Section: New Results

Controlling the Generation of Solutions

The following two results deal with controlling the generation of solutions to a constraint problem.

• The focus constraint expresses the notion that solutions are concentrated. In practice, this constraint suffers from the rigidity of its semantics. To tackle this issue, we propose three generalizations of the FOCUS constraint. We provide for each one a complete filtering algorithm. Moreover, we propose mathematical programming (ILP) and constraint programming decompositions.

• There are significant motivations for considering alternate solutions to a problem. As expressed by renowned statistician George Box The most that can be expected from any model is that it can supply a useful approximation to reality: all models are wrong; some models are useful.. Multiple solutions alone, however, are not sufficient to guarantee anything of value. If they are nearly identical nothing is gained. While most frameworks in the literature consider diversity between solutions through mathematical distances, this paper proposes alternative distance measures represented by global constraints. It introduces a constraint programming framework for optimization problems, able to generate sets of nearly-optimal solutions that are diverse. With respect to over-constrained problems, the framework can be specialized in order to generate solution sets where constraint violations are diverse.