Identify problem representations that best exploit efficient gray-box operators

Investigate and determine, for given combinatorial optimization problems, which representation of the search space (e.g., encoding and associated move set) most effectively enables the application of efficient gray-box operators such as constant-time hill climbers and partition crossover by maximizing opportunities for non-interacting, decomposable moves.

Background

The proposed unified framework leverages problem structure—via specific representations and move sets—to achieve efficient evaluation of improving moves and optimal partitioning in crossover. The choice of representation directly impacts commutativity and non-interaction properties that the framework relies upon.

The authors explicitly pose as an open question the search for the most appropriate representation per problem to realize the speed-ups offered by gray-box operators, highlighting the need to identify representations that maximize decomposition opportunities and efficient delta computations.

References

There are some open questions that can be explored in future work, like the extension of the framework to sets of non-commutative moves or the research for the most appropriate representation of a problem to get profit from the efficient gray-box operators.

— Generalizing and Unifying Gray-box Combinatorial Optimization Operators (2407.06742 - Chicano et al., 9 Jul 2024) in Section 6 (Conclusions)