evolutionary and local-search algorithms, especially by exploiting parallel and high-performance computing to accelerate the search.
Consequently, the internship may involve:
reviewing the literature on gray-box optimization, multi-objective optimization, local search, and Pareto Local Optima
analyzing existing gray-box optimization algorithms
conducting theoretical or empirical analyses of fitness landscapes and PLO structures
designing new tunneling operators and search mechanisms
implementing and experimentally evaluating new optimization algorithms
designing computational experiments and analyzing algorithmic performance
exploiting parallel and HPC computing when relevant
contributing to scientific publications and/or research software.
The internship is intended as a
research-oriented project
, and the research questions and methodology will be refined continously according to the results obtained during the internship.
Skills
A strong interest in conducting
fundamental research
and exploring open-ended applied algorithmic questions is particularly welcome.
Good programming skills
are expected.