Gray-Box Tunneling for Multi-Objective Combinatorial Optimization

Inria Villeneuve d'Ascq; Villeneuve-d'Ascq; On-site; EUR 7,200 - 11,000; Part time

Job summary

1000scholars invites a student intern to contribute to multi-objective combinatorial optimization research. The project focuses on Pareto Local Optima, tunneling mechanisms, and gray-box operators, with opportunities to analyze structure and develop new algorithms.

You will work with HPC-enabled methods, perform theoretical and empirical analyses, and contribute to software or publications. A strong interest in fundamental research and good programming skills are welcome.

Qualifications

• Strong interest in conducting fundamental research.
• Good programming skills are expected.

Responsibilities

• Analyze Pareto Local Optima in multi-objective landscapes.
• Design and evaluate tunneling operators to navigate PLOs.
• Develop and test partition-crossover-based mechanisms in gray-box settings.
• Implement and benchmark new optimization algorithms.
• Prepare computational experiments and analyze results.
• Contribute to research software and/or publications.

Skills

Programming

Job description

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

• 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.

Skills

A strong interest in conducting fundamental research and exploring open-ended applied algorithmic questions is particularly welcome. Good programming skills are expected.