Tackling the Subset Sum Problem with Fixed Size using an Integer Representation Scheme

Abstract

Addressing the subset sum problem is relevant to study resource management problems efficiently. In this paper, we study a new scheme to sample solutions for the subset sum problem based on swarm-based optimization algorithms with distinct forms of selection pressure, the balance of exploration-exploitation, the multimodality considerations, and a search space defined by numbers associated with subsets of fixed size. Our experiments show that it is feasible to find optimal subsets with few number of fitness evaluations, and that Particle Swarm Optimization with Fitness Euclidean Ratio converges faster to the global optima with zero variability over independent runs. Since the search space is one-dimensional and friendly to parallelization schemes, our work is potential to study further classes of combinatorial problems using swarm-based optimization algorithms and the representation based on numbers.