A scalable parallel genetic algorithm for the Generalized Assignment Problem

Abstract

• A scalable parallel genetic algorithm (PGA) is developed for the NP-hard GAP problem. • High scalability is achieved through a novel asynchronous migration strategy. • Our algorithmic analysis resolves the buffer overflow issue in asynchronous PGAs. • Strong and weak scaling tests demonstrate the superiority of our PGA approach. • Our approach scales to 16,384 processors with super-linear speedups observed. Known as an effective heuristic for finding optimal or near-optimal solutions to difficult optimization problems, a genetic algorithm (GA) is inherently parallel for exploiting high performance and parallel computing resources for randomized iterative evolutionary computation. It remains to be a significant challenge, however, to devise parallel genetic algorithms (PGAs) that can scale to massively parallel computer architecture (also known as the mainstream supercomputer architecture) primarily because: (1) a common PGA design adopts synchronized migration, which becomes increasingly costly as more processor cores are involved in global synchronization; and (2) asynchronous PGA design and associated performance evaluation are intricate due to the fact that PGA is a type of stochastic algorithm and the amount of computation work needed to solve a problem is not simply dependent on the problem size. To address the challenge, this paper describes a scalable coarse-grained PGA–PGAP, for a well-known NP -hard optimization problem: Generalized Assignment Problem (GAP). Specifically, an asynchronous migration strategy is developed to enable efficient deme interactions and significantly improve the overlapping of computation and communication. Buffer overflow and its relationship with migration parameters were investigated to resolve the issues of observed message buffer overflow and the loss of good solutions obtained from migration. Two algorithmic conditions were then established to detect these issues caused by communication delays and improper configuration of migration parameters and, thus, guide the dynamic tuning of PGA parameters to detect and avoid these issues. A set of computational experiments is designed to evaluate the scalability and numerical performance of PGAP. These experiments were conducted for large GAP instances on multiple supercomputers as part of the National Science Foundation Extreme Science and Engineering Discovery Environment (XSEDE). Results showed that, PGAP exhibited desirable scalability by achieving low communication cost when using up to 16,384 processor cores. Near-linear and super-linear speedups on large GAP instances were obtained in strong scaling tests. Desirable scalability to both population size and the number of processor cores were observed in weak scaling tests. The design strategies applied in PGAP are applicable to general asynchronous PGA development.