On the best search strategy in parallel branch‐and‐bound:Best‐First Search versus Lazy Depth‐First Search

Abstract

The Best‐First Search strategy (BeFS) and the Depth‐First Search strategy (DFS) areregarded as the prime strategies when solving combinatorial optimization problems by parallelBranch‐and‐Bound (B&B) ‐ BeFS because of efficiency with respect to the number of nodesexplored, and DFS for reasons of space efficiency.

We investigate the efficiency of both strategies experimentally, and two versions of eachstrategy are tested: In the first, a B&B iteration for a node consists of bounding followed bybranching on the node if necessary. For the second, the order is reversed ‐ first branchingtakes place, and then each child of the node is bounded and possibly fathomed. The first iscalled lazy, the second eager.

The strategies are tested on the Quadratic Assignment Problem and the Job Shop SchedulingProblem. We use parallel codes developed specifically for the solution of the problem inquestion, and hence containing different heuristic rules and tests to speed up computation.In both cases, we start with an initial solution close to but not equal to the optimal solution.

Surprisingly, the BeFS‐based strategies turn out to be inferior to the DFS‐based strategies,both in terms of running times and in terms of bound calculations performed. Furthermore,when tested in a sequential setting, DFS turns out to be still superior because pruning andevaluation tests are more effective in DFS due to the presence of better incumbents.