Computational methods

The ROC team contributes to the design and the implementation of exact and heuristic algorithms for efficiently solving Combinatorial Optimisation Problems. We distinguish computaitonal methods based on Constraint Programming, Mixed Integer Linear Programming, Hybrid methods and Problem-specificn algorithms.



Propagation of the cumulative constraint

Constraint Programming

The description of the feasible set follows the general CSP framework involving variables, domains, and constraints. The objectives are usually transformed in constraint(s). The team proposes efficient constraint propagation algorithms and intelligent tree search methods based on learning and SAT-inspired techniques.

Some publications on Constraint Programming


Column generation based on q-routes for vehicle routing

Mixed Integer linear programming

The feasible set and objective(s) involve only linear expressions on integer or fractional variables. In this domain, the team carries out researches on branch-and-cut, branch-and-price and more generally decomposition methods.

Some publications on MILP



Implication graph in an hybrid CP/SAT Solver


Hybrid methods for combinatorial optimization

Combining different approaches is often the key in significant computational breakthrough for combinatorial optimization. The teams carries out research in different hybridizations between several components among Mixed-Integer Linear and Non-Linear programming, Constraint Programming, Dynamic Programming, Boolean Satisfiability, Local Search.

Some publications on hybrid methods



A flow-based heuristic for a multi-skill technician allocation and scheduling problem


Dedicated Algorithms

Depending on the structure of the considered combinatorial optimization problem, the team also develops dedicated exact or approximated algorithms: specific heuristics, greedy algorithms, local search methods, dynamic programming, graph-based heuristics...

Some publications on dedicated methods