Depth-First Search versus Jurema Search on GPU Branch-and-Bound Algorithms: a case study

Branch-and-Bound (B&B) is a general problem solving paradigm and it has been successfully used to prove optimality of combinatorial optimization problems. The development of GPU-based parallel Branch-and-Bound algorithm is a brandnew and challenging topic on high performance computing and combinatorial optimization, motivated by GPU’s high performance and low cost. This work presents a strategy designed to parallelize Jurema searchbased B&B algorithms on GPUs, evaluated for the Asymmetric Traveling Salesman Problem, called Juremal. Jurema search is mainly based on DFS concepts, developed to mitigate DFS-B&B flaws. Results show the search strategy chosen (DFS or Jurema) is not critical in GPU DFS-B&B algorithms. However, it is necessary to develop a trigger mechanism to determine if the process must be halted and the remaining search space redistributed. Strategies to reduce serialization of instructions are also needed, in order to obtain higher speedups in GPU DFS-B&B based algorithms.