Enriching Solutions to Combinatorial Problems via Solution Engineering

Thierry Petit (1, 2, 3) , Andrew C Trapp (4)

1 IMT Atlantique - DAPI - Département Automatique, Productique et Informatique
2 LS2N - équipe TASC - Théorie, Algorithmes et Systèmes en Contraintes
3 LS2N - Laboratoire des Sciences du Numérique de Nantes
4 Worcester Polytechnic Institute

Existing approaches to identify multiple solutions to combinatorial problems in practice are at best limited in their ability to simultaneously incorporate both diversity among generated solutions, as well as problem-specific desires that may only be discovered or articulated by the user after further analysis of solver output. We propose a general framework for problems of a combinatorial nature that can generate a set of of multiple (near-)optimal, diverse solutions, that are further infused with desirable features. We call our approach solution engineering. A key novelty is that desirable solution properties need not be explicitly modeled in advance. We customize the framework to both the mathematical programming and constraint programming technologies, and subsequently demonstrate its prac-ticality by implementing and then conducting computational experiments on existing test instances from the literature. Our computational results confirm the very real possibility of generating sets of solutions infused with features that might otherwise remain undiscovered.

Mots clés: mathematical programming; constraint programming; diversity; quality no- tions; solution generation framework

Domaines: Informatique [cs]; Intelligence artificielle [cs.AI]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

Thierry Petit, Andrew C Trapp. Enriching Solutions to Combinatorial Problems via Solution Engineering. INFORMS Journal of Computing, 2019, ⟨10.1287/ijoc.2018.0855⟩. ⟨hal-02288583⟩