Since MAX 2SAT is one of the famous NP-hard optimization problems, many heuristics and (polynomial-time) approximation algorithms have been proposed in the literature [1,4,5,6]. To evaluate the performance of such algorithms, there are two possibilities; theoretical analysis and empirical study.
In theoretical analysis, an approximation ratio of the algorithm is often used as a measure. The approximation ratio is an upper bound on the ratio of an approximated cost to the optimal cost, and hence, this is a worst case measure. It is often difficult to analyze theoretically the performance of heuristics or hybrid algorithms.