Penalties may have collateral effects . A MAX - SAT analysis

Many incomplete approaches for MAX-SAT have been proposed in the last years. The objective of this investigation is not so much horse-racing (beating the competition on selected benchmarks) but understanding the qualitative differences between the various methods. In particular, we focus on reactive search schemes where taskdependent and local properties in the configuration space are used for the dynamic on-line tuning of local search parameters and we consider the choice between prohibition-based and penalty-based approaches. To abstract from implementation details we focus on the search trajectory characteristics and study the trade-off between diversification and bias after starting from a local minimizer. We then study the warping effects on the fitness surface of weight-update schemes and the resulting dynamics, through an exhaustive analysis of small MAX-SAT instances, and of the average evolution of individual trajectories. The results are compatible with the conclusion that penalty-based schemes achieve diversification from a starting local optimum through a complex method with global and potentially dangerous collateral effects, while prohibition-based schemes reach comparable or better results in a more direct and controllable manner. In the final part of this paper, we consider long runs of the complete algorithms on selected MAX-SAT instances, which confirm the competitiveness of prohibition-based reactive approaches.