## epsilon-Transformation: Exploiting Phase Transitions to Solve Combinatorial Optimization Problems (1994)

Venue: | Artificial Intelligence |

Citations: | 12 - 3 self |

### BibTeX

@ARTICLE{Zhang94epsilon-transformation:exploiting,

author = {Weixiong Zhang and Joseph C. Pemberton},

title = {epsilon-Transformation: Exploiting Phase Transitions to Solve Combinatorial Optimization Problems},

journal = {Artificial Intelligence},

year = {1994},

volume = {81},

pages = {297--325}

}

### Years of Citing Articles

### OpenURL

### Abstract

It has been shown that there exists a transition in the averagecase complexity of tree search problems, from exponential to polynomial in the search depth. We develop a new method, called ffl- transformation, which makes use of this complexity transition, to find a suboptimal solution. With a random tree model, we show that the expected number of nodes expanded by branch-and-bound (BnB) using ffl-transformation is at most cubic in the search depth, and that the error of the solution cost found relative to the optimal solution cost is a small constant. We also present an iterative version of ffl-transformation that can be used to find both optimal and suboptimal goal nodes. Depth-first BnB (DFBnB) using iterative ffl-transformation significantly improves upon truncated DFBnB on random trees with large branching factors and deep goal nodes, finding better solutions sooner on average. Our experiments on the asymmetric traveling salesman problem show that DFBnB using ffl- transformati...