Implementing a GPU-based parallel MAX–MIN Ant System

Abstract

The MAX-MIN Ant System (MMAS) is one of the best-known Ant Colony Optimization (ACO) algorithms proven to be efficient at finding satisfactory solutions to many difficult combinatorial optimization problems. The slow-down in Moore's law, and the availability of graphics processing units (GPUs) capable of conducting general-purpose computations at high speed, has sparked considerable research efforts into the development of GPU-based ACO implementations. In this paper, we discuss a range of novel ideas for improving the GPU-based parallel MMAS implementation, allowing it to better utilize the computing power offered by two subsequent Nvidia GPU architectures. Specifically, based on the weighted reservoir sampling algorithm we propose a novel parallel implementation of the node selection procedure, which is at the heart of the MMAS and other ACO algorithms. We also present a memory-efficient implementation of another keycomponent -the tabu list structure -which is used in the ACO's solution construction stage. The proposed implementations, combined with the existing approaches, lead to a total of six MMAS variants, which are evaluated on a set of Traveling Salesman Problem (TSP) instances ranging from 198 to 3,795 cities. The results show that our MMAS implementation is competitive with state-of-the-art GPU-based and multi-core CPU-based parallel ACO implementations: in fact, the times obtained for the Nvidia V100 Volta GPU were up to 7.18x and 21.79x smaller, respectively. The fastest of the proposed MMAS variants is able to generate over 1 million candidate solutions per second when solving a 1,002-city instance. Moreover, we show that, combined with the 2-opt local search heuristic, the proposed parallel MMAS finds high-quality solutions for the TSP instances with up to 18,512 nodes.

Multi-Strategy MAX-MIN Ant System for Solving Quota Traveling Salesman Problem with Passengers, Incomplete Ride and Collection Time

“…(9) was used. Ω is calculated using the formula (10). The average values of ν, Φ and Ω are reported in Tables 4 and 5.…”

“…Another further promising idea is the use of pheromone update rule based on ants ranking [25]. Extension of the MS-MMAS implementation design with parallel computing techniques [10] and hybridization with other meta-heuristics [26][27][28] is other interesting opportunity for the future research.…”

“…MMAS improves the design of Ant System [6], the first ACO algorithm, with three important aspects: only the best ants are allowed to add pheromone during the pheromone trail update; use of a mechanism for limiting the strengths of the pheromone trails; and, incorporation of local search algorithms to improve the best solutions. Plenty of recent studies proved good effectiveness of the MMAS in correlated problems to QTSP-PIC [7][8][9][10]. However, none of these explored the Multi-Strategy (MS) concept.…”

A Comparative Performance Analysis of Computational Intelligence Techniques to Solve the Asymmetric Travelling Salesman Problem

“…The Max-Min Ant System (MMAS) developed by Stuzzle and Hoos [ 60 ] is simply an extension of the classical Ant Colony System (ACS) algorithm by ensuring that only the best ant in each iteration or the global best ant (i.e., the ant with the best solution since the beginning of the search) is allowed to deposit pheromone along its own route. At the start of the algorithm, the pheromone trail is set to some maximum levels to ensure adequate exploration, but this is systematically reduced as the algorithm progresses.…”

Improving Ant Colony Optimization efficiency for solving large TSP instances

“…The main motivations behind developing multiple ACO variants include adaptation to new types of problems, improvements to the convergence to high-quality solutions, and more efficient utilization of computing resources. Additionally, some work was motivated by the ever-growing computational power offered by multi-core CPUs [36,47], specialized accelerators [33,44], and general-purpose graphics processing units (GPUs) [6,12,39,40]. More computational power allowed not only to reduce the computation time but also to tackle larger problems [8,35].…”