Worst Case Analysis of Max-Regret, Greedy and Other Heuristics for Multidimensional Assignment and Traveling Salesman Problems
G. Gutin, B. Goldengorin and J. Huang
In: 4th Workshop on Approximation and Online Algorithms, 13 Sept - 15 Sept, 2006, Zurich, Switzerland.
Optimization heuristics are often compared with each other to
determine which one performs best by means of worst-case
performance ratio reflecting the quality of returned solution in
the worst case. The domination number is a complement parameter
indicating the quality of the heuristic in hand by determining how
many feasible solutions are dominated by the heuristic solution.
We prove that the Max-Regret heuristic introduced by Balas and
Saltzman (1991) finds the unique worst possible solution for some
instances of the $s$-dimensional ($s\ge 3$) assignment and
asymmetric traveling salesman problems of each possible size. We
show that the Triple Interchange heuristic (for $s=3$) also
introduced by Balas and Saltzman and two new heuristics (Part and
Recursive Opt Matching) have factorial domination numbers for the
$s$-dimensional ($s\ge 3$) assignment problem.
|EPrint Type:||Conference or Workshop Item (Paper)|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Subjects:||Theory & Algorithms|
|Deposited By:||Gregory Gutin|
|Deposited On:||22 November 2006|