ACO with Tabu Search on GPUs for Fast Solution of the QAP

Abstract

In this chapter, we propose an ACO for solving quadratic assignment problems (QAPs) on a GPU by combining tabu search (TS) in the Compute Unified Device Architecture (CUDA). In TS on QAPs, there are $n(n - 1)/2$ neighbors in a candidate solution. These TS moves form two groups based on computing cost. In one group, the computing of the move cost is $\mathcal{O}(1)$, and in the other group the computing of the move cost is $\mathcal{O}(n)$. We compute these groups of moves in parallel by assigning the computations to threads of CUDA. In this assignment, we propose an efficient method which we call Move-Cost Adjusted Thread Assignment (MATA) that can reduce disabling time, as far as possible, in each thread of CUDA. As for the ACO algorithm, we use the Cunning Ant System (cAS). GPU computation with MATA shows a promising speedup compared to computation with CPU. Based on MATA, we also implement two types of parallel algorithms on multiple GPUs to solve QAPs faster. These are the island model and the master/slave model. As for the island model, we used four types of topologies. Although the results of speedup depend greatly on the instances which we use, we show that the island model IM_ELMR has a good speedup feature. As for the master/slave model, we observe reasonable speedups for large sizes of instances, where we use large numbers of agents. When we compare the island model and the master/slave model, the island model shows promising speedup values on class (iv) instances of QAP. On the other hand, the master/slave model consistently shows promising speedup values both on classes (i) and (iv) with large-size QAP instances with large numbers of agents.