A Hybrid Heuristic in GPU-CPU Based on Scatter Search for the Generalized Assignment Problem

Abstract

In the Generalized Assignment Problem (GAP), tasks must be allocated to machines with limited resources, in order to minimize processing costs. This problem has several industrial applications and often appears as a substructure in other combinatorial optimization problems. We propose a hybrid method inspired by Scatter Search metaheuristic, that efficiently generates a pool of solutions using a Tabu list criteria and an Ejection Chain mechanism. Common characteristics are extracted from the pool and solutions are combined by exploring a restricted search space, as a Binary Programming (BP) model. This method was implemented as a parallel approach to run in a Graphics Processing Unit (GPU). Experimental results show that the proposed method is very competitive to the algorithms found in the literature. On average, a gap of 0.09% is obtained over a set of 45 instances, when compared to lower bounds. Due to the integration of the method with an exact BP solver, it was capable of proving the optimality of small size instances, also finding new best known solutions for 21 instances. In terms of computational times, the proposed method performs on average 8 times faster than literature, also indicating that the proposed approach is scalable and robust for practical applications.