HYBRID ALGORITHMS FOR THE CONSTRAINT SATISFACTION PROBLEM

Abstract

It might be said that there are five basic tree search algorithms for the constraint satisfaction problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflict‐directed backjumping (CBJ), backmarking (BM), and forward checking (FC). In broad terms, BT, BJ, and CBJ describe different styles of backward move (backtracking), whereas BT, BM, and FC describe different styles of forward move (labeling of variables). This paper presents an approach that allows base algorithms to be combined, giving us new hybrids. The base algorithms are described explicitly, in terms of a forward move and a backward move. It is then shown that the forward move of one algorithm may be combined with the backward move of another, giving a new hybrid. In total, four hybrids are presented: backmarking with backjumping (BMJ), backmarking with conflict‐directed backjumping (BM‐CBJ), forward checking with backjumping (FC‐BJ), and forward checking with conflict‐directed backjumping (FC‐CBJ). The performances of the nine algorithms (BT, BJ, CBJ, BM, BMJ, BM‐CBJ, FC, FC‐BJ, FC‐CBJ) are compared empirically, using 450 instances of the ZEBRA problem, and it is shown that FC‐CBJ is by far the best of the algorithms examined.