I am looking at the wikipedia page of TSP. I am confused by this statement.
"If the distance measure is a metric (and thus symmetric), the problem becomes APX-complete and the algorithm of Christofides and Serdyukov approximates it within 1.5."
What does 1.5 mean here? Suppose the optimal value is 100. Does this algorithm generate a value of 150, or 250 ((250-100)/100)?
The approximation ratio of an algorithm $\mathcal{A}$ for a minimization problem is the maximum over all instances $I$ of $\textrm{value}(\mathcal{A}(I))/\textrm{value}(\textrm{OPT}_I)$, where $\textrm{OPT}_I$ denotes the optimal solution for $I$. Hence the solution given by the Christofides-Serdyukov algorithm is never more than 1.5 times as long as the optimal solution, in your example: 150.