An Efficient Implementation of Ant Colony Optimization on GPU for the Satisfiability Problem

Abstract

This paper focuses on solving the Boolean Satisfiability (SAT) problem using a parallel implementation of the Ant Colony Optimization (ACO) algorithm for execution on the Graphics Processing Unit (GPU) using NVIDIA CUDA (Compute Unified Device Architecture). We propose a new efficient parallel strategy for the ACO algorithm executed entirely on the CUDA architecture, and perform experiments to compare it with the best sequential version exists implemented on CPU with incomplete approaches. We show how SAT problem can benefit from the GPU solutions, leading to significant improvements in speed-up even though keeping the quality of the solution. Our results shows that the new parallel implementation executes up to 21x faster compared to its sequential counterpart.

GPU parallelization strategies for metaheuristics: a survey

“…Each subswarm runs PSO separately. To further accelerate the execution time, the solution level has been also implemented to generate, evaluate solutions, or both in parallel [21,22,28,29,32,35,54,56,62,64,88,89]. As an example, in papers like [21] [22] [32], ACO algorithm have been implemented, where tour construction phase can be performed in parallel.…”

“…On the other hand, solution quality has been considered in works like [63,64] with a small acceleration factor of at best 1.19x [63]. While in works like [32,35,54,88], the behavior of GPU parallel implementations is not modified compared to the CPU implementations (quality not improved) but a significant acceleration factor of at best 696x [54] is achieved. Few works as [21,56,60,62,68,81] made the exception.…”

“…Later in 2015, the Satisfiability Problem (SAT) has been solved in [88]. A SAT instance is represented as a matrix of clauses denoted by q of boolean values.…”

“…For the solution evaluation (solution level), three kernels are launched: The first kernel is launched with a 2-D grid of blocks of length n in x-dimension and b in y-dimension, each block size is 32*32 threads (each thread represents a literal). The second and the third kernels calculate the sum of the solved clauses and they evaluate the quality of the solutions respectively according to an appropriate function mentioned in [88]. The second stage updates pheromone levels using the best solution known by the ant colony.…”

Parallel SAT Simplification on GPU Architectures

“…data processing and memory access. In recent years, for instance, we have applied GPUs to accelerate explicit-state model checking [26,27,30], state space decomposition [28,29] and minimisation [25], metaheuristic SAT solving [31], and SAT-based test generation [22].…”